Torque Calculator
Calculate torque from force and lever arm, or the force a given torque needs.
Please note: Results use idealised models — point masses, no air resistance, ideal gases and uniform materials. Real experiments deviate. Use these for study and estimation, not for engineering sign-off.
What the Torque Calculator does
Torque is the rotational equivalent of force: it measures how effectively a force twists something about a pivot. It depends on the force, the distance from the pivot, and the angle between them — which is why a longer spanner makes a stubborn bolt easier to shift.
Formula
τ = F × r × sin(θ)F = τ ÷ (r × sin(θ))r = τ ÷ (F × sin(θ))1 lbf·ft = 1.3558 N·m
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Solve for | one of 3 options | Yes | — |
| Force | number | In some modes | Shown Solve for is Torque, or Solve for is Lever arm needed. |
| Force unit | one of 5 options | In some modes | Shown Solve for is Torque, or Solve for is Lever arm needed. |
| Lever arm | number | In some modes | Shown Solve for is Torque, or Solve for is Force needed. |
| Lever arm unit | one of 9 options | In some modes | Shown Solve for is Torque, or Solve for is Force needed. |
| Torque | N·m | In some modes | Shown Solve for is Force needed, or Solve for is Lever arm needed. |
| Angle between force and lever arm | ° | Optional | 90° is a force applied perpendicular to the arm, which is the most effective. Accepts 0 or more, up to 180. |
How to use it
- Choose Solve for.
- Fill in the remaining inputs the form shows for your choice.
- Optionally add Angle between force and lever arm.
- Select Calculate.
Worked example
Pushing perpendicular with 200 N on a spanner 30 cm long.
- Force
- 200 N
- Lever arm
- 30 cm
- Angle
- 90°
τ = 200 × 0.30 × sin(90°) = 60 N·m, which is 44.25 lbf·ft.
Frequently asked questions
Why does a longer spanner work better?
Torque is force times distance, so doubling the handle length halves the force you need for the same turning effect.
What is the difference between torque and power?
Torque is turning force; power is torque times rotational speed. An engine can make big torque at low revs while producing modest power.