Three-phase power formula
Three-phase power is the standard for industrial and commercial electrical systems. This formula gives the real power delivered from the line voltage, line current, and power factor.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| P | Real power | watts (W) |
| V | Line-to-line voltage | volts (V) |
| I | Line current | amperes (A) |
| cos φ | Power factor | 0 to 1 |
Rearranged forms
Worked example
A 400 V three-phase motor draws 10 A at a power factor of 0.9. Find the real power.
- Start from P = √3 · V I · cos φ.
- Substitute V = 400, I = 10, cos φ = 0.9 (√3 ≈ 1.732).
- Multiply: P = 1.732 × 400 × 10 × 0.9.
Use the line-to-line voltage and the line current. The square root of three (about 1.732) appears because the three phases are 120 degrees apart. Power factor is the cosine of the phase angle between voltage and current; for resistive loads it is 1, for motors typically 0.8 to 0.9.
Sizing a three-phase load?
Enter voltage, current, and power factor and the Three-Phase Power Calculator returns real, apparent, and reactive power.
How three-phase power works
In a three-phase system, three voltages peak in turn, 120 degrees apart, delivering smoother and more efficient power than single phase. The square-root-of-three factor converts line measurements into total power. Power factor accounts for the share of current that does real work versus the part that only circulates.
Where it is used
Three-phase power runs motors, pumps, HVAC, and almost all industrial and commercial equipment. The formula is essential for sizing cables, breakers, and generators, and for checking that a supply can carry a given load.
FAQ
What is the three-phase power formula?
P = √3 · V I · cos φ, using line-to-line voltage, line current, and power factor, giving real power in watts.
Why the square root of three?
The three phases are 120 degrees apart, and combining them into total power from line voltage and current introduces the factor √3, about 1.732.
What is power factor?
The cosine of the phase angle between voltage and current. It is 1 for purely resistive loads and lower for motors and reactive loads, typically 0.8 to 0.9.