This tool finds the torque or moment produced by a force applied at a distance from a pivot. The result is given in newton metres (N·m).

Key idea

Torque measures how much a force tends to rotate an object around a point. It depends on three things: the force, the distance from the pivot, and the angle between them.

Formula

Magnitude

Torque (τ) = r × F × sin(θ)

Where:

  • τ is torque in newton metres (N·m)
  • r is the lever arm (distance) in metres (m)
  • F is the force in newtons (N)
  • θ is the angle between r and F in degrees

Common special case

If the force is perpendicular to the lever arm, θ = 90° and sin(θ) = 1. Then τ = r × F.

How to use

  1. Enter the force in newtons (N).
  2. Enter the distance from the pivot in metres (m).
  3. Enter the angle between the force and the lever arm in degrees (use 90° if perpendicular).
  4. The calculator returns torque in newton metres (N·m).

Worked examples

Example 1 — perpendicular force

Force = 10 N, Distance = 0.5 m, Angle = 90°.

Torque = 0.5 × 10 × sin(90°) = 5 N·m.

Example 2 — angled force

Force = 20 N, Distance = 0.3 m, Angle = 30°.

sin(30°) = 0.5, so Torque = 0.3 × 20 × 0.5 = 3 N·m.

Example 3 — zero torque

If the force is applied through the pivot (r = 0) or along the lever (θ = 0°), torque = 0.

Units and meaning

  • Newton metre (N·m) is the SI unit for torque.
  • Do not confuse torque with energy. A joule equals one newton metre numerically, but torque is not energy.
  • Keep units consistent: distance in metres, force in newtons.

Common mistakes

  • Using centimetres for distance without converting to metres. Convert first.
  • Forgetting the angle or using the wrong angle. Use the angle between r and F.
  • Mixing units for force (e.g., kilograms instead of newtons). Convert mass to force using g if needed.
  • Calling torque energy. They are different concepts even if units match numerically.

FAQ

What is torque?

Torque is the turning effect of a force around a pivot. It tells how strongly the force will rotate the object.

How do I convert centimetres to metres?

Divide by 100. Example: 50 cm = 0.5 m.

Can I use mass in kilograms directly?

No. Mass is not force. Convert mass to force using F = m × g. Use g ≈ 9.81 m/s².

Why do you use sin(θ)?

Only the component of force perpendicular to the lever arm causes rotation. That component is F × sin(θ).

What if the angle is 180°?

sin(180°) = 0. The torque is zero because the force acts along the line to the pivot but in opposite direction.

Is torque a vector?

Yes. In full form torque is a vector given by the cross product τ = r × F. This page gives the scalar magnitude.

How precise should I be with angle?

Two decimals for angle are usually fine. Use more precision for tight engineering tolerances.

Can torque be negative?

Sign depends on the chosen rotation direction. Negative simply means rotation in the opposite direction.

How do I measure torque in the real world?

Use a torque wrench or sensor. For rough checks, multiply force at the handle by handle length.

When is torque used?

Common uses are bolts tightening, engines, levers, doors, and mechanical systems that rotate.

What if I need the full vector result?

Compute the cross product in 3D: τ = r × F. Use vector components for r and F.

How do I reverse a torque calculation?

If you know torque and distance, force = τ ÷ (r × sin(θ)), with proper checks for zero.