Three-Phase Power Calculator
Real, apparent and reactive power (kW, kVA, kvar) of a balanced three-phase load from voltage, current and power factor, or the current a load draws, for star or delta.
Result…
How it's calculated
Apparent power S = √3 × V_L × I_L Real power P = √3 × V_L × I_L × PF Reactive power Q = √(S² − P²) = S × sin φ I_L = P ÷ (√3 × V_L × PF) Star: V_L = √3 × V_phase, I_L = I_phase Delta: V_L = V_phase, I_L = √3 × I_phase
In a balanced three-phase system each phase carries a third of the power. Written with the line voltage V_L (between any two lines) and the line current I_L, the total apparent power is √3 × V_L × I_L, whether the load is connected in star or delta. The power factor, cos φ, is the share of that which does real work, in kW; the rest is reactive power, in kvar, which flows back and forth. The connection only changes how line and phase values relate: in star the phase voltage is V_L ÷ √3 and the currents are equal; in delta the voltages are equal and the phase current is I_L ÷ √3.
Your numbers, step by step
About the Three-Phase Power calculator
This three-phase power calculator gives the real power in kW, the apparent power in kVA and the reactive power in kvar of a balanced three-phase load, from the voltage, the line current and the power factor. It also works backwards: enter a load in kW or kVA and it gives the current each line carries. Choose star (wye) or delta and whether your voltage is the line voltage or the phase voltage, and it shows both, with the phase current and the power in each phase. Electricians, engineers and students use it to size supplies, compare motors and read nameplates, and it works with any supply voltage, whether 400 V, 415 V, 480 V or another. The steps show the √3 factor and each multiplication, so the working is easy to check against a textbook or a meter reading.
How to use it
- Choose what to “Find”: “Power from current” or “Current from power”.
- Pick the “Connection”, “Star (wye)” or “Delta”, and say whether the “Voltage given” is the line voltage or the phase voltage.
- Enter the “Voltage” in volts and either the “Line current” in amps or the “Power” with its “Power unit” (kW, W or kVA).
- Enter the “Power factor” from 0 to 1, from the nameplate or a power meter.
- Read kW, kVA, kvar, the line and phase voltages and currents.
Worked example
A star-connected load on 400 V line voltage draws 32 A at a power factor of 0.85. Apparent power S = √3 × 400 × 32 = 22,170 VA, or 22.17 kVA. Real power P = 22.17 × 0.85 = 18.84 kW, and reactive power Q = 22.17 × √(1 − 0.85²) = 11.68 kvar. The phase voltage is 400 ÷ √3 = 230.9 V. The other way round, a 15 kW load at the same voltage and power factor draws 15,000 ÷ (√3 × 400 × 0.85) = 25.47 A per line.
Updated
Questions people ask
How do I calculate three-phase power?
Multiply √3 (1.732) by the line voltage, the line current and the power factor: P = √3 × V_L × I × PF. Leaving out the power factor gives the apparent power in VA.
How do I work out the current of a three-phase load from kW?
Divide the power in watts by √3 × line voltage × power factor. A 15 kW load at 400 V and 0.85 power factor draws about 25.5 A per line. The phase voltage ÷ the phase current then gives each branch's impedance, as in the Ohm's law calculator.
What is the difference between kW, kVA and kvar?
kW is the real power that does work, kVA is the total the supply must deliver, and kvar is the reactive part that flows back and forth. They form a right triangle: kVA² = kW² + kvar².
Does star or delta change the power?
Not when you use line voltage and line current: the formula is the same. The connection changes how phase values relate to line values. In star the phase voltage is the line voltage ÷ √3; in delta the phase current is the line current ÷ √3.
What is a common mistake with three-phase calculations?
Multiplying the phase voltage by √3 again, or using 3 instead of √3 with line values. For single-phase circuits use the electrical power calculator instead.
Can I size cables or breakers from this?
No. It gives power and current only. Cable sizes, breakers and installation depend on local wiring rules, length and conditions, so ask a qualified electrician.