Three-Phase Power Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
Three-phase power is calculated with P = √3 × U × I × cos φ for real power, and S = √3 × U × I for apparent power. For 400 V, 10 A, and a power factor of 0.8, the real power is about 5.54 kW, for an apparent power of about 6.93 kVA.
Explanation
A three-phase circuit carries electricity over three phases offset from each other, which explains the √3 factor (about 1.732) absent from the equivalent single-phase formula (see our electrical power calculator for the single-phase case, P = U × I). Apparent power S (in kVA) represents the total power carried by the grid, while real power P (in kW) is the share actually converted into useful work (motion, heat, light): the gap between the two is captured by the power factor cos φ, which reflects the phase shift between voltage and current introduced by inductive (motors, transformers) or capacitive loads. A cos φ close to 1 (a purely resistive load, like an electric heater) means almost all the apparent power is useful; a lower cos φ (a lightly loaded induction motor, old fluorescent lighting) means a significant share of the power carried by the grid does no useful work at all, which leads electricity suppliers to charge a penalty to large industrial consumers whose power factor is too low. The voltage used here is the line-to-line voltage (between two phases, 400 V for low voltage in France), not to be confused with the line-to-neutral voltage (230 V) — this same voltage-current relationship, per Ohm's law, is what our Ohm's law calculator covers for a simple single-phase resistive circuit.
Example: 400 V, 10 A, cos φ = 0.8
Inputs
Line-to-line voltage: 400 V. Line current: 10 A. Power factor: 0.8.
Calculation
Apparent power = √3 × 400 × 10 ÷ 1000 ≈ 6.93 kVA. Real power = 6.93 × 0.8 ≈ 5.54 kW.
Result
This installation draws about 6.93 kVA of apparent power, of which about 5.54 kW is actually real power.
Frequently asked questions
What is the difference between apparent power (kVA) and real power (kW)?
Apparent power is the total power carried by the electrical grid, while real power is the share actually converted into useful work by the device (motion, heat, light). The ratio between the two is the power factor (cos φ): the closer it is to 1, the more efficiently the power carried is used.
Where does the √3 factor in the three-phase formula come from?
It comes from the 120° phase shift between the three phases of a balanced three-phase system: the mathematical combination of the three instantaneous powers, once simplified in steady state, produces this √3 factor (about 1.732) between the line-to-line voltage, the line current, and the system's total power.
Why can a low power factor cost more?
A low power factor forces the electrical grid to carry a higher current to deliver the same useful real power, which increases line losses and puts more strain on infrastructure. That's why many suppliers charge a penalty to industrial customers whose power factor drops below a contractual threshold (often around 0.9), which encourages them to install capacitor banks to raise it.