Moment of Force (Torque) Formula
Calculate torque using τ = F × d.
Learn how force and distance from a pivot create rotational motion in mechanical systems.
The Formula
Torque (or moment of force) measures the turning effect of a force about a pivot point.
The greater the force or the longer the distance from the pivot, the larger the torque.
Variables
| Symbol | Meaning |
|---|---|
| τ | Torque / moment of force (Newton-metres, N·m) |
| F | Applied force (Newtons, N) |
| d | Perpendicular distance from the pivot to the line of action of the force (metres, m) |
Example 1
A mechanic applies 80 N of force to a 0.3 m wrench. What is the torque?
τ = F × d
τ = 80 N × 0.3 m
τ = 24 N·m
Example 2
A 50 kg child sits 2 m from the pivot of a seesaw. What torque does gravity create?
First, find the force due to gravity: F = m × g = 50 × 9.81 = 490.5 N
τ = F × d = 490.5 N × 2 m
τ = 981 N·m
When to Use It
Use the torque formula when you need to:
- Calculate the turning force on bolts, nuts, or shafts
- Analyse balance in levers, seesaws, and beams
- Design motors, gears, and rotational machinery
- Determine the force needed to open or close a valve
Remember that d must be the perpendicular distance from the pivot to the force's line of action.
If the force is applied at an angle θ, use τ = F × d × sin(θ).