Three-Phase Power Calculator
kW, kVA, kVAR and amps for three-phase or single-phase, with power factor correction and the line-to-line voltage trap made explicit.
The voltage is line to line, and kW is not kVA
On a 277/480 V system the number is 480. On 120/208 it is 208. The √3 in the formula already accounts for the phase relationship between conductors, so feeding it the line-to-neutral figure applies the correction twice and lands you 42% low. This is the commonest arithmetic error in the subject and it produces an answer that looks entirely reasonable.
Generators, transformers and UPSs are rated in kVA because their limit is current and they have no idea what power factor you will present them with. Size one from a kW figure at 0.8 power factor and you have undersized it by a quarter. The plate says kVA for a reason.
- Reactive power is not wasted power. It flows out and back rather than being consumed, which is why your meter does not bill it directly. It still causes real heating in every conductor carrying it, and utilities bill demand on it — which is the entire reason power factor correction exists.
- Power factor is not efficiency. A motor at 0.8 power factor is not 80% efficient. It means the current lags the voltage, so more current is needed for the same real work.
- Wye and delta are opposites. In a wye the line voltage is √3 times the phase voltage while the currents match; in a delta the voltages match and the line current is √3 times the phase current. Same power either way.
- These formulas assume a balanced load. Real installations are not, and the neutral of a wye system carries the imbalance — plus triplen harmonics from switching supplies, which add rather than cancel and can put more current in the neutral than in any phase.
How to use
- Pick whether you know the current, the real power or the apparent power.
- Enter the LINE-TO-LINE voltage — 480 on a 277/480 system, not 277.
- Set the power factor, or leave it at 1 for a purely resistive load.
- Add a target power factor to see the correction and the current it saves.
Frequently asked questions
Which voltage do I enter for three phase?
The line-to-line figure, always. On a 277/480 volt system that is 480; on 120/208 it is 208. The square root of three in the formula already accounts for the phase relationship between conductors, so feeding it the line-to-neutral number applies the correction twice and lands you 42 percent low. This is the commonest arithmetic error in the subject and it produces an answer that looks entirely reasonable.
What is the difference between kW and kVA?
Real power against apparent power. kW is what does work and what your energy meter bills; kVA is the product of voltage and current regardless of whether they are in phase. Generators, transformers and UPSs are rated in kVA because their limit is current and they have no idea what power factor you will present them with. Size one from a kW figure at 0.8 power factor and you have undersized it by a quarter.
Is a low power factor wasting electricity?
Not directly, which surprises people. Reactive power flows out to the load and back again rather than being consumed, so it does not turn up on a domestic energy bill. It does cause real heating in every conductor carrying it, because the current is genuinely there, and commercial tariffs bill demand in kVA or apply a power factor penalty. That combination is the entire reason correction equipment exists.
How does power factor correction work?
Capacitors near the load supply the reactive current locally, so it stops travelling back and forth through the supply. The real power is unchanged — correction saves nothing on the kW — but the line current falls in proportion to the improvement in power factor. Going from 0.75 to 0.95 cuts the current by 21 percent, which reduces conductor heating and, on a commercial tariff, the demand charge.
Is power factor the same as efficiency?
No, and conflating them is common. A motor at 0.8 power factor is not 80 percent efficient. Power factor describes the phase relationship between voltage and current, so it tells you how much current is needed for a given amount of real work. Efficiency describes how much of that real work comes out as useful mechanical output rather than heat. A motor can be 94 percent efficient and 0.8 power factor at the same time.
What is the difference between wye and delta?
They relate line and phase quantities in opposite ways. In a wye, or star, the line voltage is the square root of three times the voltage across each winding, and the line current equals the winding current. In a delta the winding sees the full line voltage while carrying line current divided by the square root of three. Both carry the same total power — the difference is what each winding is subjected to.
Do these formulas hold on an unbalanced load?
Only approximately. The standard three-phase equations assume the three phases carry equal current, and real installations never quite do. The neutral of a wye system carries whatever imbalance exists, and on top of that, triplen harmonics from switching power supplies add in the neutral rather than cancelling — which can genuinely put more current in the neutral than in any phase conductor, and catches people who sized it as if it were a spare.
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