Engineering CalculatorsMotor Winding / AC Copper LossWork in progress
DC and AC-inflated copper loss for a motor stator winding — round magnet wire, flat/hairpin conductors, or litz wire — from skin and proximity effect (Dowell's equation and Sullivan & Zhang's closed-form litz/round-wire method). Pairs with the Skin Depth and MOSFET Loss calculators.
Work in progress: this calculator is still being validated and refined — treat its results as indicative and cross-check anything design-critical against FEA or measurement. It also does not yet model circulating currents between parallel winding paths (a separate calculator is planned for that).
New to Winding AC Resistance (Dowell 1966 / Sullivan & Zhang 2014)? Read the guide: Motor Winding AC Copper Loss: Skin Effect, Proximity Effect and Dowell's Equation — a plain-language explainer of the standard behind this calculator.
DC resistance R_dc = ρ(T)·MLT·N/(A_strand·n_parallel), reusing this site's copper resistivity and temperature-correction data. AC resistance is R_ac = F_R·R_dc, where F_R comes from one of two closed-form kernels depending on wire type: Sullivan & Zhang's single-term proximity formula (round wire and litz — the small-Δ limit of Dowell's equation, and litz's standard closed form), or Dowell's classical m-layer foil-winding equation (flat/hairpin conductors directly, and round wire in the Premium "full Dowell" mode via an equivalent-foil conversion). "Layers in slot" (m) counts distinct radial conductor positions across the slot depth — the field-build direction that drives proximity loss; conductors side-by-side at the same position add DC copper area only. The model assumes every conductor in the slot carries equal series current — circulating currents between parallel winding paths, a real and sometimes dominant AC loss mechanism in badly-transposed hairpin windings, are not modelled and require FEA. Litz wire's bundle-level construction check flags when the strand count exceeds what a single twisting operation can safely combine — beyond that, real AC resistance will exceed the ideal value shown. Verify against FEA or measurement before finalizing a design.
Validated: the Dowell kernel reproduces its own known asymptotic limits exactly (F_R→1 as Δ→0; F_R→Δ·(1+⅔(m²−1)) at large Δ), and a hand-worked hairpin example (2.0 mm conductor height, 400 Hz, 20°C → Δ=0.606) reproduces published-literature figures of F_R≈1.01 at a single layer and F_R≈1.24 at four layers. The round-wire Sullivan and Dowell kernels are cross-validated against each other — they agree to within 0.1% at low Δ across 1-8 layers, confirming Sullivan's formula as the correct small-Δ limit of Dowell's equation for this project's layer-count convention.