AC power
Balanced three-phase apparent power
- where
- apparent power (VA)
- line-to-line RMS voltage (V)
- line RMS current (A)
Explain this equation
Gives the total apparent power, in VA, of a balanced three-phase load. Use it to check loading on a transformer, generator or supply, which are rated in kVA.
V_L is the line-to-line RMS voltage and I_L the line current. The √3 links line and phase quantities: in a star system the line voltage is √3 times the phase voltage, so √3 × V_L × I_L equals three phases each carrying V_ph × I_ph.
Power factor is left out because windings and cables heat according to the current they carry, whatever its phase.
400 V at 10 A gives about 6.9 kVA. Turned around, a 100 kVA transformer at 400 V carries about 144 A per line at full load (100,000 ÷ (1.732 × 400)).
Watch out: work in VA, not kVA, and use line-to-line voltage. This is a steady-state figure; starting currents and harmonics need separate checks.
A transformer or balanced three-phase load can be described in kVA. This equation calculates the apparent power associated with its line voltage and current.
To estimate rated line current from kVA, multiply kVA by 1000 and divide by √3 × V_L. This is a steady-state calculation, not a protective-device selection.
Enter your values to see the result.
Common mistake
Do not insert kVA directly when the formula expects VA.
Limits
Balanced sinusoidal three-phase conditions. Equipment overload, harmonics, starting and ambient ratings require separate checks.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.