Power Factor Formula
Calculate how efficiently AC power is used in electrical systems.
Measures the ratio of real power to apparent power.
The Formula
PF = P / S = cos(φ)
Power factor measures how much of the electrical power is actually doing useful work. A power factor of 1.0 (unity) means all power is used efficiently. Lower values mean wasted energy.
Variables
| Symbol | Meaning |
|---|---|
| PF | Power factor (unitless, 0 to 1) |
| P | Real (active) power — actual work done (Watts) |
| S | Apparent power — total power supplied (Volt-Amps, VA) |
| φ | Phase angle between voltage and current |
Example 1
A motor draws 5,000 VA of apparent power but uses only 4,000 W of real power
PF = 4,000 / 5,000
PF = 0.80 (80% of the power is doing useful work)
Example 2
A circuit has a phase angle of 25°. What is the power factor?
PF = cos(25°)
PF = 0.906 (fairly efficient)
When to Use It
Use the power factor formula when:
- Evaluating the efficiency of electrical equipment
- Sizing generators and transformers for industrial loads
- Calculating power factor correction capacitor requirements
- Reducing electricity costs (utilities penalize low power factor)