Tan φ to power factor
Type a value in tan φ to get it in cos φ instantly.
0.7809cos φ
That's 1.12× as good as a half-loaded motor, while a fully loaded motor is 1.09× better. A 100 kW load at that factor draws 128.1 kVA.
Convert the other way: cos φ to tan 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 tan φ 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 tan φ = 0.780869 cos φ.
Every unit
Your power factor in every unit
Tables
tan φ to cos φ conversion table
| tan φ | cos φ |
|---|---|
| 0.2 tan φ | 0.980581 cos φ |
| 0.4 tan φ | 0.928477 cos φ |
| 0.5 tan φ | 0.894427 cos φ |
| 0.6 tan φ | 0.857493 cos φ |
| 0.7 tan φ | 0.819232 cos φ |
| 0.8 tan φ | 0.780869 cos φ |
| 0.85 tan φ | 0.761939 cos φ |
| 0.9 tan φ | 0.743294 cos φ |
| 0.95 tan φ | 0.724999 cos φ |
| 0.99 tan φ | 0.710651 cos φ |
| 1 tan φ | 0.707107 cos φ |
cos φ to tan φ conversion table
| cos φ | tan φ |
|---|---|
| 0.2 cos φ | 4.89898 tan φ |
| 0.4 cos φ | 2.29129 tan φ |
| 0.5 cos φ | 1.73205 tan φ |
| 0.6 cos φ | 1.33333 tan φ |
| 0.7 cos φ | 1.0202 tan φ |
| 0.8 cos φ | 0.75 tan φ |
| 0.85 cos φ | 0.619744 tan φ |
| 0.9 cos φ | 0.484322 tan φ |
| 0.95 cos φ | 0.328684 tan φ |
| 0.99 cos φ | 0.142492 tan φ |
| 1 cos φ | 0 tan φ |
Quick answers
Quick answers
- How many cos φ is 1 tan φ?
- 1 tan φ is 0.707107 cos φ.
- How many cos φ is 10 tan φ?
- 10 tan φ is 0.0995037 cos φ.
- How many cos φ is 0.8 tan φ?
- 0.8 tan φ is 0.780869 cos φ.
The units
About these units
Tan φ (tan φ)
Reactive over real power. How European tariffs measure it.
Power factor (cos φ)
The ratio of real power to apparent power.
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