Steel Tape Distance Corrections (Temperature, Slope, Tension, Sag)
The difference between a rough measurement and survey-grade distance: a steel tape's corrected length is the measured value plus four corrections - temperature Ct = alpha (T - T0) L (alpha 6.45e-6 /degF), slope Ch = -h^2/(2L), tension Cp = (P - P0) L/(A E), and sag Cs = -w^2 L^3/(24 P^2). A 100 ft tape read at 95 F down a 3 ft grade corrects to 99.972 ft (warm tape reads short, +0.017; slope -0.045); a cold tape flips the temperature sign. The systematic bias a warm-day traverse carries throughout. A computational aid; the tape calibration governs.
Formula and source
Ct = alpha (T - T0) L; Ch = -h^2/(2L); Cp = (P - P0) L/(A E); Cs = -w^2 L^3/(24 P^2); corrected = L + Ct + Ch + Cp + Cs. (alpha = 6.45e-6 /degF)
The four steel-tape distance corrections (temperature, slope, tension, sag) added to the measured length, as compiled in the standard surveying references (Ghilani/Wolf), by name.
Audience
This tile is built for trades and the adjacent professions in the Field, Backcountry, and SAR group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.