Calculate force from torque and lever arm, or solve for torque, distance, or angle, with metric and imperial units for perpendicular or angled loads.
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Torque to Force Formula
The following formula is used to convert a torque to a force.
- Where F is the force
- t is the torque
- r is the distance from the pivot to the point where the force acts
- a is the angle between the position vector from the pivot and the force vector
To calculate force from torque, divide the total torque by the result of the radius times the sine of the angle of the force.
| Torque (N·m) | Force at 0.1 m (N) | Force at 0.2 m (N) | Force at 0.5 m (N) | Force at 1.0 m (N) |
|---|---|---|---|---|
| 1 | 10 | 5 | 2 | 1 |
| 2 | 20 | 10 | 4 | 2 |
| 3 | 30 | 15 | 6 | 3 |
| 5 | 50 | 25 | 10 | 5 |
| 7.5 | 75 | 37.5 | 15 | 7.5 |
| 10 | 100 | 50 | 20 | 10 |
| 12 | 120 | 60 | 24 | 12 |
| 15 | 150 | 75 | 30 | 15 |
| 20 | 200 | 100 | 40 | 20 |
| 25 | 250 | 125 | 50 | 25 |
| 30 | 300 | 150 | 60 | 30 |
| 35 | 350 | 175 | 70 | 35 |
| 40 | 400 | 200 | 80 | 40 |
| 50 | 500 | 250 | 100 | 50 |
| 60 | 600 | 300 | 120 | 60 |
| 75 | 750 | 375 | 150 | 75 |
| 100 | 1,000 | 500 | 200 | 100 |
| 150 | 1,500 | 750 | 300 | 150 |
| 200 | 2,000 | 1,000 | 400 | 200 |
| 250 | 2,500 | 1,250 | 500 | 250 |
| Assumes perpendicular force (θ = 90°, sinθ = 1): F = T / r. For other angles, F = T / (r · sinθ). Units: torque in N·m, force in N, radius in meters. | ||||
Convert Torque to Force
To find a force magnitude, divide the torque magnitude by the product of the distance from the pivot and the sine of the angle between the position and force vectors. A zero effective moment arm cannot produce positive torque and does not determine a unique force when torque is zero.
Torque to Force Example
How to convert torque to force?
- First, determine the total torque.
Measure the total torque acting on an object.
- Next, determine the radius.
Measure the radius of the lever arm that the force is acting on.
- Next, determine the angle.
Measure the angle between the position vector from the pivot and the force vector. At 90 degrees the force is perpendicular to that position vector.
- Finally, calculate the force.
Calculate the force using the formula above.
FAQ
Torque measures a force’s turning effect about a pivot: its magnitude is force times the perpendicular moment arm. For constant mass, net force equals mass times acceleration; an individual force need not equal mass times acceleration.
