Torque Calculator
Inputs
90° = max torque. 0° = no torque.
Enter Force, Radius, and Angle to calculate Torque.
What is Torque?
Torque (τ) is the rotational equivalent of linear force. It measures how much a force acting on an object causes that object to rotate.
Think of using a wrench to loosen a bolt. The longer the wrench (radius) and the harder you push (force), the more torque you generate to turn the bolt.
The Torque Formula
The magnitude of torque depends on the force applied, the distance from the pivot point, and the angle of application:
τ = r × F × sin(θ)- τ (tau) = Torque (Newton-meters, N·m)
- r = Radius or lever arm length (meters, m)
- F = Force applied (Newtons, N)
- θ (theta) = Angle between force vector and lever arm
Why Angle Matters?
Torque is maximized when you push perpendicular (90°) to the lever arm (sin 90° = 1).
If you push directly towards the pivot (0°), you generate zero torque because sin 0° = 0. You're just pushing the object, not turning it.
Examples
Example 1: Using a Wrench
You use a 0.5 meter wrench and apply 100 N of force perpendicularly.
- Radius (r) = 0.5 m
- Force (F) = 100 N
- Angle = 90° (sin 90° = 1)
- Torque = 0.5 × 100 × 1 = 50 N·m
Example 2: Opening a Door
You push a door 0.8 meters from the hinge with 40 N force at a 45° angle.
- Radius (r) = 0.8 m
- Force (F) = 40 N
- Angle = 45° (sin 45° ≈ 0.707)
- Torque = 0.8 × 40 × 0.707 = 22.6 N·m
Frequently Asked Questions
Is Torque the same as Work?
No, even though they share units (N·m vs Joules). Work is energy transfer over a distance. Torque is a static or dynamic rotational force. Torque × Angle (in radians) = Work.
What does 'foot-pound' mean?
'Foot-pound' (ft·lb) is the imperial unit for torque, often used in car engines in the US. 1 N·m ≈ 0.737 ft·lb.
Can torque be negative?
Yes. Torque is a vector. By convention, counter-clockwise rotation is often positive, and clockwise rotation is negative.