Torque Formula
Calculate rotational force (torque) from force and lever arm distance.
Essential for mechanical and automotive engineering.
The Formula
τ = F × r × sin(θ)
Torque is the rotational equivalent of force. It depends on the force applied, the distance from the pivot point, and the angle of application.
Variables
| Symbol | Meaning |
|---|---|
| τ | Torque (Newton-meters, N⋅m) |
| F | Applied force (Newtons) |
| r | Distance from the axis of rotation to the force (meters) |
| θ | Angle between the force vector and the lever arm |
Example 1
You apply 50 N to a wrench 0.3 m from the bolt, perpendicular to the wrench
θ = 90°, sin(90°) = 1
τ = 50 × 0.3 × 1
τ = 15 N⋅m
Example 2
Same wrench but force applied at 60° angle
τ = 50 × 0.3 × sin(60°)
τ = 50 × 0.3 × 0.866
τ = 13.0 N⋅m (less torque because force is not perpendicular)
When to Use It
Use the torque formula when:
- Tightening bolts to specification (torque wrenches)
- Calculating engine and motor output
- Designing levers, cranks, and rotating machinery
- Analyzing the turning effect of forces in structures