Torque & Moment of Force Calculator
Torque is the rotational equivalent of linear force. Calculate wrench tightening torque, engine output torque, electric motor sizing, and mechanical lever advantages.
How it works
Torque measures the tendency of a force to rotate an object about an axis. Maximum torque is achieved when the force is applied perpendicularly ($ heta = 90^circ, sin 90^circ = 1$).
Formula
τ = r × F × sin(θ), 1 N·m ≈ 0.737562 ft-lb
Multiplies the moment arm distance by applied force and the sine of the applied angle to determine rotational turning force.
| Symbol | Variable | Unit | Description |
|---|---|---|---|
| r | Lever arm distance from rotation axis | m | |
| F | Applied force magnitude | N | |
| θ | Angle between force and lever arm vector | degrees | |
| τ | Resulting rotational torque | N·m |
Worked example
200 N force applied on a 0.5m wrench at 90°
- Radius:
- 0.5 m
- Force:
- 200 N
- Angle:
- 90°
τ = 0.5 × 200 × sin(90°) = 100.00 N·m (approx. 73.76 ft-lb).
Limitations
Assumes static mechanical equilibrium without rotational acceleration inertia ($ au = Ialpha$).
Frequently asked questions
What is the relationship between Engine Horsepower (HP) and Torque (Nm)?
Power (Watts) = Torque (N·m) × Angular Speed (rad/s). In automotive terms: HP = (Torque in lb-ft × RPM) / 5252.
Why does a longer wrench make loosening bolts easier?
Because Torque = Radius × Force, doubling the wrench length doubles the resulting torque on the fastener for the exact same muscle force applied.
What happens when the angle is 0° or 180°?
When force is applied directly along the axis of the lever arm ($sin 0^circ = 0$), no rotational moment is created and resulting torque is 0 N·m.
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Last reviewed: 2026-08-22.