How this calculation works
Every one of these uses line-to-line voltage. On a 208Y/120 system that is 208, not 120. Plugging in the phase voltage is the most common way these come out wrong by a factor of 1.732.
kW versus kVA, and why the difference matters
kW is real power — the part that does work and shows up on the bill. kVA is apparent power — the total the system has to carry, including the reactive current that sloshes back and forth without doing anything useful.
Power factor is the ratio between them. Resistive loads like heaters and incandescent lighting are close to 1.0. Motors run 0.8 to 0.9. Lightly loaded motors and older fluorescent ballasts go lower.
The practical consequence: size conductors and overcurrent devices from the amps, never from the kW. A 100 kW load at 0.8 power factor draws the same current as a 125 kW load at unity. The wire does not care how much of that current is doing useful work.
Where transformers and utilities come in
Transformers are rated in kVA, not kW, for exactly this reason — the winding heats from total current regardless of phase angle. Utilities meter kW but bill demand in kVA or apply a power factor penalty, which is why large industrial customers install capacitor banks to pull their power factor back toward unity.
Wye and delta
On a wye system, line-to-neutral voltage is line-to-line divided by 1.732. That is where 120 comes from on a 208 system, and 277 from a 480. Line current equals phase current. On a delta, line voltage equals phase voltage but line current is 1.732 times phase current. The power formula above is the same either way, which is the useful part.
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Frequently asked questions
Do I use line-to-line or line-to-neutral voltage?
Line-to-line, every time. On a 208Y/120 system that is 208. On a 480Y/277 system that is 480. Using the phase voltage in the three-phase formula is the single most common error and it puts your answer off by a factor of 1.732.
Why 1.732?
It is the square root of 3. The three phase currents peak 120 electrical degrees apart, so they never all reach maximum together. The vector sum of three phases separated that way works out to √3 times a single phase, not 3 times.
Should I size wire from kW or from amps?
Amps, always. Conductors heat from current, and current depends on power factor. A load stated in kW at 0.8 power factor draws 25% more current than the same kW at unity. Convert to amps first, then size.
What power factor should I assume?
Use the nameplate when you have it. Absent that, 0.85 to 0.9 is reasonable for a general motor load, 0.9 to 0.95 for mixed commercial, and 1.0 for purely resistive heating. Guessing high is the dangerous direction — it understates the current.
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