Phase angle to power factor
Type a value in ° to get it in cos φ instantly.
0.9999cos φ
That's about the same as a heater or lamp. A 100 kW load at that factor draws 100 kVA.
Convert the other way: cos φ to °
What it means
How much is wasted?
This is displacement power factor, for clean sine waves. Electronic loads add harmonics, and their true power factor is worse than the phase angle suggests.
The math
How to convert ° to cos φ
Power factor is the cosine of the phase angle: PF = cos φ, so φ = arccos(PF) and tan φ = √(1 − PF²) ÷ PF. Apparent power is kW ÷ PF.
Example: 0.8 ° = 0.999903 cos φ.
Every unit
Your power factor in every unit
Tables
° to cos φ conversion table
| ° | cos φ |
|---|---|
| 0.2 ° | 0.999994 cos φ |
| 0.4 ° | 0.999976 cos φ |
| 0.5 ° | 0.999962 cos φ |
| 0.6 ° | 0.999945 cos φ |
| 0.7 ° | 0.999925 cos φ |
| 0.8 ° | 0.999903 cos φ |
| 0.85 ° | 0.99989 cos φ |
| 0.9 ° | 0.999877 cos φ |
| 0.95 ° | 0.999863 cos φ |
| 0.99 ° | 0.999851 cos φ |
| 1 ° | 0.999848 cos φ |
cos φ to ° conversion table
| cos φ | ° |
|---|---|
| 0.2 cos φ | 78.463 ° |
| 0.4 cos φ | 66.4218 ° |
| 0.5 cos φ | 60 ° |
| 0.6 cos φ | 53.1301 ° |
| 0.7 cos φ | 45.573 ° |
| 0.8 cos φ | 36.8699 ° |
| 0.85 cos φ | 31.7883 ° |
| 0.9 cos φ | 25.8419 ° |
| 0.95 cos φ | 18.1949 ° |
| 0.99 cos φ | 8.10961 ° |
| 1 cos φ | 0 ° |
Quick answers
Quick answers
- How many cos φ is 1 °?
- 1 ° is 0.999848 cos φ.
- How many cos φ is 10 °?
- 10 ° is 0.984808 cos φ.
- How many cos φ is 0.8 °?
- 0.8 ° is 0.999903 cos φ.
The units
About these units
Phase angle (°)
How far current lags voltage, in degrees.
Power factor (cos φ)
The ratio of real power to apparent power.
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