Key takeaways
- Torque is τ = F × r: force times the lever arm, measured in newton-metres.
- The lever arm is measured from the pivot to where the force is applied.
- A longer lever arm produces more torque for the same force.
- This formula assumes the force is applied at a right angle to the lever arm.
In this guide
What is torque?
Torque measures the turning effect of a force around a pivot point. It's why a longer wrench makes it easier to loosen a tight bolt than a short one, even with the same amount of push.
Why does torque matter?
Torque is how engineers describe every twisting or rotating force, from tightening a bolt to rating a car engine's pulling power.
Two people pushing with exactly the same force on a door, one right next to the hinge, one near the handle, produce very different amounts of torque. The one further from the hinge opens it far more easily.
The formula
| Symbol | What it means | Example |
|---|---|---|
| τ | The torque, in newton-metres (N·m) | 12 N·m |
| F | The force applied, in newtons (N) | 40 N |
| r | The lever arm — distance from pivot to force, in metres (m) | 0.3 m |
How to calculate torque step by step
- 1Find the force. Measure it in newtons.
- 2Measure the lever arm. Find the distance from the pivot point to where the force is applied, in metres.
- 3Multiply force by that distance.
F × rgives you the torque. - 4Write the answer in newton-metres.
Try the calculator below with your own force and lever arm to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Ignoring the angle. This simple formula assumes the force is applied at a right angle, 90°, to the lever arm — pushing at an angle produces less turning effect.
- Confusing torque with force. Force makes things move in a straight line; torque makes things rotate.
- Forgetting units. Force must be in newtons and the lever arm in metres for the answer to come out in newton-metres.
Tips and tricks
- Working backwards from torque to force? Divide by the lever arm:
F = τ ÷ r. - For a quick estimate, doubling the lever arm always doubles the torque for the same push.
- Torque and work done share the same unit-shape, a force times a distance, but describe rotation instead of straight-line movement.
Where you'll use it in real life
- Tools: a longer wrench or spanner makes loosening a bolt easier by increasing the lever arm.
- Doors: handles are placed far from the hinge on purpose, to maximise torque for minimal effort.
- Vehicles: car and motorbike engines are often rated by their torque output, describing their pulling power.
- Sport: the turning effect in a golf swing or a wrench turn both come down to torque.
Quick summary
To find torque, multiply the force applied in newtons by the lever arm distance in metres. A longer lever arm always means more turning effect for the same force, which is why tools use leverage to multiply your effort. Use the calculator above to check your own numbers.
Worked example
You apply 40 N of force to a wrench at a distance of 0.3 m from the bolt. How much torque are you applying?
- 01τ = F × r
- 02τ = 40 × 0.3
- 03τ = 12 N·m
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate torque?
Multiply the force applied in newtons by the distance from the pivot in metres: τ = F × r. The result is in newton-metres (N·m).
Why is a longer wrench easier to use?
A longer wrench increases the lever arm (r), so the same force produces more torque, making it easier to loosen a tight bolt.
What's the difference between torque and force?
Force pushes or pulls an object in a straight line. Torque is a turning effect caused by a force acting at a distance from a pivot point.
What unit is torque measured in?
Newton-metres (N·m), combining the force in newtons with the lever-arm distance in metres.
