Torque Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jun 20, 2022

This torque calculator helps you find the torque arising in a rotating object. What exactly is this torque? Imagine an object that can rotate around some point called the pivot point. If you exert a force at some distance from the pivot point, then even though the force will act along a straight line, the object will begin to rotate. Continue reading if you want to learn how to calculate torque and have the torque formula explained in detail.

Torque equation

The torque (tendency of an object to rotate) depends on three different factors:

τ = rFsin(θ)

where:

  • r is the lever arm - the distance between the pivot point and the point of force application;
  • F is the force acting on the object;
  • θ is the angle between the force vector and lever arm. Typically, it is equal to 90°; and
  • τ is the torque. The units of torque are newton-meters (symbol: N·m).

Imagine that you try to open a door. The pivot point is simply where the hinges are located. The closer you are to the hinges, the larger the force you must use. If you use the handle, though, the lever arm will increase, and the door will open with less force exerted.

Do not confuse this concept with the centrifugal force - the centrifugal force is directed towards the pivot point, parallel to the lever arm. Such a force doesn't cause torque (you can check it, substituting an angle of 0° into the torque formula).

How to calculate torque

  1. Start with determining the force acting on the object. Let's assume that F = 120 N.
  2. Decide on the lever arm length. In our example, r = 0.5 m.
  3. Choose the angle between the force vector and lever arm. If it is not equal to the default 90°, open the calculator's advanced mode to change it. We will assume θ = 90°. Use advance mode to change the value of θ.
  4. Enter these values into our torque calculator. It uses the torque equation: τ = rFsin(θ) = 0.5 * 120 * sin(90°) = 60 N·m.
  5. The torque calculator can also work in reverse, finding the force or lever arm if torque is given.

If you want to learn more about the concept of force and Newton's second law, try the acceleration calculator.

FAQ

How do I calculate torque?

To calculate torque, follow the given instructions:

  1. Find out the magnitude of the applied force, F.

  2. Measure the distance, r, between the pivot point and the point the force is applied.

  3. Determine the angle θ between the direction of the applied force and the vector between the point the force is applied to the pivot point.

  4. Multiply r by F and sin θ and you will get the torque.

What is the SI unit of torque?

The SI unit of torque is newton meter or N⋅m. To express torque in imperial units we use pound-force foot or lbf·ft.

What is the dimensional formula for torque?

The magnitude of torque is equal to the product of the magnitude of the force and the lever arm. The dimensional formula for force is [M¹L¹T⁻²] while for a lever arm it is [L]. Hence, the dimensional formula for torque is [M¹L²T⁻²].

How do I convert torque to lbf·ft from N⋅m?

As we know that, 1 pound-force (lbf) = 4.448 newton (N) and 1 foot (ft) = 0.3048 meter (m). Hence, To convert torque from N⋅m to lbf·ft divide by 1.355818 or multiply by 0.737562.

Bogna Szyk
τ = rFsin(θ)
Distance (r)
ft
Force (F)
lbf
Torque (τ)
lbf·ft
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