τ = rFsin(θ)
Distance (r)
ft
Force (F)
lbf
Torque (τ)
ft-lb

# Torque Calculator

By Bogna Haponiuk
Table of contents:

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.

Bogna Haponiuk