Power factor to phase angle
Type a value in cos φ to get it in ° instantly.
36.87°
That's 1.14× as good as a half-loaded motor, while a fully loaded motor is 1.06× better. A 100 kW load at that factor draws 125 kVA.
Convert the other way: ° to cos φ
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 cos φ to °
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 cos φ = 36.8699 °.
Every unit
Your power factor in every unit
Tables
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 ° |
° 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 |
Quick answers
Quick answers
- How many ° is 1 cos φ?
- 1 cos φ is 0 °.
- How many ° is 10 cos φ?
- 10 cos φ is 0 °.
- How many ° is 0.8 cos φ?
- 0.8 cos φ is 36.8699 °.
The units
About these units
Power factor (cos φ)
The ratio of real power to apparent power.
Phase angle (°)
How far current lags voltage, in degrees.
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