Power Factor Angle
Compute power-factor angle φ and reactive power Q from cosφ and active power P (kW).
Inputs
Formula
Fundamentals
Compute power-factor angle φ and reactive power Q from cosφ and active power P (kW).
This tool computes Power Factor Angle from the formula: φ = arccos(cosφ); Q = P·tanφ
History
Design theory of gears, threads and bearings matured with machine tools and standardisation (AGMA, ISO) since the Industrial Revolution.
Engineering applications
Used for transmission design, joint strength checks and component selection.
Glossary
| Power factor cosφ | Input parameter |
| Active power P | Input parameter |
| PF angle φ | Output result |
| Reactive power Q | Output result |
How to use
- Fill in Power factor cosφ, Active power P in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read PF angle φ, Reactive power Q in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：φ = arccos(cosφ); Q = P·tanφ
输入变量：
- Power factor cosφ
pf - Active power P
P— kW
输出结果：
- PF angle φ
phi— ° - Reactive power Q
Q— kvar
假设/适用：Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
Worked Example
根据公式 φ = arccos(cosφ); Q = P·tanφ，取 Power factor cosφ = 0.85；Active power P = 10 kW。
代入计算得：PF angle φ = 31.79 °；Reactive power Q = 6.197 kvar。
Key Points
- Gearing/thread formulas assume standard, zero-backlash mounting; include error & load factors K_A.
- Compare stress with allowable stress and keep a safety factor (≥1.5, ≥2 for critical parts).
- For high speed/load also check lubrication, heat and fatigue life, not just static strength.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Power factor cosφ | pf | 0.85 | |
| Active power P (kW) | P | kW | 10 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| PF angle φ | phi | ° |
| Reactive power Q | Q | kvar |
Applications
- Common engineering use cases