Power Factor
PF = P / S = cos(φ)
Quick answer
This calculator solves PF = P / S = cos(φ) for Power Factor. With Real Power 10 W, Apparent Power 22 W, the result is 0.4545. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Power factor is the ratio of real power (watts) doing useful work to apparent power (volt-amperes) flowing in the circuit. It equals the cosine of the phase angle between voltage and current waveforms. A power factor of 1.0 (unity) means voltage and current are perfectly in phase and all power delivered is consumed as useful work. Reactive loads like motors, transformers, and fluorescent lighting have power factors below 1.0 because they draw current that is out of phase with voltage, creating reactive power that shuttles back and forth without doing useful work.
Variables
- PF — Power factor (0 to 1, dimensionless)
- P — Real (true) power in watts (W)
- S — Apparent power in volt-amperes (VA)
- φ — Phase angle between voltage and current (degrees)
Practical Notes
Industrial facilities with power factors below 0.85-0.90 typically incur penalty charges from utilities because the reactive current increases transmission losses. Power factor correction capacitors or synchronous condensers are added to bring the PF closer to unity. Modern switch-mode power supplies include active PFC circuits to achieve PF > 0.95.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| PF | Power Factor | — | — |
| P | Real Power | W | µW, mW, W, kW |
| S | Apparent Power | W | µW, mW, W, kW |
Step by step
- 1. What you know: Real Power 10 W, Apparent Power 22 W
- 2. The relation: PF = P / S = cos(φ)
- 3. Substitute: P = 10 W, S = 22 W
- 4. Result: Power Factor = 0.4545
Worked examples
Minimum range
Given: Real Power 10 mW, Apparent Power 22 mW
Result: Power Factor = 0.4545
Low range
Given: Real Power 100 mW, Apparent Power 0.22 W
Result: Power Factor = 0.4545
Typical
Given: Real Power 10 W, Apparent Power 22 W
Result: Power Factor = 0.4545
High range
Given: Real Power 1 kW, Apparent Power 2.2 kW
Result: Power Factor = 0.4545
Maximum range
Given: Real Power 10 kW, Apparent Power 22 kW
Result: Power Factor = 0.4545
Solving for each variable
Solve for Power Factor
Real Power 10 mW, Apparent Power 22 mW → 0.4545
Solve for Real Power
Power Factor 0.025, Apparent Power 22 mW → 0.55 mW
Solve for Apparent Power
Power Factor 0.025, Real Power 10 mW → 0.4 W
How Power Factor changes with Real Power
| Real Power (input) | Power Factor (result) |
|---|---|
| 1 W | 0.04545 |
| 2.5 W | 0.1136 |
| 5 W | 0.2273 |
| 7.5 W | 0.3409 |
| 10 W | 0.4545 |
| 15 W | 0.6818 |
| 20 W | 0.9091 |
| 40 W | 1.818 |
| 70 W | 3.182 |
| 100 W | 4.545 |
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<p><a href="https://vbatpower.com/formulas/power-factor/">Power Factor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Power Factor?
Use PF = P / S = cos(φ). With Real Power 10 W, Apparent Power 22 W, Power Factor works out to 0.4545.
What is the formula for Power Factor?
The formula is PF = P / S = cos(φ). Power factor is the ratio of real power (watts) doing useful work to apparent power (volt-amperes) flowing in the circuit.
How do you find Real Power when you know the other values?
Rearrange for Real Power: with Power Factor 0.025, Apparent Power 22 mW, Real Power is 0.55 mW.
How do you find Apparent Power when you know the other values?
Rearrange for Apparent Power: with Power Factor 0.025, Real Power 10 mW, Apparent Power is 0.4 W.
Related Concepts
All AC Circuits formulas →Need more features?
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