Electrical

Tools in this group

• Ohm's Law - Compute V, I, R, or P from any two known values.
• Wire Ampacity - Ampacity by gauge, conductor material, insulation rating, ambient.
• AWG Conductor Geometry (Diameter, Circular Mils, mm^2) - The bare-conductor size behind a gauge number, from the AWG definition: d = 0.005 x 92^((36 - n)/39) inches, so every 6 gauges roughly doubles the diameter. #12 AWG is 0.0808 in (2.05 mm), 6,530 circular mils, 3.31 mm^2; 4/0 is exactly 0.460 in and 211,600 cmil. Circular mils are (diameter in mils)^2, the diameter-squared area unit NEC tables use; the mm^2 is the true pi (d/2)^2 cross-section. Bare copper/aluminum, solid-equivalent -- not the over-insulation diameter (see conduit-fill). A reference; the manufacturer's conductor dimensions govern.
• Voltage Drop - Single-phase or three-phase voltage drop over length.
• Conduit Fill - Percent fill by conduit type and conductor count.
• Box Fill - Cubic-inch fill by box volume and conductor count.
• Breaker Sizing - Continuous-load 125 percent rule.
• Motor Full Load Amps - Typical FLA by horsepower, voltage, and phase.
• Transformer Sizing - Required kVA from load and voltages.
• Three-Phase Power - kW, kVA, and kVAR from line values and power factor.
• Conductor Resistance at Temperature - Resistance of copper or aluminum at temperature.
• Equipment Grounding Conductor Sizing - Minimum EGC size from overcurrent device rating.
• Service Load Calculation (Residential) - Standard demand factors over lighting, appliances, range, dryer, HVAC; output minimum service ampacity.
• Generator Sizing - Continuous and surge wattage from running totals and the largest motor's starting draw.
• Solar PV String Sizing - Cold-Voc max series and warm-Vmp min series for an inverter MPPT window.
• Battery Runtime - Hours of runtime from Ah, voltage, depth of discharge, and load (optional Peukert).
• DC Ammeter Shunt Sizing - Sizing and reading a DC current-measuring shunt -- the precision low-value resistor a DC panel meter, battery monitor, or PV/DC combiner uses to measure current. A shunt is rated as a millivolt drop at a rated current (a '50 mV, 100 A' shunt), so R = rated mV/1000 / rated current = 0.5 milliohm, and the meter reads current = rated current x (measured mV / rated mV), so 25 mV on a 50 mV/100 A shunt is 50 A. At rated current it dissipates rated current x rated volts = 5 W, which is why shunts derate to ~2/3 for continuous use. Put it in series in the return leg and sense at the potential (voltage) terminals so lead resistance does not add to the reading. A design aid; the shunt accuracy class, temperature coefficient, and the meter's input range and calibration govern.
• Voltage Imbalance - Three-phase percent imbalance and motor derate factor.
• GFCI / AFCI Requirements Reference - Plain-English summary of GFCI and AFCI requirements by occupancy area.
• Lighting Power Density - Target watts from area and occupancy class using public engineering benchmarks.
• Conductor Pulling Tension - Capstan-equation pulling tension and sidewall pressure across bends.
• Cable Reel Capacity / Length on Reel - How many feet of a given cable fit on a reel (or how much is left on a partial reel): length = fill x pi x (flange^2 - drum^2) x traverse / (48 x cable_OD^2), lengths in inches. A 30 in flange, 12 in drum, 18 in wide reel holds ~801 ft of 1 in cable; a fatter 1.5 in cable drops it to 356 ft, since the cable OD enters squared. The figure that tells the crew whether the pull is on one reel or two.
• Cable-Pulling Lubricant Quantity - Estimates the pulling lubricant a conduit run takes, so the crew does not run short mid-pull: gallons = K x length x conduit ID^2 x bend factor. A 400 ft run in 3 in conduit wants about 5.4 gallons (round to a full pail), and a bend-heavy, high-fill pull at a 1.3 bend factor pushes that past 7. K is a film-coating rule (~0.0015, the common Polywater rule); under-lubing risks a stuck cable, so round up and keep a spare pail.
• Branch-Circuit Conductor Footage Takeoff - Takes off the branch-circuit wire to order and how many rolls: total = circuits x (home run + makeup) x conductors; rolls = ceil(total / roll length). 20 circuits at a 45 ft average home run, three conductors each, with 15 ft of box makeup, is 3,600 ft - 4 thousand-foot rolls per color. Set conductors to 1 for cable (NM / romex). The panel schedule drives the count; wire is bought per color.
• Max Microinverters per AC Branch Circuit (NEC 705.60) - The most microinverters or AC modules on one AC branch circuit: their combined continuous output, as a continuous load, cannot exceed 80% of the branch overcurrent device (NEC 705.60 / 690.8(B) / 240.4), so N = floor(OCPD x 0.80 / unit max current). A 20 A branch with an Enphase IQ7+ at 1.21 A allows 13 microinverters; a 1.0 A unit allows 16, a higher-output unit fewer. Use the unit's MAXIMUM continuous AC output current from its datasheet, not the panel wattage over voltage, and size the branch conductors and the point-of-connection to the same 125% continuous rule. The microinverter datasheet, the AHJ, and the adopted NEC edition govern.
• Arc-Welder Branch-Circuit Conductor and OCPD (NEC 630.11) - Sizes an arc-welder branch circuit off the nameplate, not the running current: the conductor carries an EFFECTIVE current I_eff = primary current x the NEC Table 630.11(A) duty-cycle multiplier (the square root of the duty cycle), because a low-duty welder heats the wire less. A 40 A primary, 50%-duty welder needs conductors rated 28.3 A (a #10 Cu at 60 C). The overcurrent device may run up to 200% of the rated primary (NEC 630.12(A)), so up to an 80 A breaker on that welder. Use the nameplate rated primary current and duty cycle; the AHJ, the welder nameplate, and the adopted NEC edition govern. Resistance (spot) welders use the separate 630.31/630.32 method.
• Resistance / Spot-Welder Branch-Circuit Conductor and OCPD (NEC 630.31) - Sizes a resistance (spot / seam / projection) welder branch circuit: because the welder fires in brief pulses, the conductor carries the primary current times the square root of the duty cycle (NEC 630.31(A)(2)), the same duty-derating as an arc welder. A 100 A primary, 50%-duty spot welder needs conductors rated 70.7 A (a #4 Cu at 75 C). But the overcurrent device may run up to 300% of the rated primary (NEC 630.32(A)) -- higher than the 200% for arc welders -- so the pulses do not nuisance-trip it: up to a 300 A device on that welder. Use the nameplate rated primary current and duty cycle; the AHJ, the welder nameplate, and the adopted NEC edition govern. Arc welders use the separate 630.11/630.12 (200%) method.
• Battery-to-Inverter DC Conductor and OCPD (NEC 690.9 / 706) - Sizes the DC conductor and fuse between a battery bank and an off-grid or ESS inverter: DC input current = AC power / (battery voltage x inverter efficiency), then NEC 690.8(B) / 706 / 240.4 size the conductor and overcurrent device at 125% of that current, with the OCPD rounded up to the next standard size (240.6). A 4 kW inverter on a 48 V bank at 90% efficiency draws about 92.6 A, so the conductor is rated at least 115.7 A (a 1/0 Cu at 75 C) on a 125 A DC fuse; a 24 V bank would double the current. Use a listed DC-rated (often Class T, for a battery's high available fault current) fuse and switch, keep the run short and heavy, and terminate at the battery's rated torque. A sizing estimate; the inverter and battery datasheets, the fault-current rating, the AHJ, and the adopted NEC edition govern.
• Inverter AC Output Circuit Conductor and OCPD (NEC 690.8(B)) - Sizes the conductors and overcurrent device from a PV/ESS inverter to the point of connection: continuous output current = AC power / (voltage x [1 single-phase, sqrt(3) three-phase]), then NEC 690.8(B) / 705.60 / 240.4 size the conductor and OCPD at 125% of that current, rounding the OCPD up to the next standard size (240.6). A 9.6 kW inverter at 240 V single-phase puts out 40 A, so the conductor is at least 50 A (a #6 Cu at 75 C) on a 50 A breaker; the same inverter at 208 V three-phase is only 26.6 A. Use the inverter's RATED continuous AC output current from its datasheet if given, and check the 705.12 busbar / point-of-connection limit separately. Distinct from the DC-side pv-circuit-ampacity (690.8(A) 156% rule). A sizing estimate; the inverter datasheet, the AHJ, and the adopted NEC edition govern.
• Wenner 4-Pin Soil Resistivity - Apparent soil resistivity from a Wenner 4-pin (four-electrode, equal-spacing) earth test, the field measurement behind every ground-grid and driven-rod design: rho = 2 x pi x a x R, where a is the equal probe spacing and R is the earth-tester reading. With a converted to meters the result is ohm-meters (x100 for ohm-cm, the unit the grounding-electrode / Dwight tile wants). A 10 ft (3.048 m) spacing reading 5 ohms is 95.8 ohm-m (9,575 ohm-cm); a wider spacing probes deeper, so a set of readings at increasing spacings maps resistivity vs depth and reveals layering. Assumes the electrode depth is small vs the spacing and the 4 pins are equally spaced in a line. Resistivity swings widely with moisture, temperature, and season; the IEEE 81 / ASTM G57 method and the engineer of record govern the design value.
• Cable Bend Radius Minimum - Minimum inside bend radius as a multiple of cable OD per manufacturer bulletins.
• Power Factor Correction Capacitor - Required kVAR and capacitance to raise existing PF to target.
• Phase Balance Across Panels - Per-phase totals, imbalance percent, and a greedy swap list to rebalance.
• Branch Voltage Drop With Multiple Loads - Cumulative voltage at each tap along a run with multiple loads.
• Low-Voltage DC Drop - DC voltage drop and percent at 12 / 24 / 48 V with application-tolerance flags.
• PoE Budget and Run Distance - Power available at PD over Cat5e/6/6A given PoE class and run length.
• Transformer kVA Sizing and FLA - Total connected kVA + ANSI/IEEE step-series recommendation + primary / secondary FLA.
• Short-Circuit Current at Panel (Point-to-Point) - I_sca at transformer secondary, M-factor, and let-through fault current via the Bussmann point-to-point method.
• Generator Sizing for Motor Starting - Required generator kW / kVA from running load and motor-starting kVA at the 30% voltage-dip criterion.
• Service Entrance Demand Load (Standard Method) - NEC Article 220 Standard Method demand-factor walk; recommended service ampacity from the standard ladder.
• Panel Loading and Phase Rebalance - Per-phase totals, percent imbalance, and a swap suggestion to minimize neutral current. Companion to voltage-imbalance.
• Arc-Flash Incident-Energy Screen (Lee 1982) - Simplified pre-IEEE-1584 incident-energy estimate and PPE band. Screen only; not an IEEE 1584 study.
• Motor Branch-Circuit from Nameplate - Compute full-load current from HP / V / eta / PF; flag the design value as the larger of computed vs nameplate; 125% branch-conductor + overload sizing.
• Grounding Electrode Resistance (Dwight / IEEE 142) - Driven rod / ring / plate / Ufer resistance to earth from soil resistivity, with the 25-ohm NEC advisory and a supplemental-electrode count.
• PV Interconnection 120% Busbar Rule - Load-side PV breaker check against the NEC 705.12 busbar limit (120% opposite-end allowance / 100% otherwise), with the supply-side 705.11 alternative.
• Off-Grid Battery Bank Sizing - Required nameplate capacity (Wh and Ah) from daily load, days of autonomy, depth-of-discharge, and round-trip efficiency, per IEEE 1013 / 1561.
• Voltage Drop With Reactance - Single- or three-phase voltage drop using NEC Chapter 9 Table 9 R and X per 1000 ft and the load power factor, with the 3% / 5% advisory band.
• Power Triangle Solver (kW / kVA / kVAR / PF) - Solve the full AC power triangle from any two of real power, apparent power, reactive power, power factor, or phase angle, with a phasor diagram.
• EV Charger Continuous Load and Panel Impact - Continuous-load circuit ampacity (125% per NEC 625.41/625.42), breaker, conductor, new panel total, and headroom for an EVSE.
• EV Charge Time (AC Level 2) - How long an EV charge takes, which ev-charger-load never answers: energy = capacity x (target - start), and the AC charge power is the LESSER of the wall EVSE and the vehicle's onboard charger. A 75 kWh EV from 20 to 80% (45 kWh) on an 11.5 kW EVSE with a 7.7 kW onboard charger charges at only 7.7 kW -> 6.6 hr at 88% efficiency, and the tile flags the EVSE as oversized; a car with an 11.5 kW onboard charger finishes the same charge in 4.4 hr. The onboard-charger bottleneck is why a bigger EVSE often does not charge faster. Constant-power AC Level 2 model (DC fast charging tapers); the vehicle's charging curve governs.
• Battery Bank Series/Parallel Configuration - The series/parallel wiring of a battery bank: modules in SERIES add voltages to make the bus, modules in PARALLEL add amp-hours to make capacity. Series count = round(target bus V / module V); four 12.8 V LFP modules in series make a 51.2 V (nominal 48 V) bus, and two strings in parallel give 200 Ah. Usable energy = series x parallel x module V x module Ah x DoD / 1000: a 4S2P bank of 12.8 V / 100 Ah LFP at 80% DoD is 8.19 kWh usable. The actual bus lands on the module nominal (51.2 V), not the 48 V label; never mix chemistries, ages, or capacities on a bus. LFP ~12.8 V/80% DoD, flooded lead-acid ~12.0 V/50%. A configuration aid; the battery/BMS series-parallel limits, the inverter voltage window, and NEC 706 govern.
• Bifacial PV Rear-Side Gain - The extra output a bifacial module makes from light on its BACK side. The rear cells run at a fraction of front efficiency -- the bifaciality coefficient (phi), a datasheet number ~0.65-0.90 -- and collect the irradiance reflected onto the back. Gain over a front-only module = bifaciality x (rear irradiance / front irradiance): phi 0.75 with 150 W/m^2 rear vs 1000 W/m^2 front = 11.25% more, so a 400 W front rating becomes ~445 W. Rear irradiance climbs with ground albedo (white membrane ~0.5-0.7 vs dark asphalt ~0.1), mounting height, and row spacing -- over a white roof the same module might see 250 W/m^2 (18.75%, ~475 W). A yield estimate; the datasheet bifaciality, the actual site albedo and rear-shading, and a bifacial ray-trace (PVsyst / NREL) govern the real number, and the inverter must be sized for the boost.
• EV Range Added per Hour of Charging - How many miles of driving range an hour of charging adds -- the number that sizes an EVSE to a commute or a fleet's daily miles. Range per hour = EVSE power (kW) x charge efficiency x the vehicle's efficiency (mi/kWh): the kilowatts delivered, after the ~10-15% AC losses, times how far the car goes per kWh. A 7.7 kW Level 2 charger at 88% on a car getting 3.5 mi/kWh adds ~23.7 mi of range per hour, so a 100-mile commute replenishes in ~4.2 hr, comfortably overnight. A 9.6 kW circuit adds range proportionally faster, but the vehicle's ONBOARD charger caps the AC rate (see ev-charge-time), and a less efficient vehicle (truck / cold weather) adds fewer miles/hr. A steady AC Level 2 estimate; DC fast charging tapers, and the onboard-charger limit and actual efficiency govern.
• EV Charge Cost at the Meter - What one EV charge costs on the utility meter, not the dashboard: you pay for kWh at the meter, not at the battery. Energy to the pack = capacity x (target - start); the meter draws more because AC Level 2 loses about 10-15% to the onboard rectifier and thermal load, so grid energy = battery energy / efficiency. A 75 kWh EV, 20 to 80% (45 kWh) at $0.15/kWh and 88% efficiency draws 51.1 kWh and costs $7.67 -- not the $6.75 the dashboard math implies -- an effective $0.170/kWh, and about $0.049/mi at 3.5 mi/kWh. A public DC fast charger at $0.45/kWh runs nearly 3x that. Ignores tiered, time-of-use, and demand pricing; the local tariff governs.
• EV DC Fast-Charge Time (CC-CV Taper) - Why '80% in 20 minutes' is only the first leg: DC fast charging holds constant power (the lesser of charger and vehicle acceptance) only to about 80%, then the battery tapers to protect the cells -- modeled as three bands (0-80% full power, 80-90% ~50%, 90-100% ~25%). A 60 kWh EV from 10-100% on a 150 kW charger (100 kW acceptance) does the 10-80% fast leg in 25.2 min, then the last 20% costs another 21.6 min -- essentially the same again -- for 46.8 min total. Dividing 54 kWh by 100 kW gives 32.4 min, 14 min short, because it charges the top at power the pack never accepts. This is why fast-charge etiquette is to unplug at 80%. A planning estimate; the vehicle's charging curve governs.
• PV Equipment Grounding Conductor (NEC 690.45) - The PV-specific equipment grounding conductor per NEC 690.45: sized from the OCPD via Table 250.122, or from the PV short-circuit current where a source circuit has no overcurrent device, never smaller than 14 AWG. 690.45 waives the 250.122(B) rule, so enlarging the conductors for voltage drop does not enlarge the EGC -- the over-build the general rules cause.
• Conductor Ambient and Fill Ampacity Adjustment - Adjusted ampacity after the NEC 310.15(B)(1) ambient-temperature and 310.15(C)(1) more-than-three-conductors correction factors.
• Service Load Calculation (NEC 220.82 Optional Method) - Optional-method dwelling demand (first 10 kVA at 100% + remainder at 40% + larger HVAC), compared to the standard 220.42 method.
• Lux / Footcandle Converter and Lumen Method - Exact lux <-> footcandle conversion and the lumen-method average maintained illuminance from luminaire lumens, coefficient of utilization, and light-loss factor.
• Parallel Conductor Ampacity - Total ampacity of N paralleled conductor sets with the NEC more-than-three current-carrying-conductor and ambient adjustments, plus per-set load adequacy (1/0 AWG and larger only).
• Three-Phase Neutral Current - Unbalanced neutral current from the phasor sum of three 120-degree-displaced phase currents, with a triplen-harmonic neutral estimate and a neutral-as-CCC advisory.
• Motor Starting Voltage Dip - Voltage dip during motor start from locked-rotor current and conductor length, with terminal voltage and a pass/fail against the dip limit (contactor dropout risk).
• Conduit Offset Bend - Mark spacing, shrink, and multiplier for a two-bend conduit offset at a chosen angle.
• Conduit Saddle Bend - Three-point and four-point saddle marks, bend angles, and shrink to clear an obstruction.
• Conduit 90 Stub and Back-to-Back - Stub-up deduct mark, back-to-back spacing, and segmented-90 shot count.
• Feeder Sizing for Multiple Motors - Feeder conductor (NEC 430.24) and feeder overcurrent device (NEC 430.62) for several motors on one feeder, with the largest-motor term shown.
• Transformer Conductor and Overcurrent Protection - Primary/secondary FLA and the NEC 450.3(B) overcurrent maxima plus the 240.21(C) secondary-conductor minimum for a transformer.
• Fiber Optic Loss Budget - Total link loss (fiber + connectors + splices) and the margin against an application's maximum channel loss (TIA-568 / TIA-526 / IEEE 802.3).
• Fiber Max Length for a Loss Budget - The inverse of the fiber-loss-budget tile: the longest fiber run that still passes the channel loss budget, len_max = 1000 x (max_channel_loss - connector_loss - splice_loss) / attenuation (TIA-568 / IEEE 802.3). A 2.6 dB budget on OM4 (3.0 dB/km) with two connectors reaches about 367 m; single-mode (0.4 dB/km) reaches 2,750 m. Every connector or splice eats budget that would buy distance. Answers 'how far can I run it' instead of the loss of one length. A planning estimate; the OTDR/power-meter field test certifies the link.
• Cable Tray Fill - Cable-tray fill against the NEC 392.22 sum-of-diameters or cross-sectional-area allowance, with a pass/fail.
• IP Camera / NVR Storage and Bandwidth - Total storage, aggregate switch bandwidth, and per-camera daily storage from bitrate, recording schedule, and retention.
• CCTV Retention Days from Disk Capacity - How many days of footage a given NVR disk holds, from camera count, bitrate, and recording schedule (the inverse of the storage calculator).
• 70-Volt Distributed Speaker Line - Tap-wattage budget, reflected line impedance (Z = V^2/P), remaining taps, and run line-loss for a constant-voltage 70 V / 100 V audio line (NEC 640 / 725).
• Fire-Alarm / Security Standby Battery - Required battery amp-hours from standby and alarm loads times the aging/derate factor, with the next standard size (NFPA 72 §10.6).
• Standby Battery Runtime from Capacity - The inverse of the standby-battery-sizing tile: the standby (supervisory) hours an installed fire-alarm or security battery supports before the alarm load, Hs = (battery_Ah/derate - alarm_Ah) / standby_current (NFPA 72 §10.6). A 14.6 Ah battery at 0.5 A standby, 2 A / 5 min alarm, and 1.2 derate holds 24 h; an 18 Ah battery holds about 30 h. Answers 'how long will this battery last' instead of the size for a required time. The derate divides the usable capacity; a battery too small for even the alarm reserve is flagged. The AHJ and the panel worksheet govern.
• Coaxial Cable Attenuation - Total coax attenuation over a run, end-of-run signal level, or the maximum run for a target level (Belden / CommScope loss curves).
• Camera Lens FOV and Pixel Density (DORI) - The horizontal field of view, scene width, and pixel density of a surveillance camera, screened against the IEC 62676-4 DORI bands (Detect 8 / Observe 19 / Recognize 38 / Identify 76 ppf). FOV = 2 x atan(sensor / 2 focal); scene = distance x sensor / focal; ppf = pixels / scene. A 5.37 mm sensor, 4 mm lens at 30 ft with 1920 px gives a 67.7 deg FOV over 40.3 ft and 47.7 ppf -- Recognize but not Identify; an 8 mm lens halves the scene and reaches 95 ppf (Identify). A design aid; verify against the lens chart and a live view.
• Camera Max Distance for a Pixel Density (DORI) - The inverse of the camera-lens-fov tile: the farthest distance a camera still meets a target pixel density (a DORI task), distance = px x focal / (target ppf x sensor). A 1920 px camera with a 4 mm lens on a 5.37 mm sensor holds 76 ppf (Identify) out to about 18.8 ft; drop to 38 ppf (Recognize) and it doubles to 37.6 ft. Answers 'how far can it Identify' instead of the density at a set distance. FOV is fixed by the lens. A design aid; verify against the lens chart, low light, and a live view.
• Ceiling Speaker Coverage and Spacing - The coverage diameter, spacing, and speaker count for a distributed ceiling system: diameter = 2 x (ceiling - ear height) x tan(coverage angle / 2); spacing = the diameter edge-to-edge, or 0.7 x diameter for even (minimum-overlap) coverage; count = ceil(area / spacing^2). A 10 ft ceiling over 4 ft ears at 90 deg covers a 12 ft circle, so a 1,200 ft^2 room needs 9 speakers edge-to-edge or 18 at minimum overlap -- smoother sound, more speakers. A layout aid; verify with the speaker's coverage angle at the design frequency and the target SPL.
• Ceiling Speaker Coverage Angle for a Target Spacing - The inverse of the ceiling-speaker-coverage tile: the coverage angle a target coverage diameter (or on-center spacing) needs at a mounting drop, angle = 2 x atan( diameter / (2 x (ceiling - ear)) ). An 8 ft circle under a 10 ft ceiling over 4 ft ears needs a 67 degree speaker. Spec a speaker rated at least this wide (the angle narrows at high frequency). Answers 'what coverage angle to spec' instead of the diameter from a set angle. A layout aid; verify with the speaker spec and target SPL.
• Structured Cabling Channel Length (TIA-568) - Whether a twisted-pair horizontal channel is within the TIA-568 limits: 100 m total = a 90 m permanent link plus up to 10 m of patch and equipment cords, with the permanent-link maximum de-rating above 20 deg C (about 0.4% per deg C for UTP). An 85 m link with 8 m of cords at 20 deg C passes (93 m channel, link within the 90 m max); at 40 deg C the max link de-rates to 82.8 m so the 85 m link fails and must be shortened. A design aid; the cable's published de-rating and the adopted TIA-568 edition govern.
• Low-Voltage Cable Footage and Box Count - Cable footage and pull-box count for a drop count: total = drops x (average run + slack); boxes = ceil(total / box length). 48 drops at a 120 ft average run plus 15 ft of slack is 6,480 ft - 7 thousand-foot boxes; a denser 100-drop job at a shorter 90 ft run is 10,500 ft and 11 boxes. The slack covers service loops and rack dressing; each run's length is limited separately by structured-cabling-channel. Cable is bought by the box.
• PVC Raceway Expansion Fitting - PVC conduit thermal length change, whether an expansion fitting is required (>= 0.25 in), and the fitting count from the run length and temperature range (NEC 352.44).
• PV Racking Rail, Clamp, and Splice Takeoff - Racking hardware for a PV array: run = modules x (width + gap); rail = rows x rails x run; mid clamps = rails x rows x (modules - 1); end clamps = 2 x rails x rows; splices = (ceil(run / stock) - 1) x rails x rows. A two-row array of twelve 3.42 ft modules on two rails per row is 164 LF of rail, 44 mid clamps, 8 end clamps, and 8 splices; a single row halves the rail to 82 LF and the clamps to 22 mid / 4 end. The rail layout and clamp type come from the rack manufacturer's engineering. Counts hardware, not the array spacing pv-row-spacing gives.
• PV Flat-Roof Ballast Weight and Roof PSF Screen - Dead-load screen for a ballasted flat-roof PV array: total = modules x (module weight + ballast) + racking; added pressure = total / array area, compared to the allowable. 30 modules at 50 lb plus 40 lb of ballast each on a 150 lb rack is 2,850 lb over 630 sf -- 4.5 psf, under a 5 psf allowable; push the ballast to 60 lb and it is 5.48 psf, over the line. A SCREEN, not a design -- the PE-stamped ballast plan and the structural engineer govern; wind uplift and the roof structure govern the design.
• J-Hook / Bridle-Ring Count and Bundle Weight - J-hooks / bridle rings for a cable pathway and the bundle weight each carries: hooks = ceil(run / spacing); load per hook = cables x weight per foot x spacing. A 400 ft run at 4 ft spacing is 100 hooks, and a 50-cable bundle at 0.035 lb/ft puts 7 lb on each; a heavy 200-cable bundle puts 28 lb on each hook (0.93 of a 30-lb hook -- split or upsize). TIA-569 non-continuous support runs about 4 to 5 ft on center. Distinct from the NEC power-raceway support-spacing.
• Access-Control Power Supply and Standby Battery - Sizes the power supply and standby battery for an access-control door system: total load = maglocks x hold current + readers + request-to-exit + controller; supply >= 1.25 x load (NFPA 72 / UL 294 continuous-load headroom); standby battery Ah = load x standby hours x 1.25 for aging. Four 0.5 A maglocks, two 0.15 A readers, and a 0.225 A REX-plus-controller is a 2.53 A load -> a 4 A supply and, for 4 hr standby, a 12.6 Ah battery. Fail-safe maglocks draw continuously (and unlock on power loss for egress); fail-secure strikes draw only on unlock, cutting standby sharply. NFPA 72 sets the standby time for a system on the fire-alarm or egress path. A sizing estimate; the listed panel, the door hardware datasheets, the AHJ, and the life-safety interface govern.
• Fire-Alarm NAC Circuit Voltage Drop (End-of-Line) - Checks that a fire-alarm notification-appliance circuit (NAC) still drives its horns and strobes at the far end. The panel's usable output is its regulated minimum (CUSTV), about 85% of nominal per NFPA 72 -- 20.4 V on a 24 V panel, not 24. On a Class B circuit the current runs out and back, so the loop resistance is 2 x length x the conductor ohms/1000 ft; lumping the total appliance current at the end is the worst case: V_EOL = CUSTV - I x loop_R. A 0.8 A load on 250 ft of #14 (2.525 ohm/1000 ft) drops 1.01 V to 19.4 V -- above a 16 V device minimum, so it PASSES. If it fails, use heavier wire, shorten the run, split the circuit, or add a NAC power extender. A design screen; the panel's regulated voltage, the appliance draws and listed minimums, the wire table, and a signed fire-alarm design and AHJ govern.
• 4-20 mA Current-Loop Signal Scaling - The engineering value a 4-20 mA instrument signal represents, read off a loop meter. The loop is a LIVE ZERO: 4 mA = the low end of the range (0% of span), 20 mA = the high end (100%), so percent of span = (mA - 4) / 16 x 100 and value = range_low + percent/100 x (range_high - range_low). A transmitter ranged 0-100 psi reads 50 psi at 12 mA and 75 psi at 16 mA; a -40 to 120 F range reads 40 F at 12 mA. The live zero lets the loop tell a real zero from a dead wire (0 mA): per NAMUR NE43, 3.8-20.5 mA is the valid band, while <=3.6 mA or >=21 mA is a driven sensor/loop fault, and below 4 / above 20 is under/overrange (flagged). Linear scaling only -- a DP (square-root-extracted) flow transmitter is different; the transmitter's configured range and calibration govern.
• RTD (Pt100 / Pt1000) Resistance to Temperature - The temperature a platinum RTD's measured resistance corresponds to, by the IEC 60751 Callendar-Van Dusen relation R = R0(1 + A T + B T^2) with A = 3.9083e-3 and B = -5.775e-7 per C, solved for T. R0 is the ice-point (0 C) resistance: 100 ohms for a Pt100, 1000 ohms for a Pt1000. A Pt100 reading 119.40 ohms is at 50 C, 138.51 ohms is 100 C, and 100.00 ohms is exactly 0 C. The inverse is exact at or above 0 C; below 0 C it drops the C(T-100)T^3 term, staying within about 0.02 C to -40 C. Assumes a lead-compensated (3- or 4-wire) reading -- uncompensated 2-wire lead resistance adds to R and reads hot. The sensor's calibration, tolerance class (A/B), and self-heating govern the field accuracy.
• Pulse Flowmeter K-Factor (Frequency to Flow) - The flow rate a pulse-output flowmeter (turbine, paddlewheel, or positive-displacement) reports from its output frequency: the meter emits a fixed K-factor of pulses per gallon (stamped on the meter or its calibration cert), so rate = frequency (Hz = pulses/sec) x 60 / K-factor, and the totalized volume is the pulse count / K-factor. A 200 pulse/gal meter reading 100 Hz is 30 gpm; a coarser 100 pulse/gal meter at the same 100 Hz is 60 gpm (each pulse is worth twice the volume). The K-factor drifts with fluid viscosity and shifts below the meter's linear range, so a viscous fluid or near-zero flow reads off; some meters are rated in pulses per liter or per cubic foot (convert first). Linear frequency-to-rate scaling; the calibration certificate, the linear flow range, and the fluid govern.
• Loop-Powered (2-Wire) 4-20 mA Transmitter Voltage Budget - Whether a loop-powered 2-wire 4-20 mA transmitter has enough voltage to operate. The transmitter needs a minimum terminal (compliance / lift-off) voltage -- commonly 8-12 Vdc -- and at the 20 mA top of range the loop supply must push that current through ALL the series resistance (the sense/load resistor, the round-trip wire, plus barriers) and still leave the transmitter its minimum. Max total loop resistance = (supply - transmitter minimum) / 0.020; voltage at the transmitter = supply - 0.020 x total series resistance. A 24 Vdc loop with a 250 ohm sense resistor and 50 ohm of wire (300 ohm) leaves 18 V -- fine above a 10.5 V minimum -- and could carry up to 675 ohm; a 600 ohm run (850 ohm total) starves it at 7 V and the loop reads wrong. DC worst case at 20 mA; the transmitter datasheet's compliance voltage and the barrier burden govern.
• NTC Thermistor Resistance to Temperature (Beta Equation) - The temperature an NTC thermistor's measured resistance corresponds to, by the beta (B-parameter) equation 1/T = 1/T0 + (1/B) ln(R/R0) in kelvin. R0 is the nominal resistance at the reference temperature T0 (almost always 10 kohm at 25 C for the HVAC-standard sensor) and B (~3435-3950 K) is the material constant, both off the datasheet. Being NEGATIVE-coefficient, resistance FALLS as temperature RISES: a 10 kohm/3950 K sensor reads 25 C at 10 kohm, 41.5 C at 5 kohm, 10.2 C at 20 kohm. The beta form is a two-point fit good to about +/-0.2-1 C near T0; a wider or tighter job uses the 3-constant Steinhart-Hart. Distinct from a platinum RTD (positive-coefficient, Callendar-Van Dusen). The datasheet R-T curve, tolerance, and self-heating govern the field accuracy.
• PID Loop Tuning (Ziegler-Nichols Closed-Loop) - Starting PID gains from the Ziegler-Nichols closed-loop (ultimate-sensitivity) method: with I and D off, raise the proportional gain until the loop just oscillates steadily -- that is the ultimate gain Ku, and the oscillation period is Tu. Then PID starts at Kp = 0.6 Ku, Ti = 0.5 Tu, Td = 0.125 Tu; PI (for a noisy/fast loop) at Kp = 0.45 Ku, Ti = Tu/1.2; P-only at Kp = 0.5 Ku. With Ku 4, Tu 2 s a PID starts at Kp 2.4, Ti 1.0 s, Td 0.25 s (42% proportional band). A legacy controller may want proportional band PB = 100/Kp and reset in repeats/min (1/Ti); a parallel-form controller uses different Ki/Kd. Ziegler-Nichols is aggressive (quarter-amplitude decay, overshoots) -- back it off for a gentler loop. A starting point, not a final tune; the process, the controller algorithm form, and the technician govern.
• Hydrostatic DP Level Transmitter (Head to Level) - The liquid level a hydrostatic (differential-pressure) level transmitter reports from the head it measures: P = 0.433 x SG x H (0.433 psi/ft is water at ~60 F), so level H = P / (0.433 x SG). A tap reading 4.33 psi in water is 10 ft; the full-span (URV) pressure for a 20-ft tank is 8.66 psi, so 4.33 psi is 50% of span. A denser fluid gives more pressure per foot, so the same 4.33 psi in a 1.2-SG fluid is only 8.3 ft. Assumes an OPEN (vented) tank with the tap at zero level, no elevation/suppression: an elevated dry-leg tap needs zero suppression and a wet-leg (sealed) tank needs zero elevation, both set at calibration, and the SG is at operating temperature. The transmitter's configured range and calibration and the tank geometry govern.
• Motor Running Overload Protection (NEC 430.32) - The second of the two motor protection devices - the one motor-branch-protection defers: the running overload, sized on the NAMEPLATE FLA (not the table FLC the branch device uses). NEC 430.32(A)(1) gives 125% of FLA for a continuous-duty motor over 1 hp with a marked service factor of 1.15+ or a marked rise of 40 C or less, 115% otherwise, and 430.32(C) permits raising to 140%/130% only if the motor will not start at the base setting. A 26 A SF-1.15 motor sets at 32.5 A with a 36.4 A ceiling - the number dialed into the overload relay or the heater table. A design aid; the AHJ governs.
• Motor Locked-Rotor Current from Code Letter (NEC 430.7(B)) - Starting current from the nameplate code letter, not '6x FLA': NEC Table 430.7(B) maps the code letter (A-V) to a locked-rotor kVA/hp band, and locked_rotor_kva = hp x kVA/hp, LRA = kVA x 1000 / (sqrt(3) x V). A 25 hp code-G 460 V motor tops out at 6.29 kVA/hp -> 157 kVA -> 197 A (5.8x its 34 A FLA, so the rule of thumb fits); the same motor as code J (7.99 kVA/hp) draws 251 A -> 7.4x FLA, and an instantaneous-trip breaker or voltage-dip check sized on '6x' would be undersized. The code letter is about starting kVA and is NOT the design letter (A/B/C/D) for the torque-speed curve. A design aid; the nameplate and measured inrush govern.
• Max Motor HP for a Starting-Current Budget (NEC 430.7(B)) - The inverse of the locked-rotor tile: the largest motor a starting-current budget (a breaker, a generator's starting kVA, an SCCR / voltage-dip ceiling) can start, max_hp = starting-current / (kVA/hp x 1000 / (sqrt(3) x V)). A 300 A budget on a code-G 460 V feeder tops out at ~38 hp. The code letter is the starting-kVA letter, not the design letter; a soft starter lowers the real inrush. A design aid; the nameplate governs.
• Motor Short-Circuit Contribution (First Cycle) - The first-cycle current the utility number leaves out: for the first cycle after a fault, every spinning motor becomes a generator, feeding the fault at roughly its full-load current divided by its subtransient reactance (~4-6x FLA). contribution = motor_FLA / x_subtransient; total = utility_fault + contribution. 500 A of running motors at 16.7% reactance on a 22 kA bus adds 2,994 A (6x FLA) -> 24,994 A total, so a panel rated exactly 22 kA AIC is under-rated by the motors. A first-cycle effect that decays in a few cycles -- it drives the momentary and interrupting duty, not the steady-state fault. Grouped small motors are often lumped at 4x FLA per IEEE C37.13. A design aid; a full short-circuit study governs.
• VFD Reflected-Wave Cable Length Limit - The reflected-wave overvoltage on a long VFD-to-motor cable: L_crit = rise_time x cable_velocity / 2, and past it the peak terminal voltage doubles to 2 x the DC bus. Checked against the NEMA MG-1 Part 31 inverter-duty limit (3.1 x V_LL) and a general-purpose motor's ~1000 V. The limit is set by the drive rise time, not the horsepower.
• Rotary Phase Converter Idler Sizing - The minimum rotary-phase-converter idler to make three-phase from single-phase: idler HP = max(start factor x largest single motor, total HP running at once). The idler must both start the largest motor across the line (a ~2x factor for normal loads, ~3x for a high-inertia or hard-starting load) and run the whole aggregate load. A 10 HP lathe with a 5 HP mill also running is max(2x10, 15) = 20 HP; a shop with a small 5 HP largest but 30 HP total running is governed by the 30 HP load. Undersized, the converter stalls or will not start the big motor; oversized, it wastes idle power. A rule-of-thumb screen; the converter manufacturer's data and the motors' locked-rotor current govern.
• Motor Across-the-Line Acceleration Time - How long a motor takes to bring its load up to speed started direct across the line: t = WK^2 x dN / (308 x T_net), the rotational form of F = m x a, where WK^2 is the total inertia (lb-ft^2) reflected to the motor shaft, dN is the speed change (rpm), and T_net is the average net accelerating torque (motor torque minus load torque, lb-ft). A 100 lb-ft^2 inertia reaching 1,750 rpm on 50 lb-ft of net torque takes 100 x 1750 / (308 x 50) = 11.4 s; double the inertia or halve the net torque and the time doubles. A long start heats the rotor -- check it against the motor's thermal-limit (stall-time) curve, or the overload trips. A screen; the motor's speed-torque and thermal-damage curves, the reflected load inertia, and the drive govern.
• Motor RMS Horsepower for a Duty-Cycle Load - The smallest continuous-rated motor that will not overheat on a repeating on/off (duty-cycle) load: the RMS horsepower is the constant HP that heats the motor the same as the varying load. HP_rms = sqrt( (HP_run^2 x t_run + HP_idle^2 x t_idle) / (t_run + t_idle / K) ), where the idle or stopped time is divided by a cooling factor K (~3 stopped, ~2 unloaded) because a self-cooled motor sheds heat less well when it is not turning at speed. A 20 HP load for 10 s then a 20 s rest at K = 3 gives 15.5 HP_rms, so a 15 HP continuous motor is marginal and a 20 HP is safe. This sizes the THERMAL duty only -- the PEAK horsepower must still fall within the motor's breakdown torque, a separate check. A screen; the motor's thermal-damage curve, service factor, and the manufacturer's duty rating govern.
• Reduced-Voltage Starter Current and Torque - Why an autotransformer's line current is the tap squared: torque falls with the SQUARE of voltage, so a 65% start delivers only 42% of locked-rotor torque -- reduce too far and the motor will not break the load away. And an AUTOTRANSFORMER draws a line current of tap^2 x LRA (not tap x LRA), trading voltage for current: at a 65% tap the motor sees 65% current (390 A of a 600 A LRA) but the line sees only 42% (254 A). Wye-delta gives a fixed 1/3 on both (200 A, 33% torque); a solid-state/reactor start at 65% draws 390 A on both (no squared line cut) for the same 42% torque. The squared line-current reduction is the autotransformer's advantage. A design aid; the motor speed-torque curve and the load govern.
• Insulation Resistance PI / DAR (Megger Test) - The polarization index (PI) and dielectric absorption ratio (DAR) from a timed insulation-resistance (megger) test -- the ratios that tell whether a motor, generator, or transformer winding is clean and dry or wet and contaminated. Good insulation keeps absorbing charge, so its resistance keeps RISING over the test; wet or dirty insulation stops rising or falls. DAR = IR(60 s)/IR(30 s); PI = IR(10 min)/IR(1 min) (the 1-minute and 60-second readings are the same). By IEEE 43, PI below 1 is dangerous, 1-2 questionable, 2-4 good, above 4 excellent; DAR below 1.25 is marginal, 1.4+ good. An 800/1,040/4,160 Mohm test gives DAR 1.30, PI 4.0. A trend/screen, not a pass/fail: temperature-correct to a common base first, and on very-high-IR epoxy windings PI loses meaning per IEEE 43. The baseline trend and OEM criteria govern.
• Dwelling Service/Feeder Conductor at 83% (NEC 310.12) - Why a 200 A house runs on 2/0 copper instead of the 3/0 a straight table lookup demands: NEC 310.12 lets a single-phase 120/240 V dwelling service (and its main feeder) use conductors rated 83% of the service rating. 0.83 x the rating, then the smallest Table 310.16 75 C conductor at or above it - 200 A -> 166 A -> 2/0 Cu or 4/0 Al, 100 A -> #4 Cu, exactly what Table 310.12 tabulates. The service-load tiles produce the amperage; this turns it into the wire. Dwellings only; adjustments and the neutral are separate. A design aid; the AHJ governs.
• Continuous-Load OCPD and Conductor at 125% (NEC 210.20 / 215.3) - The single most reused NEC sizing step, standalone: the breaker and minimum conductor for a mixed load are 125% of the continuous part (on 3 hours or more) plus 100% of the rest, rounded up to a 240.6(A) standard rating. 40 A continuous + 20 A noncontinuous -> 70 A minimum -> a 70 A device; a listed 100%-rated assembly drops the factor and one device size. Before ampacity adjustment; the motor, HVAC, and welder articles carry their own percentages. A design aid; the AHJ governs.
• Generator Output Conductor at 115% (NEC 445.13) - The conductor rule from a generator to its first overcurrent device, which estimators routinely get wrong: NEC 445.13(A) sets the ampacity at not less than 115% of the generator NAMEPLATE current -- not 125% of a computed load, not the connected running load. A 150 kW, 480 V three-phase generator at 0.8 pf draws 225.6 A nameplate, so the conductor must carry 1.15 x 225.6 = 259.4 A. Where the design prevents output above nameplate (overload-limited), the basis drops to 100% and it is just 225.6 A. Enter the nameplate current directly or derive it from kW, voltage, phase, and pf. The 110.14(C) termination limit and 310.15 adjustments still apply. A design aid; the AHJ governs.
• Existing-Facility Load by Peak Demand (NEC 220.87) - Adding load without a service upgrade, on the metered peak: NEC 220.87 lets an EXISTING building use the maximum demand the utility actually metered (a year of data, or a 30-day recording) instead of summing connected loads, which overstates what a service carries. basis = 125% of the recorded peak; total = basis + new load; headroom = service rating - total. A 200 A service with a 120 A recorded peak adding a 40 A EVSE is 1.25 x 120 + 40 = 190 A -> 10 A of headroom, fits with no upgrade; a busier 145 A peak is 221 A, over the 200 A service. VOID where the recorded data reflects on-site PV or peak-shaving that hides the true peak. A design aid; the AHJ and utility data govern.
• EV Load-Management (EVEMS) Diversified Load (NEC 625.42) - The diversified service load of a bank of EV chargers under a NEC 625.42(A) energy management system: without an EVEMS the service carries the SUM of every charger at 125% (forcing an upgrade); with a listed EVEMS the demand is 125% of the aggregate limit it enforces, not the sum. Four 40 A chargers held to 80 A: 200 A sum vs 100 A managed -- 100 A freed, so four chargers land on a panel sized for one.
• EV Charger Throttled-Current Schedule (NEC 625.42) - What each car actually gets when the EVEMS throttles, the operating side of ev-load-management-ems: throttled = min(charger_max, aggregate_limit / active_chargers). Four 40 A chargers on a 100 A EVEMS budget do not each get 40 A - the system throttles all four to 25 A, and only two could run at full rate at once. Drop to two active and both get their full 40 A. Predicts charge times and explains why the last car in slows the rest. A planning aid, not the EVEMS configuration.
• NEC Pull and Junction Box Sizing - The minimum pull or junction box dimension for large raceways under NEC 314.28 -- 8x the largest raceway for a straight pull, 6x plus the same-row others for an angle or U pull, and the 6x between-entries rule. box-fill is the separate 314.16 conductor-volume fill.
• Lumen-Method Luminaire Count - How many fixtures to hit a target maintained footcandle level in a room, the IES lumen method: target x area / (lumens x CU x LLF), rounded up, with the achieved footcandles at that count. lux-to-footcandle does the forward illuminance from a known total.
• Room Cavity Ratio (RCR) for CU Lookup - The shape number a lighting designer needs to read the coefficient of utilization (CU) off a luminaire's photometric report before the lumen method: RCR = 5 x cavity height x (length + width) / (length x width), where the cavity height is from the luminaire plane down to the WORK plane (~2.5 ft above floor), NOT floor-to-ceiling. A 40 x 30 ft room with an 8 ft luminaire-to-workplane cavity has RCR 2.33. A tall, narrow room (big cavity vs floor area) has a HIGH RCR -- more light hits the walls, less reaches the work plane, so a lower CU; a low, wide room has a low RCR and higher CU. Enter this RCR with the ceiling/wall/floor reflectances into the manufacturer's CU table, then that CU feeds the lumen-method fixture count. A design input; the fixture's IES photometric file and the actual surface reflectances govern the CU.
• Luminaire Spacing-to-Mounting-Height Ratio - The maximum center-to-center spacing between luminaires for reasonably uniform light, from the fixture's spacing criterion (SC), historically the spacing-to-mounting-height ratio (S/MH): max spacing = SMH x mounting height ABOVE THE WORK PLANE (not floor-to-ceiling). A fixture with an SMH of 1.3 mounted 8 ft above the work plane can be spaced up to 1.3 x 8 = 10.4 ft; a 9 ft layout is fine, a 12 ft layout leaves dark scallops. Narrow-beam / high-bay optics have a lower SMH (0.5-1.0) and must be spaced tighter; wide troffers run higher (1.2-1.5). The perimeter row is set at about half this spacing off the wall. A layout screen; the fixture's actual photometric distribution, the room reflectances, and the target uniformity govern the final spacing.
• Grounding Electrode Conductor Sizing - The grounding electrode conductor (GEC) from the largest ungrounded service conductor per NEC Table 250.66, with the 250.66(A)-(C) electrode caps applied: a rod/pipe/plate sole connection need not exceed 6 AWG copper, a concrete-encased (Ufer) 4 AWG copper, while a water-pipe or structural-steel electrode takes the full table size. The AHJ-adopted edition governs.
• Bonding Jumper Sizing (Supply-Side and Equipment) - The main / supply-side bonding jumper from Table 250.66 by the service conductor (with the 12.5% rule above 1100 kcmil copper / 1750 kcmil aluminum), and the equipment (load-side) bonding jumper from Table 250.122 by the overcurrent device, a full-size jumper in each parallel raceway. NEC 250.28 / 250.102; the AHJ governs.
• Minimum Conductor Size for a Voltage-Drop Target - The inverse of the voltage-drop tile: the smallest standard copper and aluminum conductor that keeps the drop at or below a target percent (default 3%) over the run, from the load current, one-way length, and system voltage, with the resulting drop and an ampacity / termination reminder. The voltage-drop size is a floor, not a substitute for the 310.16 ampacity check.
• Maximum Circuit Length for a Voltage-Drop Target - The longest one-way run that still meets a voltage-drop target -- the other inverse of the VD tile (given the wire, how far can I run it?). L = VD_target x cmil / (factor x K x I), factor 2 single-phase / sqrt(3) three-phase, K = 12.9 Cu / 21.2 Al, VD_target = target% x source V, cmil the conductor circular mils. A #12 Cu (6,530 cmil) at 20 A on a 120 V single-phase branch reaches ~45 ft before 3% drop; the same wire on 208 V three-phase reaches ~91 ft (sqrt(3) factor + higher voltage). Doubling the current halves the length; a bigger wire or higher voltage lengthens it. DC-resistance drop only (reactance adds on larger conductors -- see voltage-drop-reactance); the 3%/5% figures are NEC recommendations. Still pass the 310.16 ampacity check; the AHJ governs.
• Conduit Nipple 60% Fill (NEC Ch. 9 Note 4) - The conductor fill allowed in a NIPPLE -- a raceway no longer than 24 in between boxes, cabinets, or wireways. NEC Chapter 9 Note 4 permits 60% fill (vs the normal 40% for 3+ conductors, 31% for two, 53% for one) because a short nipple sheds heat easily. Fill% = count x conductor area / conduit total area (Table 4 conduit area, Table 5 conductor area). 20 #10 THHN (0.0211 in^2) in a 1 in EMT nipple (0.864 in^2) = 48.8%: legal in a nipple (60% allows 24) but OVER the normal 40% (allows only 16). Note 4 ALSO exempts nipples from the 310.15(C)(1) ampacity adjustment, so conductors keep full table ampacity. A fill check; the exact Table 4/5 areas, the box/pull-can sizing, and the AHJ and adopted NEC edition govern.
• Open-Delta (V-V) Transformer Bank Capacity - The balanced three-phase capacity of an open-delta (V-V) bank -- two single-phase transformers serving three-phase, common where a third unit failed or a light load does not justify a full bank. Two units do NOT give twice one unit: available three-phase kVA = sqrt(3) x one unit's rating (1.732, not 2), because each carries the load / sqrt(3) and the phase angle caps the combined output at 86.6% of the two installed. Two 25 kVA units serve 1.732 x 25 = 43.3 kVA, each at 21.65 kVA (86.6% of rating). That is only 57.7% of the closed-delta three-unit bank (43.3 vs 75 kVA), so removing one of three drops it to 57.7%, not 66.7%. Reports each unit's loading and flags an overload. A sizing screen; the nameplate kVA and impedance, the load balance and power factor, and the utility govern.
• Motor Synchronous Speed, Slip, and Rotor Frequency - The synchronous speed Ns = 120 x frequency / poles, the slip relative to the nameplate full-load speed, and the rotor (slip) frequency, for commissioning a motor, reading a VFD parameter set, or diagnosing a wrong-speed complaint. The nameplate full-load speed governs.
• Motor Pole Count from Nameplate RPM - The inverse of the synchronous-speed tile, for a tech who only reads a speed off the plate: from the nameplate full-load rpm and line frequency, the pole count is the nearest even integer to 120 x f / rpm - pole-pairs = round(60 x f / rpm), poles = 2 x pole-pairs, then Ns = 120 x f / poles and the slip. A 1750 rpm 60 Hz motor is 4-pole (Ns 1800, 2.78% slip); 1150 rpm is 6-pole, 3450 rpm is 2-pole. A speed at/above the identified Ns (zero or negative slip) never appears on an induction nameplate - recheck the rpm. The nameplate governs.
• Motor Shaft Torque, Horsepower, and Speed - The horsepower-speed-torque triangle T = 5252 x HP / RPM, solving either way: supply horsepower to get shaft torque, or torque to get horsepower, for coupling, belt, gearbox, and VFD torque-limit selection. The nameplate and driven load govern the service-factor margin.
• Motor Input Power, Annual Energy, and Cost - The input kilowatts a motor draws at its efficiency (HP x 0.746 x load / efficiency), the annual kilowatt-hours at a given duty, and the energy cost, with the efficiency-driven delta that justifies a premium-motor retrofit. The energy charge only; the utility tariff governs demand, time-of-use, and power-factor penalties.
• Motor Run Hours for an Energy Budget - The inverse of the motor-cost tile: the run hours an annual energy budget buys, hours = budget / (input_kW x rate), input_kW = HP x 0.746 x load / efficiency. A 25 HP motor at 93% and $0.12/kWh draws 20.05 kW, so a $5,000 budget covers about 2,078 hours. Answers 'how long can I run it' instead of the cost from a set duty. Energy charge only; the utility tariff (demand, time-of-use, power-factor) governs the full bill, so the real hours are fewer.
• Feeder for a Group of Motors (NEC 430.24 / 430.62) - The feeder conductor ampacity (125% of the largest motor full-load current plus the sum of the rest, NEC 430.24) and the feeder overcurrent-device ceiling (largest branch device plus the sum of the others, rounded down to a standard size, NEC 430.62) for a panel feeding several motors. Full-load currents are the NEC table values; the AHJ governs.
• Conductor Short-Circuit Thermal Withstand (Onderdonk / ICEA) - Whether a conductor survives the available fault current for the protective device's clearing time without exceeding its insulation short-circuit temperature, by the public-domain ICEA / Onderdonk adiabatic equation, plus the minimum size for the actual fault. A thermal-withstand screen, not a substitute for an engineered study.
• PVC Conduit Thermal Expansion (NEC 352.44) - The longitudinal length change of a PVC raceway across its temperature swing (delta_L = coefficient x length x temperature change) against the NEC 352.44 quarter-inch expansion-fitting trigger, for outdoor or unconditioned runs. The AHJ and the conduit manufacturer govern.
• PVC Conduit Max Run Before an Expansion Fitting - The inverse of the conduit-thermal-expansion tile: the longest straight PVC run between anchors before an expansion fitting is required, L_max = trigger / (coefficient x 12 x temperature swing) (NEC 352.44). At a 50 deg F swing a run over about 12.3 ft reaches the quarter-inch trigger; at 100 deg F it is about 6.2 ft. Answers 'how long a run can I make before I need a fitting' instead of checking one length. The AHJ and the conduit manufacturer govern.
• EGC Proportional Upsize for Increased Conductors (NEC 250.122(B)) - When ungrounded conductors are increased in size for voltage drop or future capacity, the equipment grounding conductor increases in the same circular-mil proportion per NEC 250.122(B). Base EGC and base phase area are user-supplied table values; the EGC need not exceed the ungrounded conductors. The AHJ governs.
• Wye / Delta Line-to-Phase Voltage and Current - The mapping between line and phase (winding) quantities for both three-phase connections: in a wye the line voltage is root-3 times the phase voltage while currents are equal; in a delta the line current is root-3 times the phase current while voltages are equal, with the connection-independent apparent power. The equipment nameplate governs the connection.
• Feeder Tap Conductor 10-ft / 25-ft Rule (NEC 240.21(B)) - The minimum ampacity an unprotected feeder tap conductor must carry under the 10-ft and 25-ft tap rules of NEC 240.21(B)(1) and (B)(2): at least 1/10 of the feeder overcurrent device for a tap up to 10 ft, or 1/3 for a tap up to 25 ft, with a verdict against the proposed conductor's 75 C ampacity (400 A feeder, 22 ft tap -> 133 A minimum). A tap over 25 ft falls under neither short-tap rule. The other 240.21(B) conditions (physical protection, single-OCPD termination, the supplied-device rating) apply; the AHJ and design engineer govern.
• Buck-Boost Transformer Sizing (Single-Phase) - The autotransformer (buck-boost) kVA to correct a line voltage up or down for a load: boost/buck = desired minus supply voltage, and the unit is rated only for that boost times the load current, a fraction of the full load kVA (208 V to 230 V at 50 A -> a 1.10 kVA unit supports an 11.5 kVA load). Sizing a buck-boost by the full load kVA grossly oversizes it. NEC Article 450; the buck-boost selection, connection, and overcurrent protection are the manufacturer's and the AHJ's.
• Wireway / Auxiliary Gutter 20% Fill (NEC 376.22) - Sizes a metal wireway (and, by 366.22, an auxiliary gutter) against the NEC 376.22 limits: conductor cross-section no more than 20% of the interior, and the 30 current-carrying conductor threshold for ampacity adjustment (4x4 in carrying 2.5 in^2, 18 CCC -> 15.6% fill, within). Over 30 conductors triggers a 310.15(C)(1) adjustment, not a prohibition; signal conductors and the article exceptions are excluded from the count. The AHJ governs.
• Rooftop Conduit Sunlight Ambient Adder (NEC 310.15(B)(2)) - Applies the NEC 310.15(B)(2) rooftop sunlight adder, 33 C (60 F) where a raceway is less than 7/8 in above the roof, to a measured ambient and then the 90 C-column temperature correction (a #8 at 55 A in a 95 F ambient on the roof -> 155 F design ambient -> ~0.58 -> ~32 A). Raising the raceway onto standoffs at or above 7/8 in removes the adder and recovers most of the ampacity. The AHJ-adopted edition governs.
• Working-Space Clearance Lookup (NEC 110.26) - Returns the NEC 110.26(A) working space in front of electrical equipment: the depth by voltage-to-ground and Condition 1/2/3 (0-150 V is 3 ft; 151-600 V is 3 / 3.5 / 4 ft), the width as the greater of 30 in or the equipment width, and 6.5 ft of headroom with a required 90-degree door swing. 110.26(E) adds the dedicated equipment space. A reference lookup; the AHJ governs.
• Household Range Demand Load (NEC Table 220.55 Col. C) - The demand load for household electric ranges by NEC Table 220.55 Column C, with the Note 1 over-12 kW increase: one 12 kW range demands 8 kW (not 12), so 33.3 A at 240 V; a 16 kW range adds 5% per kW over 12 (20%) to 9.6 kW / 40 A. Multiple equal-rated ranges read Column C directly. Notes 2-4 (the Columns A/B paths and unequal-rating averaging) and the AHJ govern the other cases.
• Household Clothes Dryer Demand Load (NEC 220.54) - The clothes-dryer feeder/service demand under NEC 220.54: each dryer counts at the larger of 5,000 W or its nameplate, then a Table 220.54 demand factor applies at five or more (four 4.5 kW dryers -> 20 kW / 83.3 A; five 5 kW dryers -> 85% -> 21.25 kW / 88.5 A). Five dryers demand only slightly more than four once the factor kicks in. The AHJ governs counts beyond the table.
• Feeder/Service Neutral Demand Load (NEC 220.61) - Sizes the feeder/service neutral under NEC 220.61: it carries the maximum unbalanced load, but the portion over 200 A may be taken at 70% (a 250 A unbalanced load -> 200 + 0.70x50 = 235 A). 220.61(C) prohibits the reduction for nonlinear-load portions (electric-discharge lighting, electronic loads), which stay at 100%. A sizing demand, not an operating current; the AHJ and the load classification govern.
• Motor Derating for Voltage Unbalance (NEMA MG-1) - Turns a measured three-phase voltage unbalance into a NEMA MG-1 motor derating factor and the do-not-operate flag above 5%: unbalance = max deviation from the average / the average (460/455/450 V -> 1.1% -> derate ~0.98). The MG-1 curve is interpolated; above 5% the motor should not be operated. Correct the unbalance source first; the manufacturer and MG-1 govern the final figure.
• Point-Method Illuminance (Inverse-Square + Cosine) - Horizontal illuminance at a point from a luminaire of known candlepower by the IES point method: E = candela x cos(angle)^3 / mounting-height^2 (a 1,000 cd source 10 ft up gives 10 fc directly below, 6.5 fc at 30 deg off nadir; lux = fc x 10.764). The direct illuminance from one source, ignoring interreflection, complementing the lumen/zonal average method. The photometric file and the IES target govern.
• Luminaire Mounting Height for a Target Illuminance - The inverse of the point-illuminance tile: the mounting height that lands a target horizontal illuminance at a point, height = sqrt( candela x cos(angle)^3 / E ). A 1,000 cd source needs a 10 ft mount for 10 fc directly below. Solves for HEIGHT (the point-method-required-candela tile solves for the candela). A higher mount lowers the illuminance. Direct illuminance from one source, ignoring interreflection; the photometric file and the IES target govern.
• Point-Method Required Candela for a Target - The inverse of the point-illuminance tile: the luminous intensity a fixture must aim toward a point to hit a target illuminance, I = E x mounting-height^2 / cos(angle)^3 (E in footcandles, lux / 10.764). Hitting 10 fc from 10 ft up straight below needs 1,000 cd; the same 10 fc at a point 30 deg to the side needs about 1,540 cd (the cos^3 penalty off-nadir). Answers 'what candlepower do I need' instead of the illuminance from one fixture. Direct component only; the photometric file and the IES target govern.
• Lighting Light-Loss Factor (Maintained/Initial) - Light-loss factor = the product of the IES recovery factors (lamp lumen depreciation, luminaire/room dirt, ballast, burnout), and maintained lumens = initial x LLF. LLD 0.85 x LDD 0.90 x BF 0.95 = 0.727; a 4,000 lm fixture holds 2,908 maintained. The IES tables and maintenance schedule govern.
• Lighting Illuminance Uniformity Ratio - Avg/min, max/min, and U0 = min/avg from a grid of illuminance readings, against a target ratio. Readings 50/45/60/55/40 fc -> 1.25 avg/min, 1.50 max/min; a patchy 70/20/65/25/30 fails a 3:1 target the average hides. The IES RP for the space governs.
• Egress Lighting Illuminance Compliance Check (NFPA 101 / IBC) - Egress illuminance against NFPA 101 / IBC: normal 1.0 fc avg / 0.1 fc min, emergency 90-min end 0.6 / 0.06, max/min <= 40:1. A 1.2/0.15/3.0 fc corridor is compliant; a 0.05 fc dark spot fails the emergency minimum even at a good average. The adopted code and AHJ govern.
• Industrial Control Panel SCCR (UL 508A) - The short-circuit current rating of an industrial control panel by the UL 508A weakest-link method: the panel SCCR is the LOWEST of its power-circuit components' individual ratings (and the feeder OCPD interrupting rating), not the main breaker -- one 5 kA contactor caps the whole panel. Checked against the available fault per NEC 409.110. A current-limiting fuse can raise a weak component's combination rating.
• Tolerable Step and Touch Voltage (IEEE 80) - The IEEE Std 80 tolerable step and touch voltages a grounding grid is checked against -- what meeting a grid-resistance target does not guarantee. The crushed-rock surface layer raises the limit via the Cs derating factor, and the limits scale inversely with the square root of the fault clearing time (a faster relay allows more). Touch governs over step.
• Ground Potential Rise Screen (IEEE 80) - The yard-voltage side of step-touch-voltage: GPR = grid_current x grid_resistance, screened against the tolerable touch voltage. The IEEE 80 shortcut - a GPR at or below the tolerable touch means no yard point can exceed it, so no mesh/step analysis is needed. A 200-A grid current on a 0.5-ohm grid rises just 100 V (passes a 200-V limit outright); a 5,000-A fault on a 1-ohm grid rises 5,000 V (25x the limit, full mesh/step study required). A screen, not a grounding design.
• Lightning Rolling-Sphere Zone of Protection - The ground area a lightning mast or air terminal shields, by the NFPA 780 rolling-sphere method: roll a sphere of radius R (150 ft standard) over the structure -- lightning strikes wherever it touches, and a mast of height h <= R protects a ground circle of radius d = sqrt(2 R h - h^2). A 30 ft mast with the 150 ft sphere protects a 90 ft radius (about 25,400 ft^2). A single-mast estimate; two masts protect the overlapping zone between them, higher than either alone, and a mast taller than R caps at R with side-flash exposure above. Sizes the zone only, not the down-conductor, bonding, or grounding a complete system needs. NFPA 780 and a lightning-protection engineer govern.
• Max Grounding-Grid Resistance for the GPR Screen (IEEE 80) - The inverse of the GPR screen: the grid resistance target that keeps the ground potential rise at or below the tolerable touch voltage, max_R_g = tolerable_touch / grid_current. A 200-V touch limit with a 200-A grid current needs a grid resistance of 1.0 ohm or less to clear the IEEE 80 screen without a full mesh/step study. IEEE Std 80 and a qualified grounding study govern.
• Neutral Grounding Resistor Sizing (IEEE 142) - Sizing the NGR off line-to-neutral, not line-to-line: a resistance-grounded transformer neutral limits a ground fault to a known current -- a few amps (HRG, keep running through the first fault) or 100-400 A (LRG, fast tripping). The resistor sees V_LN = V_LL / sqrt(3), NOT V_LL, so sizing off V_LL makes it sqrt(3) too large and the fault too small to sense. R = V_LN / I_ground; P = I^2 R = V_LN x I. A 480 V system at a 5 A HRG target: the resistor sees 277 V -> 55.4 ohm, 1,386 W continuous. HRG resistors are rated continuous, LRG for the short trip time. A design aid; IEEE 142 and the protection scheme govern.
• Underground Burial Cover-Depth Lookup (NEC Table 300.5) - Returns the minimum cover for underground wiring by method and location from NEC Table 300.5 (<= 1000 V): direct-burial cable 24 in, PVC 18 in, RMC/IMC 6 in in general earth, all methods 24 in under public streets/driveways, and 0 in (in raceway) under a building. Cover is measured to the top of the raceway/cable; the table footnotes modify specific cells and the AHJ governs.
• Raceway / Cable Support-Spacing Lookup (NEC Chapter 3) - The securing and support intervals for the common wiring methods from their NEC Chapter 3 .30 sections: EMT within 3 ft of a box and every 10 ft, NM within 12 in and every 4.5 ft, MC within 12 in and every 6 ft, AC within 12 in and every 4.5 ft; RMC and PVC intervals vary with trade size. The securing exceptions (fishing, terminations) and the AHJ govern.
• Motor Branch-Circuit Protection and Disconnect (NEC 430.52 / 430.110) - Sizes the maximum motor branch-circuit short-circuit and ground-fault protective device from the table FLC and device type per NEC Table 430.52 (250% inverse-time breaker, 175% dual-element fuse, 300% nontime-delay fuse, 800% instantaneous-trip), with the 430.52(C)(1) Exception 1 round-up to the next standard size (240.6), plus the 430.110 disconnect at 115% of FLC. Overload is sized separately (430.32); the AHJ governs.
• Commercial General-Lighting and Receptacle Load (NEC 220.12 / 220.44) - Computes the commercial general-lighting load (area x the Table 220.12 unit load) plus the general-use receptacle load at 180 VA per strap (220.14(I)) with the 220.44 demand factor (100% of the first 10 kVA, 50% of the remainder), then the total VA and amps. The 125% continuous factor is applied at the OCPD; the energy code may set the lighting load and the AHJ governs.
• Noncoincident Loads: Larger of Heating vs A/C (NEC 220.60) - Applies NEC 220.60: where two loads (electric heat vs air-conditioning) are unlikely to run at the same time, the service calc carries only the larger and omits the smaller; the exception adds both where they operate simultaneously (a heat-pump compressor with supplemental strip heat). The AHJ judges noncoincidence.
• VFD Retrofit Energy and Cost Savings (Affinity Cube Law) - The number that sells a variable-frequency drive: the annual kWh and dollars it saves on a centrifugal pump or fan. A throttled or dampered constant-speed machine keeps drawing near-full power; slowed by a VFD it draws the cube of the speed ratio (the affinity law), so at 60 percent flow it uses about a fifth of the power. The saving is that gap integrated over a three-bin duty cycle - and the whole case turns on the load profile, not the horsepower: the identical drive on the identical pump saves six times less if the pump mostly runs at full flow. A screening estimate, not a metered M&V.
• LED Lighting Retrofit Savings and Payback - The four numbers on every lighting proposal: the energy saved from the wattage reduction (fixtures x (W_old - W_new) x hours x rate), the demand-charge reduction if the load runs at the utility peak, the total annual saving, and the simple payback against install cost. The demand term - which a lighting proposal that ignores the demand side leaves out - often shortens the payback by a third. The burn hours are the actual operating hours; a controls retrofit is a separate credit and an air-conditioned space gains a cooling credit not included here. A simple payback, not a life-cycle analysis.
• Power-Factor Correction Demand-Billing Savings - The dollars a power-factor capacitor returns: a low power factor draws more apparent power (kVA) than real power (kW), and where the utility bills demand in kVA (or adds a low-power-factor penalty) correcting it cuts the billed demand every month and releases transformer and feeder capacity. The saving is the kVA reduction times the demand charge, twelve months a year, usually paying the bank back in under a year. Correction has sharply diminishing returns above ~0.9, which is why 0.95, not unity, is the usual target. A billing estimate, not a rate-tariff analysis.
• PV Circuit Maximum Current and Ampacity (NEC 690.8, the 156% Rule) - Sizes the PV source/output-circuit maximum current = module Isc x paralleled strings x 125% (690.8(A)(1)) and the minimum conductor ampacity = that maximum x another 125% (690.8(B)(1)), the two factors stacking to 156% of Isc, before any conditions-of-use derate. The conductor must also satisfy 690.8(B)(2) and the greater governs; the engineer governs.
• PV Annual Energy, Specific Yield, and Capacity Factor - The first question a solar customer asks, answered with the NREL PVWatts energy model: annual kWh = DC nameplate x peak-sun-hours x 365 x performance ratio, plus the two benchmarks every designer compares systems by - specific yield (kWh per kW installed) and capacity factor. The same hardware makes a quarter more energy at a desert site than an average one, so the estimate starts from the site's plane-of-array irradiation, not a rule-of-thumb kWh-per-kW. The performance ratio (default 0.77) rolls up soiling, shading, mismatch, wiring, and inverter losses. A pre-design estimate, not a bankable production model.
• PV Array Size from a Target Annual Energy - The inverse of the PV energy-yield tile: the DC array size needed to offset a target annual production, from the NREL PVWatts model - DC = target_annual_kWh / (peak-sun-hours x 365 x performance ratio). To offset a 12,000 kWh/yr bill at 5 peak-sun-hours and a 0.77 performance ratio takes an 8.54 kW DC array (specific yield 1,405 kWh/kWp). Enter the annual total (monthly bill x 12) to size from a utility bill. The performance ratio (default 0.77) is the biggest lever. A pre-design estimate, not a bankable model; module count and roof area then follow.
• PV Inter-Row Spacing and Ground-Coverage Ratio - The row layout for a ground mount, carport, or ballasted flat roof: the row pitch is the panel's horizontal footprint plus the shadow its top edge throws at the minimum winter-design sun angle, and the ground-coverage ratio (collector length over pitch) drives both the land area and the inter-row shading. Pack the rows tight for more kilowatts on the lot, or spread them for clean panels - a shallow tilt throws a far shorter shadow and packs nearly 50 percent more array on the same field. The profile angle is the winter sun elevation from latitude or solar-times. A layout geometry, not an annual shading-loss model.
• PV Shade-Free Sun Angle from Row Pitch - The inverse of the row-spacing tile: with the row pitch fixed by the roof or lot, the lowest solar profile (elevation) angle the layout stays shade-free to, prof = atan(L sin tilt / (pitch - L cos tilt)). A 6.5 ft module at 30 deg tilt with 12 ft of pitch is clear down to a 27 deg sun. Compare it to the winter-design sun elevation. Assumes due-south rows and a level field.
• Sun Shadow Length - The ground shadow a vertical object casts on level ground: shadow = object height / tan(sun altitude), so the shadow is height x cot(altitude) and the shadow-to-height ratio depends only on the sun angle. A 10 ft object under a 30 degree sun throws a 17.3 ft shadow (1.73 x its height); at a 45 degree sun the shadow equals the height, and a low winter sun throws one nearly three times as long. Use the winter-design sun elevation for the worst-case shade -- the case a solar-access, tree-planting, or building-setback study turns on. Level ground and a vertical object assumed; the sun path and terrain govern.
• PV Inverter Loading Ratio (DC:AC) and Clipping Onset - The array-to-inverter power match: the inverter loading ratio (DC nameplate over AC rating, the DC:AC or ILR), with the cost-optimal band (commonly 1.1 to 1.3) and the clipping onset as a fraction of STC nameplate. An array is deliberately oversized so it fills the inverter's ceiling for more of the day, but push it too far and the inverter clips every clear-day peak. The clipping ceiling is fixed by the inverter; raising the array lowers the fraction of nameplate at which it bites - the diminishing return that puts the sweet spot near 1.2. A sizing sanity check, not a clipping-loss model.
• PV Cell Temperature and Temperature-Derated Power - Cell temperature from the NOCT model T_cell = T_amb + (NOCT-20) G/800 and the temperature-derated power P = P_stc(1 + gamma(T_cell-25)). A 400 W module at 30 C air, 800 W/m^2 runs 55 C and makes 358 W (10.5% loss); a cool 10 C morning makes 386 W. The datasheet governs.
• PV Max Ambient Temperature for a Target Power - The inverse of the PV cell-temperature tile: the highest ambient temperature a module still makes a target power, since a negative power coefficient means a hotter cell makes less. T_cell = 25 + (P/P_stc - 1) x 100/gamma, then T_amb = T_cell - (NOCT-20) x G/800. A 400 W module holding 358 W at 800 W/m^2 tops out at 30 C air (55 C cell). Answers 'how hot before it drops below target' instead of the power from a set air temp. Temperature derate only; the datasheet governs.
• PV Performance Ratio from Stacked Losses - Performance ratio as the product of (1 - loss) over the PVWatts-style derate stack (soiling, temperature, wiring, inverter, mismatch, shading, etc.). A typical rooftop stack lands near 0.75-0.82; attacking the two largest losses moves it most, the multiplicative leverage made visible. A screening stack, not a metered PR.
• PV Source-Circuit Fuse Sizing (NEC 690.9) - PV source-circuit overcurrent per NEC 690.9: fuse >= 1.56 x Isc, rounded up to a 240.6(A) standard rating and checked against the module label maximum; fuses required with 3+ paralleled strings. Isc 10 A -> a 20 A fuse; a 25 A requirement on a 20 A module max is non-compliant. The NEC and AHJ govern.
• Battery Time-of-Use Arbitrage Value - What a time-of-use spread actually pays a grid-tied battery: charge cheap off-peak and discharge dear on-peak, but the round trip loses ~15 percent, so the daily value is usable energy at the peak price minus the larger amount bought at off-peak to store it (daily = usable x peak - usable/RTE x offpeak). The catch every arbitrage pitch skips is that the peak has to beat off-peak by more than the round-trip loss (break-even = 1/RTE) just to break even, so a spread that looks like a tempting 1.56x nets almost nothing. The NREL round-trip framing; RTE is AC-to-AC, DoD is warranty-usable. A gross spread-value aid, not a financed payback.
• Battery Peak-Shaving Demand-Charge Savings - Sizes a battery to shave a commercial demand peak and prices it: the demand charge (often $10-30/kW on the single highest 15-minute reading of the month) times the shave, but the shave is energy-limited - a battery holds a given kW reduction only as long as its usable energy lasts (sustainable = usable / duration, actual = min(target, sustainable)). Shaving a 40 kW peak that persists three hours needs 120 kWh; a wide afternoon plateau demands far more storage per kW than a brief spike. The duration comes from an interval-meter load profile. A demand-savings estimate, not a metered bill.
• Battery C-Rate: Deliverable Power and Discharge Duration - A battery's power is not its energy: the C-rate caps how fast the pack discharges (power = nameplate x C) and the inverter caps how much reaches the panel, so the deliverable power is the lesser of the two and the usable energy lasts that many hours at it. A 40 kWh pack at 0.5C pushes 20 kW, but behind a 15 kW inverter only 15 kW comes out - it runs longer at lower power. The check that keeps a designer from specifying a peak-shave or backup load the pack physically cannot deliver. Continuous, not surge, rating. A nameplate power check, not a cell-level thermal model.
• Transformer K-Factor From the Harmonic Spectrum (UL 1561) - Computes the transformer K-factor from a measured harmonic current spectrum, K = sum(Ih^2 x h^2) / sum(Ih^2) with the harmonics entered as per-unit of the fundamental (UL 1561 / IEEE C57.110), then rounds up to the next standard K-rating (K-1 standard, then K-4 / K-9 / K-13 / K-20 / K-30 / K-40). The measured spectrum and the manufacturer govern.
• Max Capacitor kVAR at Motor Terminals (Self-Excitation Limit) - Returns the largest power-factor capacitor that can be switched with a motor before self-excitation overvoltage: magnetizing kVAR = sqrt(3) x V x no-load current / 1000 (NEMA MG-1 / IEEE 18), times a safety factor (default 0.90). The manufacturer's max-kVAR table by HP and speed governs; pair with the PF-correction tile and keep the smaller value.
• Series R-L-C Reactance, Impedance, and Resonant Frequency - The base AC-circuit relations behind filter, coil, and cable-reactance work: inductive reactance XL = 2 pi f L (rises with frequency), capacitive reactance XC = 1/(2 pi f C) (falls with it), series impedance Z = sqrt(R^2 + (XL - XC)^2), and power factor R/Z. At 60 Hz a 10 ohm / 0.05 H / 50 uF branch has XL 18.85, XC 53.05 ohm, so it is capacitive (leading), Z = 35.6 ohm, PF 0.28. The branch resonates where XL = XC, at f0 = 1/(2 pi sqrt(L C)) = 100.7 Hz, where the reactances cancel, Z collapses to just R, and current peaks -- the frequency a passive filter is tuned to and a cap bank must avoid. Single-frequency, linear, lumped-element steady state; a real cable/coil is distributed, and a harmonic or transient study governs a power-system resonance.
• Harmonic Parallel-Resonance Order - Why a bigger PF cap bank can land on the 5th harmonic, the check pf-correction never makes: the power-factor capacitors and the source inductance form a parallel LC circuit whose resonant order is h = sqrt(MVA_sc / MVAR_cap). If it lands on a harmonic the nonlinear loads produce (5/7/11/13th), the resonance AMPLIFIES it into destructive overvoltage and current. A 200 MVA bus with a 1.2 MVAR bank resonates at the 12.9th -- near the 13th, so the flag fires; double the bank to 2.4 MVAR and it walks DOWN to the 9.1th, because a bigger bank lowers the order toward the strong low harmonics. Ignores load damping; a detuning reactor or harmonic study is the fix. A screening aid; a harmonic study governs.
• Max PF Capacitor Bank to Keep Resonance Off a Harmonic - The inverse of the harmonic-resonance tile: the largest PF capacitor bank that keeps the parallel-resonance order at or above a target, MVAR_cap = MVA_sc / h^2. A 200-MVA bus targeting an order of 4.7 (to stay below the 5th) caps the bank at ~9.05 MVAR; a bigger bank walks the resonance down onto the 5th. Split into smaller banks or add a detuning reactor for more correction. A screening aid; a harmonic study governs.
• Total Demand Distortion Limit Check (IEEE 519-2022) - The distortion limit that loosens as the supply gets stiffer, the number a utility actually holds you to at the PCC: IEEE 519 limits total demand distortion (harmonic current over the maximum DEMAND load), not THD or a flat 5%. ratio = Isc/IL sets the limit: < 20 -> 5%, 20-50 -> 8%, 50-100 -> 12%, 100-1000 -> 15%, > 1000 -> 20%. Isc 10,000 A / IL 400 A is a ratio of 25 -> 8% limit, so a measured 6% TDD PASSES; on a soft service (Isc 6,000 A -> ratio 15) the limit tightens to 5% and the identical 6% FAILS. The distortion did not change; the supply stiffness did. Even/individual sub-limits also apply. A screening aid; the utility agreement and a measurement study govern.
• Conduit Bends Between Pull Points (360-Degree Rule) - Sums up to six conduit bend angles and checks the NEC 358.26 (and matching Chapter 3 .26) limit of 360 degrees of total bend (four quarter bends) between pull points, with the equivalent quarter-bend count and the verdict to add a pull point. An offset counts both of its bends and a saddle all three; the AHJ governs.
• Shock Approach Boundaries (NFPA 70E Table 130.4) - Looks up the NFPA 70E Table 130.4 AC shock approach boundaries by nominal voltage: the limited approach (separate distances for an exposed movable conductor vs a fixed circuit part) and the restricted approach. Below 50 V no boundary is specified. Shock boundaries only (the arc-flash boundary is separate); the employer's safety program and 70E govern.
• Conduit Jam Ratio for Three Same-Size Conductors (NEC Ch. 9) - Three same-size conductors can wedge in a bend when the conduit ID / conductor OD ratio lands in the ~2.8-3.2 band. Three 0.65 in conductors in 2 in EMT (ID 2.067) -> ratio 3.18, jam-prone; 3.22 is just clear. Jamming needs exactly three conductors. A pull caution, not a code limit; the NEC and AHJ govern.
• Premium Motor Upgrade Energy Savings - The annual energy and dollars a premium-efficiency motor saves over the one it replaces: input kW = HP x 0.746 x load / efficiency, so the saving = (kW at the old efficiency - kW at the new) x run hours x rate. A 50 hp motor at 75% load going 90% -> 94.5% over 4,000 hr at $0.12 saves about $710/yr; at full load the same swap saves about $947, because the fixed efficiency gap acts on more power. Energy charge only; the utility tariff and any rebate change the payback. A screening estimate, not a metered M&V.
• Transformer Loading Efficiency and Losses - The efficiency and losses of a transformer at a given load: output kW = kVA x load x PF, total loss = the fixed no-load (core) loss plus the load^2 x full-load (copper) loss, efficiency = output / (output + loss). A 75 kVA unit with 200 W core and 1,200 W copper loss at 75% load runs 98.47% efficient, with peak efficiency near sqrt(200/1200) = 41% load; a lightly loaded oversized transformer suffers because the core loss becomes a bigger fraction of a small throughput. A design/screening aid; the manufacturer's test report governs.
• Economic Conductor Sizing (I2R Payback) - Whether upsizing a conductor pays for itself in reduced I^2R heat loss: three-phase loss = 3 x I^2 x R, so the annual saving = (loss at the small size - loss at the large) x run hours x rate, and payback = the added copper cost / that saving. A 100 A feeder from 0.20 to 0.125 ohm over 4,000 hr at $0.12 saves $1,080/yr, paying back an $800 upsize in 0.7 years; at 40 A the same upsize saves only $173/yr, a 4.6-year payback -- upsizing only pays on heavily loaded, long-hour feeders. A screening estimate; the code minimum still governs the conductor.
• Generator Fuel Runtime and Backup Duration - How long a standby generator runs on its fuel, the fuel-supply companion to generator-sizing and battery-runtime: runtime = usable fuel / consumption, where usable = tank x usable% (default 90%). A 100 gal tank at 3.0 gph runs 30 hr (1.25 days); for a 72-hour outage design basis it needs 216 gal of fuel and a 240 gal tank, so the 100 gal tank does not meet it. Enter the consumption at load from the genset data plate (a diesel burns ~0.05-0.08 gal/hr per kW at load). Liquid-fuel-tank case; a utility gas feed has no tank limit. A planning aid; the published fuel curve and the AHJ's fuel-storage rules govern.
• Transformer Turns / Voltage / Current / Impedance Ratio - The nameplate ratio the transformer tiles never compute directly: the turns ratio a = Np/Ns equals the voltage ratio Vp/Vs, the inverse current ratio Is/Ip, and the square root of the impedance ratio, so a secondary load Zs reflects to the primary as a^2 x Zs. A 480-to-120 V unit is 4:1; 50 A on the secondary is 12.5 A on the primary, and an 8 ohm load looks like 128 ohm to the source. That a^2 impedance transformation is exactly how a 70 V speaker line or an audio output stage matches a load. Ideal lossless ratio; the winding resistance and leakage reactance that sag real voltage under load are the transformer-voltage-regulation tile. A design aid; the nameplate governs.
• Transformer Voltage Regulation from %R and %X - What the secondary voltage actually does under load, which the loading-efficiency tile never answers: VR% = load x (%R cos + %X sin) + load^2 x (%X cos - %R sin)^2 / 200. The nameplate %Z alone does not give it -- the drop depends on the %R / %X split and the load power factor. With %R 1.2, %X 5.0 at 0.85 lagging, full load, the secondary sags +3.72% from no-load to full-load; make the same 0.85 power factor LEADING (a PV-exporting or over-corrected bus) and the voltage RISES -1.50% above nominal, tripping over-voltage relays. Returns the signed regulation so both the sag and the rise are visible -- the number the tap changer is set from. Terminal regulation, not the feeder drop; the utility's voltage study governs.
• Capacitor Discharge Time and Bleed Resistor (NEC 460.6) - Sizes the bleed resistor that keeps a switched-off power-factor or DC-bus capacitor from staying lethal: NEC 460.6 requires the residual voltage to fall to 50 V within 1 minute at or below 600 V (5 minutes above 600 V). V(t) = V0 e^(-t/RC), so R_max = t_limit / (C ln(V0/50)) and the continuous burn is V0^2/R. A 100 uF, 600 V cap needs a 241 kohm-or-smaller resistor, dissipating 1.49 W -- a permanently connected 220 kohm 2 W resistor does it. A 1 uF, 4160 V surge cap gets the 5-minute allowance, so 67.9 Mohm at 0.26 W suffices. The discharge means must be permanent or automatic on loss of line -- a manually switched bleed does not comply. A design aid; the equipment listing governs.
• Asymmetrical and Peak Fault Current from X/R - The first-cycle fault current the symmetrical value hides: a DC offset rides the AC wave, sized by the circuit X/R ratio. I_peak = sqrt(2) x I_sym x (1 + e^(-pi/(X/R))) and the asymmetrical RMS multiplier = sqrt(1 + 2 e^(-2 pi/(X/R))). At 20 kA symmetrical, X/R 15 (a stiff service near a large transformer) the first peak is 51.2 kA (2.56x) and the asymmetrical RMS 30.4 kA (1.52x) -- a bus braced only for 20 kA is badly under-rated; at X/R 5 the DC decays faster, so 43.4 kA peak and 25.1 kA RMS. A device's peak-withstand and bus bracing must survive the asymmetrical first-cycle, not the symmetrical RMS. A design aid; the interrupting-duty rating and coordination study govern.
• Battery Room Hydrogen Ventilation (IEEE 1635) - The cells-not-jars exhaust rate that keeps a battery room under the LEL: charging vented lead-acid/flooded cells liberate hydrogen, and IEEE 1635 sets Q = 0.054 x I x N cfm to hold the room average below 1% (a 75% margin under the 4% explosive limit). The catch that undersizes real rooms is the formula counts individual 2 V CELLS, not jars -- a 12 V jar is six 2 V cells, so twenty-four 12 V jars is 144 cells, not 24. A 24-cell string at 20 A needs 25.9 cfm (1.9 ACH in an 800 ft^3 room); counted as jars (144 cells) it is really 155.5 cfm, six times the airflow. Sealed VRLA in float gasses far less. A design aid; the applicable code and room design govern.
• Battery Room Max Charge Current from Available Airflow - The inverse of the battery-hydrogen-vent tile: the highest maximum charge current a room's exhaust can safely support, I_max = available_cfm / (0.054 x N) (IEEE 1635), where N is the number of individual 2 V CELLS, not jars. An exhaust of 100 cfm over a 24-cell string supports 77 A; counted as 144 cells (twenty-four 12 V jars) it is only 12.9 A, so mistaking jars for cells overstates the safe current six-fold. Answers 'how much charge current can my fan handle' instead of sizing the fan. A design aid; the applicable code and room design govern.
• Transformer Inrush Coordination Point - Why a code-legal primary device still trips on energization: a device meeting the NEC 450.3 percentage limits can still nuisance-trip on the magnetizing inrush. Energized at an unfavorable point on the wave, the core saturates and draws 8-12x FLA (up to ~25x in the first sub-cycle), decaying over a few cycles. FLA = kVA x 1000 / (sqrt(3) x V); inrush point = multiple x FLA at the stated time. A 75 kVA, 480 V transformer draws 90.2 A FLA, so the 12x inrush point is 1,083 A at 0.1 s (and 2,255 A at 0.01 s) -- the primary device's curve must sit RIGHT of that point and LEFT of the damage curve, or it trips every energization. A design aid; the manufacturer's inrush data and a coordination study govern.
• Termination Temperature Ampacity Limit (NEC 110.14(C)) - The NEC 110.14(C) termination rule wire-ampacity leaves out: the usable ampacity is the LESSER of the lowest-rated termination column (60 or 75 C) and the derated 90 C value. The 90 C column is for the ambient/fill derating math only -- it never reaches the terminals. Circuits <= 100 A default to 60 C unless listed 75 C; over 100 A use 75 C.
• Swimming-Pool Equipotential Bonding Checklist (NEC 680.26) - Returns the NEC 680.26(B) equipotential-bonding component list by pool type (the pool shell/rebar, the 3 ft perimeter, underwater forming shells, metal fittings 1 in and larger, the pump motor, metal piping within 5 ft, and the listed water bond), with the #8 AWG solid copper minimum and irreversible connections. A reference checklist; the AHJ governs the inspection.