AllMyCalculators

Three-Phase Power Calculator

Power in a balanced three-phase system from the line voltage, line current and power factor.

V

400 V in most of the world, 208 V or 480 V in North America. This is the voltage between any two phases.

A
Real power
kW

Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.

Apparent power kVA
Reactive power kVAR
Phase-to-neutral voltage V
Real power per phase kW
Reading this

The formula

S = √3 × V_line × I_line P = S × PF V_phase = V_line ÷ √3

The √3 appears because the three phases are 120° apart, so the line-to-line voltage is √3 times the phase-to-neutral voltage rather than twice it. Every three-phase formula either has a √3 in it or has already absorbed one.

What to watch out for

Two voltages exist in the same system and confusing them is the usual error:

  • Line-to-line is measured between any two phases — 400 V in a typical European supply.
  • Phase-to-neutral is one phase against neutral — 230 V in the same system, because 400 ÷ √3 is 231.

These formulas assume a balanced load, meaning all three phases draw the same current. An unbalanced load has to be worked out phase by phase, and it puts current in the neutral that a balanced system does not.

Frequently Asked Questions

What is the formula for three-phase power?

P = √3 × line voltage × line current × power factor. At 400 V and 20 A with a power factor of 0.85, that is about 11.8 kW.

Why is there a √3 in three-phase calculations?

Because the phases are 120° apart. Adding two phase voltages that are 120° out of step gives √3 times one of them, not two times — so the line-to-line voltage is 1.732 times the phase voltage.

Why is 400 V three-phase also 230 V?

They are the same supply measured differently. 400 V is between two phases; 230 V is one phase to neutral. 400 ÷ √3 = 231, which is where the domestic voltage comes from.