Formula
Single-phase real power is volts × amps × power factor. Three-phase real power, using the line-to-line voltage, multiplies by √3. Apparent power leaves the power factor out, so VA is always at least the watts. Solving for amps or volts divides by the same product. A power factor of 1 is a heater or an incandescent lamp. A motor nameplate is often 0.8 to 0.9.
P = V × I × PF
P = √3 × V × I × PF
VA = P ÷ PF
This does not apply the continuous-load 125%, and it does not pick a breaker. Take the amps to the wire size calculator for NEC Table 310.16, and to the voltage drop calculator for the K method. The box fill calculator counts the conductors after you know the size. A resistive load, with no power factor, is the Ohm’s law calculator.
Worked examples
120 V, 10 A, power factor 1, single phase. 1,200 W and 1,200 VA.
208 V, 20 A, power factor 0.9, three phase. √3 × 208 × 20 × 0.9 = 6,485 W. Apparent power is 7,205 VA.
5,000 W at 240 V, single phase, power factor 1. The current is 20.8 A. That is the number the wire page wants, not a wire size by itself.
Reference
√3 is 1.732. A balanced three-phase load at the same volts and amps is 1.732 times the single-phase product.
Questions
How many watts is 120 volts at 10 amps?
1,200 W at a power factor of 1. Apparent power is also 1,200 VA. A power factor of 0.9 would make the real power 1,080 W and leave the volt-amperes at 1,200.
How do three phases change it?
Multiply by √3. A 208 V, 20 A, three-phase load at power factor 0.9 is √3 × 208 × 20 × 0.9 = 6,485 W.
Does this pick a wire?
No. It turns watts, amps, and volts into each other. The wire size page takes the amps from here and applies the NEC ampacity table. Voltage drop takes the same amps and a length.
Sources
- Single-phase power P = V I PF. Three-phase power P = √3 V I PF, with V the line-to-line voltage.
- Apparent power is the same product without PF. Wire sizing and voltage drop are on the linked pages and are not repeated here.