There is a simple formula to calculate the linear force from an applied torque but you first need to understand the concepts behind it. To begin with, it is necessary to know the definitions of the factors involved. Force or “Linear Force” is defined as, energy applied in a specific direction where Torque is defined as Force applied in a rotational direction. Rotational Force is another name for torque. To measure force you use either metric units or US. The most common unites are Foot Pounds or Newton Meters (Newtons).
Think of linear force as the energy you expend trying to push a box along the ground in a straight line or drawing a line from point A to point B with a pencil. You are applying force in a specific direction. Then think of torque as the energy you expend when turning the steering wheel of a large truck. You are applying force in a circle or “Rotational Direction”.
The third factor needed to complete this calculation is the moment or “Arm” of the applied rotational force. Aircraft engineers when calculating the center of gravity or center of pressure in an airframe commonly use moment. They have the zero point at or near the nose of the airframe and any distance forward of that is a negative measurement and any distance aft of that is a positive measurement.
To find the arm, make a measurement in a straight line from the spot the force is input, to the spot the force is output to a rotation. Think of this as if you were turning a bolt with a wrench that is 10 inches long. Your hand pushes on the end of the wrench and the force applied is output to torque at the other end 10 inches away. Those 10 inches is the “Arm” in this calculation.
The formula is T=FA or F=T/A where “T” equals the torque, “F” equals the force and “A” equals the arm or moment. Therefore, an example would be to torque a bolt on a cylinder head in an engine. The required torque from the manufacturer is 100 Ft. Lbs. (Foot Pounds). We can determine the force needed to apply this kind of torque by using the formula. We have a torque wrench that is 18 inches long (1.5 Feet) the formula would look like, F=100/1.5 or F=66.66 Ft. Lbs. The reverse or reciprocal of this would be T=66.66*1.5 or 100.
Another way to think of force is if you were to spin a wheel and touch the surface, you would feel your hand moved in a straight direction away from the surface of the wheel, this is torque converted to linear force at the radius of the wheel.