Three-phase power calculator

The power of a three-phase load comes from the line-to-line voltage, the current and the power factor. Use it to find out how many kW a machine draws by measuring the amps with a clamp meter, to choose a transformer or a generator (rated in kVA), or to know how much current a heater or an oven will draw. Enter the current to get the power, or the power to get the amps.

Supply Voltage (V) Current (A) Active power (kW) Power factor (cos φ)

The formulas

Power	Three-phase	Single-phase
Active P (kW)	P = √3 × V × I × PF	P = V × I × PF
Apparent S (kVA)	S = √3 × V × I	S = V × I
Reactive Q (kVAR)	Q = √3 × V × I × sin φ	Q = V × I × sin φ
Current I (A)	I = P / (√3 × V × PF)	I = P / (V × PF)

In three-phase, V is the line-to-line voltage (400 V in Europe; 480 V or 208 V in North America) and I is the current in each line. The formulas apply to balanced loads such as motors, ovens and three-phase heaters, and give the same result whether the load is connected in star (wye) or delta.

Example

A machine on a 400 V supply draws 10 A per phase with a power factor of 0.85:

Apparent power: 1.732 × 400 × 10 = 6928 VA, about 6.9 kVA.
Active power: 6.93 × 0.85 = 5.89 kW.
Reactive power: 6.93 × 0.53 = 3.65 kVAR (the sine of φ when the cosine is 0.85).

And the other way round: an 11 kW resistance oven at 400 V (power factor 1, because it is a resistive load) draws 11000 / (1.732 × 400) ≈ 15.9 A per phase. On a 480 V supply the same oven would draw about 13.2 A.

kW, kVA and kVAR: what each one means

Active (kW): the power turned into work or heat. It is what you pay for on the bill.
Apparent (kVA): what cables, transformers and generators have to carry, because it depends on the total current. That is why that equipment is rated in kVA.
Reactive (kVAR): what motors and ballasts need to build their magnetic field. It flows back and forth without doing work, but it loads the installation. It is compensated with capacitor banks.

For motors, use the motor calculatorA motor’s nameplate power is what it delivers at the shaft, not what it takes from the supply: to go from kW to amps you also need its efficiency. Use the motor current calculator.

Typical mistakeUsing the line-to-neutral voltage (230 V, or 277 V on a 480 V system) in the three-phase formula with √3. For the example you would get 1.732 × 230 × 10 × 0.85 = 3.39 kW instead of 5.89 kW. With √3 you use the line-to-line voltage; with the line-to-neutral voltage, multiply by 3 instead of √3.

To understand the topic in depth: Practical electrical theory, with theory and a practice test.

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