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.
Example
You enter
- Real power (kW; blank if unknown) 100
- Power factor (0-1; blank if unknown) 0.8
- Reactive sign lagging
You get
- Apparent power (kVA) 125
- Kvar 75
- Power factor 0.8
- Phase angle (deg) 36.87
Checked against published worked examples from: IEEE.
Details, formula, and sources
ScopeSolve the full AC power triangle from any two of real power, apparent power, reactive power, power factor, or phase angle, with a phasor diagram.
Formula or tablekVA^2 = kW^2 + kVAR^2; PF = kW / kVA; theta = arccos(PF). Any two of kW / kVA / kVAR / PF / angle fix the triangle, provided at least one is a magnitude.
Source and editionIEEE 1459 (Definitions for the Measurement of Electric Power Quantities). Sinusoidal-case algebra.
Free accessstandards.ieee.org for the IEEE 1459 abstract.
What governsEstimate. AHJ and licensed electrician govern. Verify against the NEC edition adopted in your jurisdiction.
API field nameskw, pf, sign, kva, kvar, angle_deg
- Sinusoidal system the classic power triangle applies to sinusoidal voltage and current; non-sinusoidal systems add a distortion-power termIEEE 1459
- Reactive sign lagging (inductive) reactive power is drawn by motors and shown positive (IEEE 1459); leading (capacitive) by over-correction, shown negativefirst-principles AC theory