Power factor to tan φ
Type a value in cos φ to get it in tan φ instantly.
0.75tan 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.
Convert the other way: tan φ 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 tan 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 = 0.75 tan φ.
Every unit
Your power factor in every unit
Tables
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 |
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 |
Quick answers
Quick answers
- How many tan φ is 1 cos φ?
- 1 cos φ is 0 tan φ.
- How many tan φ is 0.8 cos φ?
- 0.8 cos φ is 0.75 tan φ.
The units
About these units
Power factor (cos φ)
The ratio of real power to apparent power.
Tan φ (tan φ)
Reactive over real power. How European tariffs measure it.
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