About this calculator
Torque is the turning effect of a force about an axis. It decides whether a bolt is tight enough, whether a motor can drive a load, and what a shaft or coupling must carry. Use the first mode when you know a force and the lever arm (a spanner, crank or pulley radius). Use the second mode when you know the power and speed of a rotating shaft, such as a motor or gearbox output. The third mode works the other way round: from a measured or rated torque and speed it gives the mechanical power at the shaft.
Formula
Force × lever arm
T = F × r
T = torque (N·m), F = force at 90° to the arm (N), r = lever arm (m).
Power and speed
T = P ÷ ω, where ω = 2πn ÷ 60
P = power (W), ω = angular speed (rad/s), n = speed (rpm). In practical units this becomes T (N·m) = 9549 × P (kW) ÷ n (rpm).
Find power (torque and speed)
P = T × ω = T × 2πn ÷ 60
P = mechanical shaft power (W), T = torque (N·m), ω = angular speed (rad/s), n = speed (rpm). In practical units: P (kW) = T (N·m) × n (rpm) ÷ 9549, and P (hp) = T (lbf·ft) × n (rpm) ÷ 5252.
Worked example
Spanner: a 250 N push on a spanner 0.4 m long gives T = 250 × 0.4 = 100 N·m (about 73.76 lbf·ft).
Motor: a 7.5 kW motor running at 1450 rpm. ω = 2π × 1450 ÷ 60 = 151.84 rad/s, so T = 7500 ÷ 151.84 = 49.39 N·m.
Shaft power: a shaft carrying 100 N·m at 3000 rpm. ω = 2π × 3000 ÷ 60 = 314.16 rad/s, so P = 100 × 314.16 = 31 416 W ≈ 31.42 kW (about 42.13 hp).
Assumptions and limitations
- The force acts at right angles to the lever arm. For a force at an angle θ to the arm, the torque is F × r × sin θ.
- Power mode gives the steady running torque. It does not include starting torque, shock loads or service factors.
- A motor’s nameplate power is its rated output; the actual torque depends on the load it is driving.
- Shaft power is mechanical output power. It is not the electrical power drawn by a motor; no motor efficiency is assumed.
References
- ISO 80000-4: quantities and units of mechanics (moment of force, power = torque × angular velocity).