Power factor to reactive fraction
Type a value in cos φ to get it in sin φ instantly.
0.6sin φ
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.
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 sin 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 cos φ = 0.6 sin φ.
Every unit
Your power factor in every unit
Tables
cos φ to sin φ conversion table
| cos φ | sin φ |
|---|---|
| 0.2 cos φ | 0.979796 sin φ |
| 0.4 cos φ | 0.916515 sin φ |
| 0.5 cos φ | 0.866025 sin φ |
| 0.6 cos φ | 0.8 sin φ |
| 0.7 cos φ | 0.714143 sin φ |
| 0.8 cos φ | 0.6 sin φ |
| 0.85 cos φ | 0.526783 sin φ |
| 0.9 cos φ | 0.43589 sin φ |
| 0.95 cos φ | 0.31225 sin φ |
| 0.99 cos φ | 0.141067 sin φ |
| 1 cos φ | 0 sin φ |
sin φ to cos φ conversion table
| sin φ | cos φ |
|---|---|
| 0 sin φ | 1 cos φ |
| 0.141 sin φ | 0.99001 cos φ |
| 0.312 sin φ | 0.950082 cos φ |
| 0.436 sin φ | 0.899947 cos φ |
| 0.527 sin φ | 0.849865 cos φ |
| 0.6 sin φ | 0.8 cos φ |
| 0.714 sin φ | 0.700146 cos φ |
| 0.8 sin φ | 0.6 cos φ |
| 0.866 sin φ | 0.500044 cos φ |
| 0.917 sin φ | 0.398887 cos φ |
| 0.98 sin φ | 0.198997 cos φ |
Quick answers
Quick answers
- How many sin φ is 1 cos φ?
- 1 cos φ is 0 sin φ.
- How many sin φ is 0.8 cos φ?
- 0.8 cos φ is 0.6 sin φ.
The units
About these units
Power factor (cos φ)
The ratio of real power to apparent power.
Reactive fraction (sin φ)
The reactive part as a fraction of apparent power.
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