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Three-Phase Apparent Power

Also known as FLA from kVA · transformer full-load current · transformer secondary amps · rated current · kVA to amps · nameplate current

S=3 VLILS = \sqrt{3} \, V_{L} I_{L}
sig figs

Worked example: 208 V, 50 A → 18.01 kVA. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
3=1.7320508075688772\sqrt{3} = 1.7320508075688772Square Root of Three · exact

Where Three-Phase Apparent Power fits

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Your answer feeds
Power Factor from Real and Apparent PowerReactive Power (Power Triangle)Transformer Efficiency from Core and Copper LossesTransformer Percent-Impedance Voltage Drop
In this toolkit

See also

Three-Phase Motor Full-Load Current: Both use line-to-line voltage and line current.Transformer Full-Load Current: Both use apparent power and line current.Available Short-Circuit Current from Percent Impedance: Both use line current.Motor Locked-Rotor Starting Current: Both use line-to-line voltage.Three-Phase Real Power: Both use line-to-line voltage.Wye Line and Phase Voltage: Both use line-to-line voltage.
4 more relatedPower Factor from Real and Apparent Power: Both use apparent power.Reactive Power (Power Triangle): Both use apparent power.Transformer Percent-Impedance Voltage Drop: Both use apparent power.Transformer Efficiency from Core and Copper Losses: Both use apparent power.
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Three-Phase Apparent Power explained

SVLIL

Apparent power is the product the copper actually feels: every amp heats the conductor whether or not it is in phase with the voltage. Volt-amperes and watts have identical dimensions (this solver's watt fields double as volt-amperes, and kW as kVA) but tradition keeps the names separate to remind you that S ≥ P always. A 208 V panel drawing 50 A per line is handling 1.732 × 208 × 50 ≈ 18 kVA regardless of what the loads are doing.

This is the number on a transformer's nameplate, and the reason it is: the transformer's limits are its winding heat (amps) and its core saturation (volts), neither of which knows anything about power factor. To size a service, work in kVA; to size a bill or a generator's engine, work in kW. Drop the √3 for single-phase and the formula is just S = VI.

Three-Phase Apparent Power formula

S=3 VLILS = \sqrt{3} \, V_{L} I_{L}
Where
  • SS= Apparent power (VA) (W)
  • VLV_{L}= Line-to-line voltage (V)
  • ILI_{L}= Line current (A)
In this toolkit

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.

Revised 16 October 2026
Cite this page

formula.expert. (2026, October 16). Three-Phase Apparent Power Formula & Calculator. https://formula.expert/solvers/apparent-power-three-phase

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