Motor Control Tools

Copper Loss (I²R)

Calculate three-phase winding copper loss from RMS phase current and phase resistance.

Current convention
A
Ω

Assumption

Assumes three balanced phases with equal resistance and equal RMS current — no star/delta connection assumption is needed for the per-phase figure, since it uses the actual winding current and resistance directly.

Total three-phase copper loss51.84W
Per-phase copper loss17.28W

Formula

Three-phase copper loss

Pcu,phase = Irms² · Rphase Pcu,total = 3 · Pcu,phase

Pcu,phase
Per-phase copper (I²R) loss [W]
Pcu,total
Total three-phase copper loss [W]
Irms
RMS current through that phase winding [A]
Rphase
That phase's winding resistance [Ω]

Copper loss depends on RMS current only — a peak-current input is converted to RMS (÷√2, sinusoidal waveform assumed) before applying I²R. The ×3 total assumes three balanced phases with equal resistance and current; no star/delta connection assumption is required for the per-phase figure itself.

Why RMS, not peak

Copper loss is real dissipated power, so it only depends on the RMS value of the current waveform — peak current briefly heats the winding more, but RMS is what determines the average I²R loss over a full electrical cycle. Using a peak current value directly in I²R overstates loss by a factor of 2 (since Ipeak² = 2 · Irms² for a sinusoid), which is why this calculator converts a peak input to RMS before computing anything.

Worked example

A motor draws 12 A RMS per phase with a phase resistance of 0.12 Ω:

  • Per-phase loss: 12² × 0.12 = 17.28 W
  • Total three-phase loss: 3 × 17.28 = 51.84 W

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