Torque Calculator

About the Torque Calculator

Torque is a turning force. When you tighten a bolt, open a door, pedal a bicycle or turn a steering wheel, you are applying torque. It depends on three things: how hard you push, how far from the pivot you push, and the angle of the push. The same force does far more turning at the end of a long wrench than close to the bolt, which is why mechanics reach for a longer bar when a nut is stuck.

This torque calculator finds torque from a force, a lever arm and an angle, or works backwards to the force or the lever length a given torque needs. Forces can be in newtons, kilonewtons, pounds-force or kilograms-force; lengths in metres, centimetres, feet or inches; and torque in newton metres, pound-feet, pound-inches or kilogram-force metres. It shows the answer in all four torque units and tells you how the angle affects the result.

How to Use the Torque Calculator

Choose Find torque, Find force or Find lever length.

Enter the known values and choose their units.

Enter the angle between the lever and the force if you are not pushing at right angles; leave it at 90° for a straight, perpendicular push.

The Formula

  τ = r × F × sin θ

  τ = torque (N·m)
  r = lever arm: distance from the pivot to where the force acts (m)
  F = force (N)
  θ = angle between the lever and the force

  F = τ ÷ (r sin θ)      r = τ ÷ (F sin θ)
  1 lb·ft ≈ 1.3558 N·m      1 N·m ≈ 0.7376 lb·ft

Step-by-Step Examples

A spanner. A force of 50 N is applied at right angles to the end of a 0.3 m spanner.

  τ = 0.3 × 50 × sin 90° = 15 N·m ≈ 11.063 lb·ft

A one-foot wrench. 100 pounds-force at the end of a one-foot wrench gives 100 lb·ft, which is about 135.58 N·m.

An angled push. 100 N applied at 30° to a 0.5 m lever:

  τ = 0.5 × 100 × sin 30° = 0.5 × 100 × 0.5 = 25 N·m

A push at right angles would have given 50 N·m.

Tightening a wheel nut to 120 N·m with a 0.4 m wrench needs F = 120 ÷ 0.4 = 300 N. With 200 N of force, the wrench would need to be 120 ÷ 200 = 0.6 m long.

Why the Lever Arm Matters

Torque grows in proportion to the distance from the pivot. Double the length of a wrench and the same push produces twice the torque; halve it and you need twice the force. That is the principle of the lever that Archimedes described, and it is why door handles sit far from the hinges, why long-handled bolt cutters make short work of thick wire, and why a breaker bar is used on seized nuts. The distance that counts is the perpendicular distance from the pivot to the line of the force.

Why the Angle Matters

Only the part of the force at right angles to the lever turns it. A push straight along the lever, towards or away from the pivot, produces no torque at all. At 30° only half the force turns the lever, because sin 30° is 0.5; at 60° about 87 percent does. For the most torque from a given effort, always push at right angles to the handle. The calculator shows how much torque you would gain by doing so.

Torque in Engines and Vehicles

Car and motorcycle engines are rated by their torque as well as their power. Torque is the twisting force the engine applies to the crankshaft; power is torque multiplied by rotational speed. An engine with high torque at low revs pulls strongly from a standstill and when towing, while high power at high revs gives a high top speed. An engine producing 300 N·m delivers about 221 lb·ft. Gears multiply torque at the wheels, which is why first gear gives strong acceleration and top gear gives economical cruising.

Torque Specifications and Torque Wrenches

Manufacturers specify how tightly bolts should be done up, in N·m or lb·ft, because too little torque lets them work loose and too much can stretch or snap them or strip the threads. Wheel nuts on cars are commonly specified at around 80 to 140 N·m, while small bolts on bicycles may need only 4 to 6 N·m. A torque wrench clicks or signals when the set torque is reached. Always follow the specification for the particular part, and note whether it assumes clean, dry or lubricated threads.

Torque and Rotational Motion

Torque is to turning what force is to straight-line motion. Just as a net force makes an object accelerate, a net torque makes it spin faster or slower, and the harder an object is to spin — its moment of inertia — the less its rotation changes. When the torques on an object balance, it does not start to rotate, which is how see-saws, balances and cranes are kept stable.

Understanding Your Result

The headline is the torque, force or lever length you asked for.

The torque in other units line gives the torque in N·m, lb·ft, lb·in and kgf·m.

The force and lever line restates the force, lever arm and angle.

The worth knowing line explains the effect of the angle or lever length.

When Should You Use This Calculator?

Use it to tighten bolts to a specification without a torque wrench.

Use it for physics homework on moments and levers.

Use it to convert torque between N·m and lb·ft.

Common Mistakes

Measuring the lever from the wrong point. Measure from the centre of the bolt or pivot.

Pushing at an angle. Only the perpendicular part of the force counts.

Confusing torque with energy. Both can use N·m, but they are different quantities.

Mixing lb·ft and lb·in. One pound-foot is twelve pound-inches.