Amps to kW: Three Formulas, Power Factor, and the Mistakes That Trip People Up
Single-phase, three-phase, and DC each use a different formula. Power factor changes the answer by 30% or more. Using the wrong formula or skipping power factor undersizes wires, breakers, and generator capacity.
An electrician sizes a feeder for a 50-amp 240-volt continuous load and uses the single-phase formula. Twelve kilowatts. He picks a 60-amp breaker and runs the wire. Six weeks later the breaker trips, the wire runs hot, and the inspector flags the install.
The load was three-phase, not single-phase. The real power was about 21 kW. The wire and breaker were undersized by 73 percent.
This is the most common amps-to-kW mistake. Same numbers, two formulas, very different answer. There are three formulas, and you have to pick the right one before doing anything else. Power factor changes the result. The NEC requires another adjustment for continuous loads. Skipping any of the three is what causes problems.
Quick Reference
| Circuit type | Formula |
|---|---|
| DC | kW = (V × I) / 1000 |
| Single-phase AC | kW = (V × I × PF) / 1000 |
| Three-phase AC (line-to-line voltage) | kW = (V × I × PF × √3) / 1000 |
√3 ≈ 1.732. Use the three-phase formula only with line-to-line voltage. For continuous loads, multiply the resulting amperage by 1.25 before sizing the breaker.
The Three Formulas, in Plain Form
DC circuit:
kW = (V × I) / 1000
Single-phase AC:
kW = (V × I × PF) / 1000
Three-phase AC (line-to-line voltage):
kW = (V × I × PF × √3) / 1000
The three-phase formula has a multiplier of √3 ≈ 1.732. That number is not optional. It is the geometric consequence of three voltage waveforms 120 degrees apart. Drop it and the answer is 42 percent too low. Use it on a single-phase circuit and the answer is 73 percent too high.
Power Factor Is Not Always 1.0
The power factor (PF) term turns apparent power into real power. Apparent power (kVA) is what the wires carry; real power (kW) is what does work. They are equal only when the load is purely resistive.
| Load type | Typical PF |
|---|---|
| Electric resistance heater | 1.00 |
| Incandescent lighting | 1.00 |
| Modern LED driver with PFC | 0.95-0.99 |
| Older LED, magnetic fluorescent ballast | 0.50-0.85 |
| Single-phase induction motor | 0.70-0.85 |
| Three-phase motor at full load | 0.85-0.92 |
| Variable-frequency drive (VFD) | 0.95-1.00 |
| Server rack with PSU (80 PLUS Bronze+) | 0.95-0.99 |
| Welder (transformer type) | 0.40-0.60 |
If you do not know the PF, you cannot accurately convert amps to kW for an AC circuit. The number on the equipment nameplate is the right one to use. With no nameplate, assume 0.85 for mixed loads. Use 1.0 only for confirmed resistive heat.
The Three-Phase Voltage Trap
Three-phase systems have two voltages: line-to-line and line-to-neutral. The standard three-phase formula requires line-to-line.
In a US 120/208 wye system, line-to-neutral is 120 volts and line-to-line is 208 volts. Plugging 120 into the three-phase formula gives an answer that is 1.732 times too low.
Common North American three-phase line-to-line voltages:
- 208V — from a 120/208 wye system, common in apartment buildings and small commercial.
- 240V — from a 240V delta system, used in some industrial.
- 480V — from a 277/480 wye system, the standard for medium and large commercial buildings.
Outside North America the common values are 400V (Europe, 230/400 wye) and 415V (UK, before harmonization to 400V). If the load nameplate says 400V, the system is line-to-line.
The NEC Continuous-Load Rule
If a load runs continuously for three hours or more, NEC Articles 210.19 and 210.20 require the circuit to be sized for 125 percent of the continuous load current. EV charging is the textbook example. A Level 2 charger pulling 40 amps continuously needs a 50-amp circuit, not a 40-amp circuit.
So when you compute amps from kW for sizing, multiply by 1.25 before picking a breaker:
- 50 amp continuous load × 1.25 = 62.5 amps required circuit
- Pick the next standard breaker up: 70 amps
- Pick wire rated for 70 amps in the 75°C column: #4 copper, #2 aluminum (per NEC 310.16)
Stopping at "50A breaker for 50A load" leaves the breaker nuisance-tripping and the wire running hot. The 80 percent rule is not optional and not conservative engineering. It is code.
Generators: kVA and kW Both Matter
A generator nameplate typically shows two numbers, like 50 kVA / 40 kW. Both are correct, and both matter.
The kVA rating is the maximum apparent power the alternator can deliver. The wires, windings, and cooling are sized for that current. The kW rating is the real power the engine can produce.
The ratio between them is the assumed power factor, almost always 0.8 for standby and prime gensets. So 50 kVA × 0.8 PF = 40 kW. If your real load runs at PF higher than 0.8 (an IT load at 0.95), you can pull more real power before hitting the kVA limit. If your load runs at PF lower than 0.8 (an unloaded motor), you hit the kVA limit before reaching the engine's kW limit.
For sizing, if you have a 30 kW load with a PF of 0.7, you need at least 30 / 0.7 = 42.9 kVA of generator. Buying a 30 kVA generator and assuming it covers a 30 kW load undersizes by about 33 percent.
Worked Example: EV Charger Feed
A common request: install a 240V Level 2 charger drawing 48 amps. What is the kW, what size breaker, what wire?
kW: Single-phase 240V at PF 1.0 (EVSE charging is essentially resistive at the panel).
kW = (240 × 48 × 1.0) / 1000 = 11.52 kW
Continuous-load circuit current:
48A × 1.25 = 60A
Breaker: 60A is a standard size. Pick 60A.
Wire: 60A in NEC 310.16 75°C column = #6 copper THHN.
Common mistake: picking a 50A breaker because "the charger says 48 amps." The breaker will nuisance-trip after about 30 minutes of charging. The fix is a 60A breaker.
Worked Example: Three-Phase Motor
A nameplate reads: 480V three-phase, 22 amps full load, PF 0.87.
kW = (480 × 22 × 0.87 × 1.732) / 1000 = 15.92 kW
If you used the single-phase formula by mistake:
kW = (480 × 22 × 0.87) / 1000 = 9.19 kW
You would conclude the motor draws 9 kW when it actually draws 16. Sizing a generator for that load would buy a 12 kVA unit instead of the 20 kVA you actually need.
Sanity Check
If you finish a calculation and want a 30-second sanity check, look at the kVA number. kVA = (V × I × phase factor) / 1000, with phase factor of 1 for single-phase or DC and √3 for three-phase. The kVA number is always equal to or larger than the kW number. If your kW comes out higher than the kVA, there is a sign or formula error.
Use the amps to kW calculator as a cross-check. The calculator handles all three phase types, supports power factor, and outputs both kVA and kW so the sanity check is automatic.
Five Rules That Stop Most Mistakes
- Confirm whether the circuit is DC, single-phase, or three-phase before reaching for a formula.
- For three-phase, use line-to-line voltage. If the nameplate says 277V, that is line-to-neutral; multiply by √3 first or use a different formula.
- Look up the actual power factor from the nameplate. Do not assume 1.0 for anything with a coil in it.
- Apply the 125 percent continuous-load multiplier when sizing breakers and conductors.
- For generator sizing, divide load kW by 0.8 to estimate kVA, then check the generator's kW rating against your real load.
None of this is theoretical. The formula you pick determines whether the wire melts. Pick the right formula, look up the real PF, apply the code multiplier, and the math works.
