Torque Formula
The torque formula calculates rotational force as the product of force and lever arm distance from the pivot point.
The Formula
Torque (also called moment of force) measures the tendency of a force to rotate an object around an axis or pivot point. It depends on both the magnitude of the force and the distance from the axis of rotation.
Variables
| Symbol | Meaning |
|---|---|
| T (or τ) | Torque (measured in newton-meters, N·m, or foot-pounds, ft·lb) |
| F | Force applied perpendicular to the lever arm (measured in newtons, N, or pounds, lb) |
| d | Distance from the pivot point to where the force is applied, also called the lever arm or moment arm (measured in meters or feet) |
Example 1
A mechanic applies 80 N of force to a wrench that is 0.3 m long. What is the torque on the bolt?
Identify the values: F = 80 N, d = 0.3 m
Apply the formula: T = F x d = 80 x 0.3
T = 24 N·m
Example 2
A door requires 15 N·m of torque to open. If the handle is 0.75 m from the hinge, how much force is needed?
Rearrange: F = T / d
F = 15 / 0.75
F = 20 N
Example 3 (Imperial Units)
A bolt specification requires 75 ft-lb of torque. If your wrench is 1.5 feet long, what force must you apply?
Rearrange: F = T / d = 75 / 1.5
F = 50 pounds of force
When to Use It
Use the torque formula whenever you need to calculate rotational force.
- Tightening bolts and nuts to specification (automotive, construction)
- Designing levers, gears, and mechanical systems
- Calculating the force needed to open doors, turn valves, or operate tools
- Comparing the effectiveness of different lever arm lengths
- Understanding why longer wrenches make bolts easier to turn
Important Notes
The formula T = F x d assumes the force is applied perpendicular (at 90 degrees) to the lever arm. If the force is at an angle, use the full formula: T = F x d x sin(theta), where theta is the angle between the force direction and the lever arm.
Unit conversions: 1 N·m = 0.7376 ft·lb. 1 ft·lb = 1.3558 N·m.