Non-linear loads such as variable-frequency drives, UPS systems, and switching power supplies draw current rich in harmonics. Those harmonics cause extra eddy-current heating in a transformer’s windings, and because the loss scales with the square of frequency, high-order harmonics are far more damaging than their amplitude alone suggests. The K-factor quantifies this so you can specify a transformer built to handle it.
How the K-factor is computed
The K-factor weights each harmonic current by the square of its order:
Σ ( I_h^2 × h^2 )
K-factor = -----------------
Σ ( I_h^2 )Here I_h is the RMS current of harmonic order h and the sum runs over every
harmonic present. The denominator is the total RMS-squared current, so the
result is independent of whether you enter amps or percent of fundamental. A
purely linear load (only the fundamental) gives a K-factor of exactly 1.0.
Selecting the rating
Transformers are manufactured in standard K-ratings: K-1, K-4, K-9, K-13, K-20, K-30, K-40, and K-50. The tool rounds the computed K-factor up to the next standard rating. For example, a spectrum that computes to 7.2 calls for a K-9 transformer.
Worked example: six-pulse VFD load
A typical six-pulse variable-frequency drive without a line reactor produces a harmonic current spectrum dominated by the fifth and seventh orders. For illustration, suppose a power-quality meter reads:
| Harmonic order (h) | I_h (% of fundamental) |
|---|---|
| 1 (fundamental) | 100% |
| 5 | 38% |
| 7 | 14% |
| 11 | 9% |
| 13 | 7% |
| 17 | 4% |
| 19 | 3% |
Plugging into the formula:
Numerator = 1²×100² + 5²×38² + 7²×14² + 11²×9² + 13²×7² + 17²×4² + 19²×3²
= 10000 + 36100 + 9604 + 9801 + 8281 + 4624 + 3249 = 81659
Denominator = 100² + 38² + 14² + 9² + 7² + 4² + 3²
= 10000 + 1444 + 196 + 81 + 49 + 16 + 9 = 11795
K-factor ≈ 81659 / 11795 ≈ 6.9That rounds up to a K-9 transformer. Adding a 3% line reactor to the same drive would cut the fifth-harmonic current roughly in half, pulling the K-factor down toward 4 and allowing a less expensive K-4 unit.
Typical K-factors by load type
Use these as sanity checks against a computed value — a spectrum that lands far outside the expected band for its load type usually means a measurement or data-entry error:
| Load type | Typical K-factor | Common transformer choice |
|---|---|---|
| Purely resistive (heaters, incandescent) | 1.0 | K-1 (standard) |
| Motors, mixed commercial | 1–4 | K-1 to K-4 |
| Six-pulse VFDs with line reactors | 4–9 | K-4 to K-9 |
| Six-pulse VFDs without reactors | 9–13 | K-13 |
| Data centres, heavy switch-mode / UPS | 13–20 | K-13 to K-20 |
| Extreme: welders, arc loads, dense electronics | 20–50 | K-20 to K-50 |
The K-factor is bounded below by 1 (a linear load) and rises with both the magnitude and the order of the harmonics present, because the h² weighting punishes high-order content. This is why two loads with the same total harmonic distortion (THD) can have very different K-factors: a load whose distortion sits mostly at the 3rd harmonic is far gentler on a transformer than one with the same THD concentrated at the 25th.
What affects the result
Drive topology — six-pulse drives without reactors are the most harmonic-rich; twelve-pulse or active-front-end drives can cut the K-factor dramatically.
Line reactors and DC bus chokes — even a modest 3% impedance reactor can reduce the fifth and seventh harmonic currents enough to drop the K-rating by one tier.
Load mix — a transformer supplying a mix of non-linear and linear loads will see a blended spectrum. Measure the total load current at the transformer secondary for the most accurate K-factor, rather than summing individual load spectra.
Power-quality meter resolution — most meters report to the 25th or 50th harmonic; higher orders contribute very little weight because their amplitudes decay faster than h² grows for most practical loads.
Common mistakes
- Using nameplate kVA instead of measuring — a transformer may be rated K-4 but running in a K-13 environment because the load mix was not assessed at commissioning.
- Forgetting the handling shrink — some engineers compute K-factor but forget to derate the transformer kVA for elevated ambient temperature or altitude.
- Treating K-factor as a derating multiplier — it is a selection index, not a ratio to divide by. A K-9 transformer is wound to handle the eddy-current losses corresponding to a K-factor of 9; it does not derate to 1/9 of its nameplate kVA.
When a full IEEE C57.110 study is required
The K-factor gives you a transformer selection, but IEEE C57.110 also defines a harmonic loss factor (FHL) approach for evaluating whether an existing transformer can safely carry a new non-linear load. That method accounts for the actual winding geometry and eddy-loss coefficient. Use this calculator for upfront specification; engage a power-quality engineer or transformer manufacturer for retrofit assessments on existing equipment.
Sources and references
- IEEE C57.110 — Recommended Practice for Establishing Liquid-Filled and Dry-Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal Load Currents — the K-factor and harmonic-loss-factor methods
- UL 1561 — Dry-Type General Purpose and Power Transformers (K-rating labelling) — the standard K-1…K-50 ratings
- IEEE 519 — Harmonic Control in Electric Power Systems — harmonic limits and measurement context
Maintained by the Gera Tools editorial team. K-factor = Σ(I_h²·h²) ÷ Σ(I_h²); the result is a transformer selection index rounded up to the next standard rating, not a kVA derating multiplier. For an existing transformer, use the C57.110 FHL method with an engineer. Last reviewed 2026-07-02.