Torque Calculator
Use our torque calculator to calculate torque from force, lever arm distance, and angle. Includes the torque formula with angle (τ = r × F × sinθ), how torque is calculated, and step-by-step torque examples.
What Is Torque?
Torque is the turning effect of a force applied at a distance from a pivot (like a bolt, axle, hinge, or shaft). It tells you how strongly the force tends to rotate an object around that pivot.
Torque depends on three things: the lever arm distance (r), the force magnitude (F), and the angle (θ) between the lever arm and the force direction. The angle matters because only the perpendicular part of the force produces rotation.
In this calculator, r is in feet (ft), F is in pound-force (lbf), and the result is torque in foot-pounds (ft·lbf).
Torque Formula With Angle
To calculate torque when the force is applied at an angle, multiply the distance by the force and by sin(θ). This accounts for the perpendicular component of the force.
If θ = 90°, sin(θ) = 1 and torque is maximized: τ = r × F. If θ = 0°, sin(θ) = 0 and torque is 0.
A smaller angle reduces torque because less of the force is perpendicular to the lever arm.
When you pull perfectly perpendicular, you get the full r × F torque.
Sin(θ) Quick Chart
Quick reference values for sin(θ), which is the torque multiplier in τ = r × F × sin(θ).
| Angle (deg) | sin(θ) |
|---|---|
| 0° | 0 |
| 15° | 0.2588 |
| 30° | 0.5 |
| 45° | 0.7071 |
| 60° | 0.8660 |
| 75° | 0.9659 |
| 90° | 1 |
How to Calculate Torque
- 1
Enter the distance (r) in feet (ft).
- 2
Enter the force (F) in pound-force (lbf).
- 3
Enter the angle (θ) in degrees (deg).
- 4
The calculator computes torque using τ = r × F × sin(θ).
Frequently Asked Questions
Torque is calculated as distance times force times the sine of the angle between them: τ = r × F × sin(θ).
If θ = 90°, sin(θ) = 1, so torque simplifies to τ = r × F.
Because only the component of the force that is perpendicular to the lever arm produces rotation. sin(θ) gives the fraction of the force that is perpendicular.
Torque becomes 0 because sin(0°) = 0. A force applied directly along the lever arm does not create rotation.
This page uses r in feet (ft), F in pound-force (lbf), and outputs torque in foot-pounds (ft·lbf).