Three-Phase Power Calculator

Real power (kW), apparent power (kVA) and reactive power (kVAR) of a balanced three-phase load from line voltage, current and power factor.

V
Average of the three line-to-line readings, e.g. 208, 400, 480 V.
A
Average of the three phase currents.
Between 0 and 1 (cos φ). Use 1 for purely resistive loads.
Real power P
22.97
Apparent power S
30.10 kVA
Reactive power Q
19.46 kVAR
Line-to-neutral voltage (wye)
271.2 V

Estimate generated with SortedSums: https://sortedsums.com/three-phase-power-calculator/. For informational purposes only; verify before relying on it.

Estimate only. This tool is for informational and educational purposes. Results depend on your inputs and simplifying assumptions, and are not a substitute for professional engineering, design or financial advice. Always verify with a qualified professional and applicable codes before purchasing, building or making decisions.

How it’s calculated

For a balanced three-phase load, real power is √3 times line-to-line voltage times line current times power factor. Apparent power omits the power factor, and reactive power makes up the rest of the power triangle. Assumes balanced, sinusoidal voltages and currents (use averages of the three phases for slightly unbalanced loads).

P (W) = √3 × V_LL × I × PF S (VA) = √3 × V_LL × I Q (VAR) = √(S² − P²) I = P / (√3 × V_LL × PF)

Example (U.S. DOE motor fact sheet): measured averages of 469.7 V, 37 A and PF 0.763 give P = 469.7 × 37 × 0.763 × √3 ÷ 1000 = 22.9 kW input to the motor.

The √3 appears because the line-to-line voltage of a three-phase system is √3 times the line-to-neutral voltage (e.g. 120 V phase, 208 V line).

Frequently asked questions

Why multiply by √3 and not 3?

Three phases each deliver V_LN × I × PF, so P = 3 × V_LN × I × PF. Because V_LN = V_LL / √3, this equals √3 × V_LL × I × PF.

What is the difference between kW and kVA?

kW is real power that does work; kVA is the product of voltage and current. Their ratio is the power factor. Transformers and generators are rated in kVA.

How many amps does a 10 kW three-phase load draw at 400 V?

At PF 1: 10,000 ÷ (1.732 × 400) ≈ 14.4 A per line. At PF 0.8 it rises to about 18 A.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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