Torque to Force Calculator

This calculator solves the torque-magnitude equation for force. Enter a non-negative torque in newton metres (N·m), the distance from the pivot to the point of application in metres, and the angle between the radius vector and the force direction.

The result is the force magnitude in newtons (N) for that idealized single-force geometry. It is not a conversion between interchangeable units: the radius and angle are essential parts of the calculation.

Formula used

For one force acting at a point relative to a pivot, torque magnitude is:

τ = r × F × sin θ

Solving for force gives:

F = τ ÷ (r × sin θ)

where:

F is force magnitude in newtons;
τ is torque magnitude in newton metres;
r is the pivot-to-application distance in metres;
θ is the angle between the radius vector and the force vector.

The input uses degrees. The calculator converts degrees to radians before evaluating the sine function. The allowed angle is greater than 0° and less than 180°. At 0° or 180°, the force acts along the radius and produces no torque, so a non-zero torque cannot be solved by dividing by sin θ.

Worked example

Suppose a measured torque magnitude is 50 N·m, the application point is 0.2 m from the pivot, and the force is perpendicular to the radius:

F = 50 N·m ÷ (0.2 m × sin 90°) = 250 N

Because sin 90° = 1, a perpendicular force produces the largest torque for a given force and radius. The calculator returns 250.00 N.

For an angled case, 30 N·m at 0.3 m and 30° gives:

F = 30 ÷ (0.3 × 0.5) = 200 N

The same torque requires more force when the angle moves away from 90° because only the perpendicular component contributes to the torque magnitude.

What the result means

The output is the magnitude of a single applied force that would produce the entered torque under the stated geometry. It does not establish the direction of rotation. Direction requires the vector cross product and a sign convention or the right-hand rule.

Measure r from the chosen pivot or axis to the actual point where the force is applied. Measure θ between that radius vector and the force vector—not between the force and an unrelated surface. A wrench pulled at 90° to its handle is the simplest example; pulling partly along the handle makes sin θ smaller.

The unit N·m is used for moment of force. Although a joule can also be written from the same base dimensions, torque and energy are different physical quantities and should not be labelled interchangeably.

Accuracy and limitations

The model treats the radius, force, and angle as exact scalar magnitudes for a single force.
It does not combine multiple forces, distributed loads, couples, friction, elasticity, tool deflection, drivetrain losses, or dynamic effects.
Near 0° and 180°, small angle errors cause very large changes in the calculated force. The calculator rejects the singular endpoints, but a numerically valid result near an endpoint can still be physically unreliable.
Radius must be positive. Torque magnitude may be zero, which produces zero force when the geometry is otherwise valid.
A negative torque is directional information rather than a magnitude and is outside this calculator's input model.
Engineering design must use the correct load cases, safety factors, material limits, calibration uncertainty, and applicable standards. This result alone is not a design approval.

Sources

Editorial record

Written and manually reviewed by the SoupCalc Editorial Team. The equation, angle boundaries, zero-torque case, and worked examples were checked against the calculator implementation. Last reviewed: August 10, 2026. This page remains unavailable for indexing and advertising until all approved localizations pass review.