Torque Calculator

1. Enter any two of torque, force and lever arm.
2. Leave the one you want to find blank.
3. Set the angle if the force is not at a right angle (it defaults to 90 degrees).
4. Read the result and the formula used.

Here is what each result means:

Torque is the turning effect of a force. It measures how strongly a force tends to rotate an object about a pivot, and it depends not just on how hard you push but on how far from the pivot you push and at what angle. Pushing a door near the hinge barely moves it, while the same push at the handle swings it easily.

Torque equals the force times the lever arm times the sine of the angle between them. The lever arm is the distance from the pivot to the point where the force acts. The sine term means a force aimed straight along the arm produces no turning at all, while a force at a right angle produces the most. In SI units torque is measured in newton meters.

Torque is what tightens a bolt, spins an engine and balances a see-saw. Because it grows with the length of the lever arm, a longer wrench or spanner lets you produce more torque from the same effort. This is the principle behind every lever, gear and steering wheel, and why the point and angle of a push matter as much as its size.

It rearranges one relation to solve for whichever value you leave blank, using the angle you set.

1. For torque, multiply force by lever arm by the sine of the angle.
2. For force, divide torque by the lever arm times the sine.
3. For lever arm, divide torque by the force times the sine.

At a right angle the sine is 1, so torque is simply force times lever arm. Torque builds on force; see the force calculator and work calculator.

A 50 newton force acts on a 0.3 meter lever arm at a right angle.

Calculation: T = F r sin(90) = 50 x 0.3 x 1 = 15 newton meters. To find the force needed for a torque of 20 newton meters on a 0.5 meter arm at a right angle, divide: 20 over 0.5 is 40 newtons.

One relation, rearranged for whatever you need to find.

All three come from torque equals F r sine of the angle, so any two of the values give the third once the angle is set. Because the sine of a right angle is one, most simple problems reduce to torque equals force times lever arm, which is the form taught first in school.

The angle between the force and the lever arm changes how much of the force actually turns the object.

Only the part of the force at right angles to the arm produces turning. A force aimed straight toward or away from the pivot cannot rotate the object, which is why the sine term appears. Pushing a spanner at a right angle always gives the most torque for a given effort.

The Force

A larger force gives more torque at the same lever arm and angle, in direct proportion.

The Lever Arm

A longer arm gives more torque. Doubling the distance from the pivot doubles the torque.

The Angle

Torque is greatest at a right angle and falls to zero when the force lines up with the arm.

Physics Homework

Solve for torque, force or lever arm in a rotation or balance problem.

Mechanics and DIY

Work out the force on a wrench or the setting to tighten a bolt.

Engineering

Check the turning effect on a shaft, beam or lever.

1. Forgetting the Angle

Only the part of the force at right angles turns the object. A non-right angle needs the sine term.

2. Wrong Lever Arm

Measure the distance from the pivot to where the force acts, not the length of the whole object.

3. Mixing Units

Use newtons and meters for a torque in newton meters. Convert centimeters first.

4. Confusing Torque with Force

Force is a straight push; torque is its turning effect about a pivot.

5. Zero Lever Arm or Angle

A lever arm of zero, or a force along the arm, produces no torque.

The relation is exact; only the displayed decimals are rounded.

Torque is the turning effect of a force about a pivot. It equals force times the lever arm times the sine of the angle. A 50 newton force on a 0.3 meter arm at a right angle gives 15 newton meters.

Multiply the force by the lever arm and by the sine of the angle between them. At a right angle the sine is 1, so torque is just force times the lever-arm length.

Divide the torque by the lever arm times the sine of the angle. Leave the force field blank and enter the other values to solve for it.

Because only the part of the force at right angles to the arm turns the object. The sine of the angle gives that fraction, and it is largest at 90 degrees.

The lever arm is the distance from the pivot to the point where the force is applied. A longer lever arm produces more torque from the same force.

The SI unit is the newton meter, when force is in newtons and the lever arm in meters. It is written N m and should not be confused with the joule.

No. Both use force times distance, but torque is a turning effect about a pivot and is measured in newton meters, while work is energy transferred and is measured in joules.

Use the angle between the force and the lever arm. If the force is at a right angle to the arm, use 90 degrees, which gives the maximum torque.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Torque (Wikipedia).
• Moment of a force (Maths Is Fun).
• Lever (Wikipedia).