Free · Rotational and periodic motion calculators 🌎

Force, Radius & Angle Torque Magnitude

Calculate the magnitude of a single force’s torque about a pivot, including its direction angle.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 10 N force applied 2 m from the pivot at an included angle of 30° produces 10 N·m of torque. At 90°, the same force produces 20 N·m.

Torque magnitude = radius × force magnitude × sin(included angle)

Worked example

Enter these known values and leave the other values blank.

Pivot-to-force radius: 2 m
Force magnitude: 10 N
Included radius-to-force angle: 30 deg

Torque magnitude: 10 N·m

Assumptions and limitations

Force and radius are positive. The included angle is between 0° and 180°, and torque magnitude is nonnegative and cannot exceed radius times force.
The angle is measured between the pivot-to-application radius vector and the force. This calculates magnitude, not clockwise/counterclockwise sign or vector components.
The angle starts locked at 90°. Unlock and clear it to solve an angle from known force, radius and torque. The inverse returns the principal angle between 0° and 90°; its supplementary angle gives the same magnitude.
At 0° or 180° the ideal torque is zero. Zero torque at a collinear angle cannot uniquely determine force or radius. Numerical evaluation can leave a tiny residual at 180°.

Common questions

When is torque largest?

For fixed positive force and radius, it is largest at 90°, when force is perpendicular to the radius.

Is radius the same as the perpendicular moment arm?

Only at 90°. The perpendicular moment arm is radius multiplied by sin(angle). Do not apply that angle factor twice.

References

Bookify requires positive force and radius, an included angle from 0° to 180°, and torque magnitude between zero and force times radius. The pound-force uses the exact international pound and standard gravity instead of the rounded captured factor. Kilogram-force centimeters use standard gravity and exactly one centimeter. Pound-force feet use the exact international pound and foot with standard gravity. Pound-force inches use the exact international pound and inch with standard gravity.

Explore rotational and periodic motion calculators 🌎 or browse all physics calculators.