Torque Calculator
Use the calculator below to calculate torque using the τ = r × F × sin(θ) torque formula.
Results: Torque
Torque Formula:
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Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.
How to Calculate Torque
Torque is a measure of the rotational force applied to an object around a pivot point or axis. It describes how effectively a force causes an object to rotate, such as turning a wrench, tightening a bolt, or spinning a wheel.
You can calculate torque using a formula given the amount of force applied, the distance from the pivot point where the force is applied, and the angle between the applied force and the lever arm.
Torque Formula
The torque formula states:
τ = r × F × sin(θ)
Thus, the torque τ (in newton-meters) is equal to the distance r from the pivot point where the force is applied (in meters) times the amount of force applied F (in newtons) times the sine of the angle θ between the force and the lever arm.
For example, let’s calculate the torque when you apply 50 newtons of force to the end of an 8″ long wrench at a 90° angle.
Apply the torque formula to calculate:
τ = 8″ × 50 N × sin(90°)
To calculate the torque, you’ll need to first convert the 8″ to meters and substitute. 8 inches is equal to 0.2032 meters.
τ = 0.2032 m × 50 N × sin(90°)
Now, solve.
τ = 10.16 Nm
So, the resulting torque is 10.16 newton-meters. You can convert to pound-feet using our newton-meter to pound-feet converter.
Why the Angle Matters
The angle has a significant effect on the amount of torque produced.
- 90° produces the maximum possible torque because sin(90°) = 1.
- 0° or 180° produces no torque because the force acts directly along the lever arm, making sin(0°) = sin(180°) = 0.
- Angles between 0° and 90° produce partial torque proportional to the sine of the angle.
For this reason, wrenches and breaker bars are most effective when the applied force is perpendicular to the handle.
Factors That Affect Torque
Several factors determine the amount of torque generated:
- Greater force produces greater torque.
- A longer lever arm increases torque for the same applied force.
- A larger angle (up to 90°) increases torque because the perpendicular component of the force becomes larger.
These principles explain why long-handled tools require less effort to loosen tight fasteners.
You can also calculate torque using the amount of power applied and the speed about axis using our engine torque calculator.