About the Torque Calculator
This torque calculator finds the turning effect of a force — the moment of force — from how hard you push, how far from the pivot you push, and the angle between the force and the lever. It uses τ = r × F × sin θ and reports the answer in newton-meters, pound-feet and pound-inches.
Use it for physics problems, for working out how long a breaker bar needs to be to reach a bolt’s torque spec, for checking a wrench setting, or for balancing a see-saw or crane arm. The chart shows how torque changes as the angle varies from 0° to 180°: it is greatest when you push at right angles to the lever.
Forces can be entered in newtons, kilonewtons or pound-force and lengths in meters, centimeters, feet or inches. The calculator assumes a rigid lever and measures the angle between the lever arm and the line of the force.
With the default inputs, the torque is 15 N·m. Change any value above to recalculate instantly.
How to use the torque calculator
- 1Enter the force and choose its unit.
- 2Enter the lever arm — the distance from the pivot to where you push.
- 3Enter the angle between the lever and the force (90° if pushing square-on).
- 4Read the torque in N·m, lb·ft and lb·in.
- 5Use the chart to see how much torque you lose at other angles.
Formula and method
Torque is the rotational equivalent of force. Only the part of the force perpendicular to the lever, F·sin θ, turns it, so torque equals the lever arm length times that perpendicular component. At 90° sin θ = 1 and you get the full r × F; at 0° or 180° the force points along the lever and produces no torque at all.
Force is converted to newtons and length to meters, giving torque in newton-meters. One pound-foot equals 1.35582 N·m (1 lbf × 0.3048 m), and one pound-foot equals 12 pound-inches.
- τ
- Torque (N·m)
- r
- Lever arm: distance from pivot to point of force (m)
- F
- Applied force (N)
- θ
- Angle between the lever arm and the force
Worked examples
50 N on a 30 cm wrench at 90°
τ = 0.3 m × 50 N × sin 90° = 15 N·m, which is about 11.06 lb·ft — a typical small-bolt torque.
100 N at 60° on a 25 cm lever
Only the perpendicular component counts: 100 × sin 60° = 86.6 N. Multiplying by 0.25 m gives 21.65 N·m instead of the 25 N·m you would get at 90°.
200 N pushing at 30° on a 0.4 m arm
sin 30° = 0.5, so τ = 0.4 × 200 × 0.5 = 40 N·m — half of the 80 N·m available if the force were at right angles.
40 lbf on a 1.5 ft breaker bar
40 lbf × 1.5 ft = 60 lb·ft, which converts to about 81.35 N·m — enough for many car wheel lug nuts.
Frequently asked questions
What is the formula for torque?+
Torque τ = r × F × sin θ, where r is the distance from the pivot, F the force and θ the angle between the lever and the force. At 90° it simplifies to τ = r × F.
How do I convert N·m to lb·ft?+
Divide newton-meters by 1.35582 to get pound-feet, or multiply lb·ft by 1.35582 to get N·m. For example, 100 N·m is about 73.76 lb·ft.
Why does a longer wrench make bolts easier to turn?+
Torque is force times lever length, so doubling the handle length halves the force you need for the same torque. That is why mechanics use breaker bars on stubborn nuts.
Is torque the same as work or energy?+
Both can be expressed in N·m, but they are different quantities. Torque is a turning force (a vector); work is energy transferred (a scalar) and is usually written in joules to avoid confusion.
At what angle is torque greatest?+
Torque is greatest when the force is perpendicular (90°) to the lever arm, because sin 90° = 1. It drops to zero when the force points straight along the lever toward or away from the pivot.