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}

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

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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)