Power
Transmitted mechanical power.
Mechanics · Transmission and rotation
Torque, power and rotational speed
Choose the unknown quantity and enter the other two values. The calculation uses P = T·ω.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Torque
Driving or resisting torque.
Rotational speed
Shaft speed.
Relation and numerical substitution
P = T · ω = 2π · T · n / 60—
Steady operation. Power and torque on the same shaft. Losses excluded.
01Formulas and symbols
Formulas used
P
T · ωMechanical powerω
2πn / 60Angular speedT
P / ωTorque02Assumptions and limits
Scope of validity
- Steady operation.
- Power and torque on the same shaft.
- Losses excluded.
03Validation example
Reference numerical case
- T = 95.493 N·m and n = 1,500 rpm.
- P = 15.000 kW.
04References
Technical references
- Mechanical relation P = T·ω.
- BIPM, SI units.
Power transmission
Relations between torque, power, speed and ratio
A ratio trades speed for torque without creating power. Efficiency reduces available torque.
Torque from P and n
With P in kW and n in rpm, the result is in N·m.
T = 9 549,3 · P / nRatio
Gears: Z₂/Z₁. Pulleys: D₂/D₁ without slip.
n₂ = n₁ / iOutput torque
Apply ratio and then efficiency.
T₂ = T₁ · i · η