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