About this calculator
Torque is a turning force: how hard something twists. It is τ = F × d × sin θ, force times distance from the pivot, times the sine of the angle between them.
Choose what you want to find, then fill in the other two values. Leave the angle at 90° for a push at right angles to the spanner, which gives the most turning effect.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
50 N on a 0.3 m spanner
- Torque
- 15 N·m
- Force
- 50 N
- Distance from the pivot
- 0.3 m
- Torque in pound-feet
- 11.063432 lbf·ft
A force of 50 N at 0.3 m from the pivot gives 15 N·m of torque.
Show the working
- Torque is the turning effect of a force: τ = F × d × sin θ, where d is the distance from the pivot and θ the angle between the force and the lever arm.
- Torque = F × d × sin θ = 50 × 0.3 × sin(90°) = 15 N·m.
- A longer spanner means less force for the same torque. 1 N·m = 0.7376 lbf·ft.
The same push at 60 degrees
- Torque
- 12.990381 N·m
- Force
- 50 N
- Distance from the pivot
- 0.3 m
- Torque in pound-feet
- 9.581213 lbf·ft
A force of 50 N at 0.3 m from the pivot gives 12.990381 N·m of torque.
Show the working
- Torque is the turning effect of a force: τ = F × d × sin θ, where d is the distance from the pivot and θ the angle between the force and the lever arm.
- Torque = F × d × sin θ = 50 × 0.3 × sin(60°) = 12.990381 N·m.
- A longer spanner means less force for the same torque. 1 N·m = 0.7376 lbf·ft.
Force needed for 120 N·m (wheel nut) on a 0.5 m bar
- Force
- 240 N
- Torque
- 120 N·m
- Distance from the pivot
- 0.5 m
- Torque in pound-feet
- 88.507458 lbf·ft
To get 120 N·m at 0.5 m you need a force of 240 N.
Show the working
- Torque is the turning effect of a force: τ = F × d × sin θ, where d is the distance from the pivot and θ the angle between the force and the lever arm.
- Force = torque ÷ (d × sin θ) = 120 ÷ (0.5 × 1) = 240 N.
- A longer spanner means less force for the same torque. 1 N·m = 0.7376 lbf·ft.
Bar length for 15 N·m with a 30 N push
- Distance from the pivot
- 0.5 m
- Torque
- 15 N·m
- Force
- 30 N
- Torque in pound-feet
- 11.063432 lbf·ft
To get 15 N·m with 30 N you need a lever arm of 0.5 m.
Show the working
- Torque is the turning effect of a force: τ = F × d × sin θ, where d is the distance from the pivot and θ the angle between the force and the lever arm.
- Distance = torque ÷ (F × sin θ) = 15 ÷ (30 × 1) = 0.5 m.
- A longer spanner means less force for the same torque. 1 N·m = 0.7376 lbf·ft.
The formula
τ = F × d × sin θ. The torque is in newton-metres (N·m). Doubling the lever length doubles the torque for the same force, which is why a long spanner frees a stubborn nut. At 90° the sine is 1; at 0° (pushing straight along the lever) it is 0 and nothing turns.
Handy conversions
- 1 N·m = 0.7376 pound-feet (lbf·ft)
- Wheel nuts on a car: roughly 100 to 140 N·m (check your handbook)
- A weight of 10 kg hanging on a 0.5 m arm gives about 49 N·m
Balance and levers
Something balances when the clockwise and anticlockwise torques are equal: a heavy weight near the pivot balances a light one far away. The same idea explains see-saws, crowbars and wheelbarrows.
Frequently asked questions
What is torque?
The turning effect of a force about a pivot, measured in newton-metres.
How do I calculate torque?
Multiply the force by the distance from the pivot (and by sin of the angle if it is not at right angles).
What is the difference between torque and force?
Force pushes in a straight line; torque makes something rotate. The same force gives more torque at a greater distance.
How do I convert N·m to lbf·ft?
Multiply by 0.7376. The calculator shows both.
Why does the angle matter?
Only the part of the force at right angles to the lever turns it: that is F × sin θ.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.