# How to calculate linear force from torque

Written by jenny roberts
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Linear force has many applications from the simple turning of the crank with a bicycle pedal to the more complex like thrust produced from a propeller. Calculating the linear force is an important aspect in the design of any rotating component that is subject to torque. Torque, also known as turning or rotational force. An example of torque, is when you are tightening or loosening a nut with a spanner, you are creating a turning motion with the spanner. When you apply any kind of force, anywhere along the radius of that turning circle, in this case the radius being the length between the nut and where you hold the spanner to apply the force, here is where torque is produced.

Skill level:
Easy

• Pen
• Paper
• Calculator
• Tape measure
• Torque gauge

## Instructions

1. 1

Calculate the amount of torque produced, this is measured in newton meters, where any distances are in meters and force is in newtons, for those more used to working in kilograms, there are approximately 10 newtons to a kilogram (1nm = 0.1019 of a kilogram). On the given example above, a spanner tightening a nut, the values needed for the calculation would be the distance between the nut, and where the spanner is gripped, 250mm (10 inches) multiplied by the force applied, 100 newtons (10kg approx). So the calculation would be 0.25 x 100 = 25nm (newton meter).

2. 2

Calculate the linear force using the torque value. Force in torque, divided by the radial distance. For example: 25nm divided by 0.25 of a meter, so the force is 100 newtons of linear force.

3. 3

Use the same unit of measurement for each calculation, meters and kilograms (metric) or feet, inches and pounds, (imperial) otherwise you will have incorrect results.

#### Tips and warnings

• The equations needed to calculate torque into linear force is as follows: F = T divided by R where;
• T stands for torque in newton-meters
• F is force in newtons
• R is the radius in meters
• The anomaly in this equation is the amount of force being applied to the object to create the force. The only accurate way to measure this would be with a gauge that measures actual force applied.
• Knowing the torque value and the length of the lever makes it easy to calculate the maximum force that can be applied without causing damage to the nut.
• Never mix metric unit values with imperial unit values.

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