Enter the line-to-line voltage, the line current and the power factor. Three-phase power is the square root of 3 times the voltage times the current times the power factor, and the apparent power omits the power factor. Take voltage and current from a meter, a nameplate or the load's rating.
Use the measured or nameplate power factor for the load. A purely resistive ideal load has unity power factor.
The formula assumes balanced loads across the three phases, which may not hold in practice. Voltage refers to line-to-line. Harmonic distortion and unbalance change the numbers.
Electrical measurements should be taken by a qualified person using proper instruments.
Real power (kW) from line-to-line voltage
| Line-to-line voltage | 480 |
|---|---|
| Line current | 50 |
| Power factor | 0.9 |
| Real power (kW) | 37.4 |
| Apparent power (KVA) | 41.6 |
Common error: Using the single-phase formula for a three-phase load. The square root of three factor is missing, and the power comes out about 42 percent too low.
Three-Phase Power: formula
Three-Phase Power: changing Line-to-line voltage
| Line-to-line voltage | Real power (kW) | Apparent power (KVA) |
|---|---|---|
| 384 | 29.9 | 33.3 |
| 432 | 33.7 | 37.4 |
| 480 (example) | 37.4 | 41.6 |
| 528 | 41.2 | 45.7 |
| 576 | 44.9 | 49.9 |
Three-Phase Power: compare input ranges
| Input | Tested from | To | Real power (kW): low input | Real power (kW): high input | Swing |
|---|---|---|---|---|---|
| Line-to-line voltage | 432 | 528 | 33.7 | 41.2 | 7.5 (20%) |
| Line current | 45 | 55 | 33.7 | 41.2 | 7.5 (20%) |
| Power factor | 0.81 | 0.99 | 33.7 | 41.2 | 7.5 (20%) |
Three-Phase Power: individual input comparisons
| Input | Value | Real power (kW) | Apparent power (KVA) |
|---|---|---|---|
| Line-to-line voltage | 384 | 29.9 | 33.3 |
| 432 | 33.7 | 37.4 | |
| 480 | 37.4 | 41.6 | |
| 528 | 41.2 | 45.7 | |
| 576 | 44.9 | 49.9 | |
| Line current | 40 | 29.9 | 33.3 |
| 45 | 33.7 | 37.4 | |
| 50 | 37.4 | 41.6 | |
| 55 | 41.2 | 45.7 | |
| 60 | 44.9 | 49.9 | |
| Power factor | 0.72 | 29.9 | 41.6 |
| 0.81 | 33.7 | 41.6 | |
| 0.9 | 37.4 | 41.6 | |
| 0.99 | 41.2 | 41.6 | |
| 1.1 | 44.9 | 41.6 |
Real power (kW): Line-to-line voltage against Line current
| Line-to-line voltage / Line current | 40 | 50 | 60 |
|---|---|---|---|
| 384 | 23.9 | 29.9 | 35.9 |
| 432 | 26.9 | 33.7 | 40.4 |
| 480 | 29.9 | 37.4 | 44.9 |
| 528 | 32.9 | 41.2 | 49.4 |
| 576 | 35.9 | 44.9 | 53.9 |
Three-Phase Power: values and definitions
| Quantity and definition | Value used |
|---|---|
| Line-to-line voltage — Line-to-line voltage, in volts. | 480 |
| Line current — Measured or rated line current, in amps. | 50 |
| Power factor — Power factor of the load, from 0 to 1. | 0.9 |
| Real power (kW) | 37.4 |
| Apparent power (KVA) | 41.6 |
Line-to-line voltage: half and double
| Line-to-line voltage | Real power (kW) |
|---|---|
| 240 | 18.7 |
| 480 | 37.4 |
| 960 | 74.8 |
In a three-phase system, real power depends on the line voltage, the current and how well the current lines up with the voltage, the power factor. At 480 volts, 50 amps and a power factor of 0.9, the real power is about 37.4 kilowatts, while the apparent power is about 41.6 kilovolt-amps. The utility and the wiring must carry the apparent power, and only the real power does work, which is why a low power factor wastes capacity.
Measure or look up the actual power factor of the load. Motors and lighting ballasts run below one, and correcting it can lower demand charges.
See single-phase current on the watts to amps calculator, transformer currents on the transformer sizing page and wire limits on the wire ampacity calculator. The voltage drop and conduit fill pages support installation, and the power and energy converters change units.
Why use the square root of 3 in three-phase formulas?
It comes from the 120 degree phase offset between the three lines, which relates line-to-line voltage to per-phase voltage.
Why does a low power factor matter?
It means more current is needed for the same useful power, which increases losses and wire size and can bring utility penalties.