Transformer K-Factor (Harmonics)
Calculates a transformer's K-factor per ANSI/IEEE C57.110: the sum of squared harmonic currents weighted by the squared harmonic order, divided by the sum of squared currents. A purely sinusoidal load gives K equal to one; you pick the commercial class immediately above the computed value. Enter the fundamental and the odd harmonics up to the 13th.
Result
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Why a transformer cooks with no overload on the meter
The transformer draws less than rated rms current, the breaker stays quiet, and the winding still runs past its thermal class. Harmonics are usually behind it: electronic loads pull distorted current, and eddy current loss in the conductors climbs with the square of frequency, so a 13th order component heats one hundred and sixty-nine times harder than a fundamental of matching amplitude. The K-factor turns a measured spectrum into a purchasing requirement, and anyone feeding a data centre, an inverter room, an LED bank or a drive lineup needs it before the order goes out.
Per ANSI/IEEE C57.110, K = Σ(Ih² × h²) ÷ Σ(Ih²), with h over the odd orders 1 through 13. Ih is the rms current at each order and h the order. Numerator and denominator carry the same dimension, so scale drops out: amperes, per unit values or percent of fundamental all work, as long as every entry shares one base. A purely sinusoidal load returns exactly 1. The spectrum on screen — 100, 33, 20, 14, 11, 9 and 7 A — returns 5.637, which pushes the specification to the next commercial class up, K-13. Common classes run K-4 for mixed load, K-13 for offices and schools thick with electronics, and K-20 for data centres; UL 1561 also lists K-9, K-30, K-40 and K-50.
The standard normalises harmonic currents against the rated current of the transformer, not against the measured sum. This page uses the sum you enter, so the value shown belongs to that waveform at full load: a unit running below nameplate suffers less than the number implies. The sum stops at the 13th order, so content between the 15th and the 25th comes out understated, where the squared weighting bites hardest. Mind the name too: the European factor K of HD 538.3.1 is a different quantity, a derating multiplier between 1 and 2. And 3rd and 9th order currents circulate inside a delta winding, so a primary reading on a delta-wye unit differs from a secondary one.
Frequently asked questions
Does a result of 5.637 call for a K-6 transformer?
Can I enter the harmonics as a percent of the fundamental?
When does the calculator refuse the values entered?
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