Wrench example
Given: F = 200 N, r = 0.30 m, θ = 90°
Working: T = 200 × 0.30 × 1
Torque = 60 N·m.
Mechanical Engineering
Torque Formula
Learn the torque formula T = F × r × sinθ with units, worked examples and a live calculator. Also see the torque-power-RPM relationship used for rotating machines.
Governing equation
T = F × r × sin(θ)
Torque is the turning effect of a force about an axis. It depends on the force magnitude, the distance from the axis and the angle between the force and lever arm.
When the force acts perpendicular to the lever arm, θ = 90° and sinθ = 1, so the formula simplifies to T = F × r.
Live calculator
Quick torque calculator
Calculates static moment from force, radius and force angle.
Result
60N·m
T = 200 × 0.3 × sin(90°)
Formula variables and units
| Symbol | Meaning | Typical SI unit |
|---|---|---|
| T | Torque | N·m |
| F | Applied force | N |
| r | Distance from axis to force application point | m |
| θ | Angle between lever arm and force | degrees |
How to calculate it
- 1Identify the axis or pivot about which rotation is considered.
- 2Measure the perpendicular lever-arm distance or use the force angle explicitly.
- 3Convert force to newtons and distance to metres for torque in N·m.
- 4Apply T = F × r × sinθ.
- 5For motors, you can also relate torque to power and speed using T ≈ 9550 × P(kW) / RPM.
Common mistakes
- Using centimetres as metres without conversion.
- Ignoring the force angle.
- Using total distance instead of the perpendicular lever arm.
- Confusing torque (N·m) with energy (J) even though the unit dimensions look similar.
Worked examples
Angled force example
Given: F = 100 N, r = 0.50 m, θ = 30°
Working: T = 100 × 0.50 × sin30°
Torque = 25 N·m.
Go deeper
Use the dedicated OneCalcApp tool
The quick calculator above demonstrates the governing equation. Open the related engineering tool for broader inputs, outputs and calculation context where available.
Frequently asked questions
What is the torque formula?
The general formula is T = F × r × sinθ. For a force perpendicular to the lever arm, it simplifies to T = F × r.
How do I calculate motor torque from power and RPM?
A common metric relationship is T(N·m) ≈ 9550 × P(kW) / RPM.
What is the SI unit of torque?
The SI unit of torque is the newton-metre (N·m).
Why does torque depend on angle?
Only the component of force perpendicular to the lever arm produces rotational moment about the axis.
Related formula guides
Continue with another problem-first engineering equation.