Physical Science - Other

# How to Calculate Force from Torque

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To calculate linear force from torque, it is necessary to first understand what Torque (also known as Turning Moment) is.

When you apply a linear (tangential) force at a radial point of a circle away from center to create a rotary movement by the application of that force, a turning moment (torque) is produced.

Example: You want to tighten a screw by using a spanner.  The force is applied by you at the gripping area of the spanner tangentially to create a circular movement and this action tightens the screw.  If you multiply the force applied by the radius distance at which the force is applied, you get the Torque value, whose unit is nothing but a “force unit” x “length unit”.

In this example, assume that a force of 20 pounds is applied at the spanner gripping area which is, at a distance of, say 8 inches.

Now the torque applied to tighten the screw is 20 x 8 = 160 lb.in. (i.e. pound inches).

This example is given in imperial units.

In metric units, the unit of force is Newton and the unit of distance is meter.

So, assuming in this example of tightening of the screw, if the force applied is say 150 Newtons and the distance is 200 millimeter (= 0.2 meter, since 1 meter = 1000 millimeter) , then the torque applied is 150x0.2 = 30 NM (= Newton Meter)

For those who find it difficult to imagine the unit of force of Newtons, but familiar with kilogram force as an understandable unit, then one Newton is nothing but 0.10197 Kilogram force, or approximately one tenth of a  kilogram force.

So, if you want to know the torque in a more familiar term, in this example, the force is 15 kgf (i.e. approximately 1/10 of force in Newtons) and the distance is 200 mm, you can express torque the torque as 15 x 200 = 3000 Kgmm (Kilogram millimeter).

Now it will be obvious to you how you would calculate linear force, from a given Torque value.  To calculate it, obviously  you should know at what radial distance the force is to be calculated.

Assuming that Torque is represented by “T” the radial distance is “R”, then the force is

F = T/R (that is, Torque divided by radial distance).

Example:

A bolt specification says that it should not be tightened beyond 48 NM torque.

So, how much of linear (tangential) force can you apply to tighten the bolt, without damaging it?

If the spanner’s handle distance is say 300 mm (0.3 m ) from center, then the maximum force you can apply is

48 /0.3 = 160 Newtons (or approximately 16 kgf).

Make sure always that the unit of torque and the units of force and distance are properly matching. Else, you will get incorrect results.