Torque Calculator
Torque is the rotational equivalent of force, the tendency of a force to turn an object about an axis. It equals the lever arm length times the force times the sine of the angle between them, tau = r times F times sin(theta), and is measured in newton metres. Only the component of force perpendicular to the lever arm produces rotation, which is what the sine term captures: a perpendicular force gives the maximum torque, while a force along the arm gives none. This calculator takes the lever arm in metres, the force in newtons, and the angle in degrees, and returns the torque along with the perpendicular force component and the maximum possible torque for that arm and force.
Torque formula
Torque tau = r * F * sin(theta)
Perpendicular force = F * sin(theta)
Maximum torque = r * F (at theta = 90 degrees)
Torque (lb ft) = torque N m / 1.3558179483
theta is the angle between the lever arm and the force. The angle is converted from degrees to radians before taking the sine.
Torque context
- Torque is the rotational analogue of force and is measured in newton metres.
- Only the perpendicular component of force produces rotation.
- Maximum torque occurs when the force is perpendicular to the lever arm.
- Torque scales linearly with lever arm length, so longer handles turn bolts more easily.
- One pound-foot equals about 1.3558 newton metres.
Torque: frequently asked questions
What is the torque formula?
Torque is the rotational equivalent of force: tau equals the lever arm length times the force times the sine of the angle between them, tau = r times F times sin(theta). When the force is perpendicular to the lever arm the angle is 90 degrees and sin is 1, giving the maximum torque of r times F.
What are the units of torque?
In SI units torque is measured in newton metres (N m), the product of a force in newtons and a distance in metres. It has the same dimensions as energy but is a distinct quantity, so it is not expressed in joules. This calculator works in newtons and metres.
Why does the angle matter?
Only the component of force perpendicular to the lever arm produces rotation. The sine term captures this: a force applied along the lever arm (angle 0) produces no torque, while a perpendicular force (angle 90 degrees) produces the most. Angles in between scale by their sine.
What is the difference between torque and moment?
In engineering the terms are often used interchangeably; both describe a force's tendency to rotate an object about an axis. Torque usually refers to a twisting action such as on a shaft, while moment is common in statics, but the formula r times F times sin(theta) applies to both.
How do I increase torque?
Increase the force, lengthen the lever arm, or apply the force closer to perpendicular. Because torque scales linearly with the lever arm, a longer wrench or spanner produces more torque for the same force, which is why long handles loosen tight bolts.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.