Apparent power and real power are not the same thing
kVA is apparent power: volts times amps, without regard to what the load does with them. kW is real power: the part that actually does work and shows up on your meter. The ratio between them is the power factor.
For a purely resistive load such as a heater, the two are equal and the power factor is 1. For motors, transformers and anything with a magnetic field or a rectifier front end, current and voltage fall out of step and kVA exceeds kW.
This matters commercially because equipment is rated in kVA while you are billed, for the most part, in kW. A transformer or generator must supply the apparent power, so a 100 kVA set with a load at 0.75 power factor can only deliver 75 kW of useful work.
The formulas, by system
| System | kVA | Amps from kVA |
|---|---|---|
| DC | V × I ÷ 1000 | kVA × 1000 ÷ V |
| Single-phase AC | V × I ÷ 1000 | kVA × 1000 ÷ V |
| Three-phase AC | √3 × V × I ÷ 1000 | kVA × 1000 ÷ (√3 × V) |
The square root of 3, about 1.732, appears in three-phase formulas because the three phase voltages are offset by 120 degrees and the resulting vector sum is larger than any single phase. In a three-phase system, V is the line-to-line voltage, not the line-to-neutral voltage.
Three worked examples
1. Sizing a standby generator
A facility has 80 kW of load at a power factor of 0.8. The apparent power is 80 ÷ 0.8 = 100 kVA. A 100 kVA generator would be running at its limit, so in practice a 125 kVA set is chosen to allow for motor starting and future load. Note that the generator must be sized on kVA, not on the 80 kW figure that appears on the load schedule.
2. Checking a service in amps
A 45 kVA transformer secondary at 208 V three-phase. Current equals 45,000 ÷ (1.732 × 208) = 125 A. That is why 45 kVA is a common transformer size for a 125 A service — the numbers line up exactly.
3. A single-phase machine
A 10 kW single-phase load at 240 V and 0.9 power factor draws 10,000 ÷ (240 × 0.9) = 46.3 A. Ignoring the power factor would give 41.7 A and a circuit sized about 10% too small.
What a low power factor costs you
- Larger equipment for the same work. Cables, transformers, switchgear and generators all have to carry the full apparent current, so a low power factor means paying for capacity you cannot use.
- Higher losses. Resistive losses rise with the square of current, so the extra current needed to deliver the same real power produces disproportionately more heat.
- Utility penalties. Most commercial tariffs include a reactive power charge or a minimum power factor requirement, commonly 0.90 or 0.95. Falling below it adds a line item to the bill.
- Voltage drop increases. Because the current is higher for the same delivered power, the percentage drop along the feeder rises too.
Correcting a poor power factor with capacitors is usually straightforward and pays for itself quickly under a tariff with a reactive charge. The power factor calculator on this site sizes the correction for you.
How this calculator is verified
The relationships implemented here are the standard definitions of apparent, real and reactive power in single-phase and balanced three-phase systems. Results assume a sinusoidal supply and a balanced load. Non-linear loads such as variable frequency drives and switch-mode supplies need harmonic analysis, which this calculator does not perform.
- IEEE — IEEE 1459, the standard for definitions of power quantities under sinusoidal, non-sinusoidal, balanced and unbalanced conditions.
- NIST — SI definitions of the watt, volt and ampere.
- NEMA — motor and generator rating standards, including the kVA basis for machine ratings.
Formulas and worked examples last verified: 19 September 2026.