How it’s calculated
Rotational power is torque times angular velocity (in radians per second). One revolution is 2π radians, so ω = 2π × rpm ÷ 60. Assumes steady rotation at constant torque.
Example (OpenStax University Physics, Example 10.19): a boat engine delivers 9.0 × 10⁴ W at 300 rpm. ω = 300 × 2π ÷ 60 = 31.4 rad/s, so τ = P ÷ ω = 90,000 ÷ 31.4 ≈ 2,865 N·m.
The 5252 constant is 33,000 ft·lbf/min per hp ÷ 2π: at 5,252 rpm torque in lbf·ft equals horsepower.
Frequently asked questions
How do I convert torque to horsepower?
hp = torque (lbf·ft) × rpm ÷ 5252. In SI, kW = torque (N·m) × rpm ÷ 9549.
Why use rad/s?
P = τω only works with angular velocity in radians per second; radians are dimensionless so N·m × rad/s = W.
Is the result shaft power or electrical power?
Shaft (mechanical) power. Motor electrical input is higher by the motor’s efficiency.
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Sources
- University Physics Vol. 1, 10.8 Work and Power for Rotational Motion — OpenStax
- NIST Guide to the SI (SP 811), Appendix B conversion factors — U.S. National Institute of Standards and Technology
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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