Torque Calculator

Torque (moment of force) is the turning effect of a force about a pivot.

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Enter Values

Applied force F (N)

Lever-arm length / radius r

Angle between force and lever arm θ (deg)

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

Enter the applied force F in newtons and the lever-arm length (radius) r in metres from the pivot to where the force acts.
Optionally enter the angle θ between the force and the lever arm; leave it blank to assume 90° (force perpendicular to the arm, maximum torque).
Read the turning torque in N·m, with lb·ft and kgf·m equivalents and the effective perpendicular lever arm.

How it works

Torque (moment of force) is the turning effect of a force about a pivot. It is the product of the force, the distance from the pivot to the point where the force acts, and the sine of the angle between the force and the lever arm: T = F × r × sin(θ). Only the component of the force perpendicular to the arm produces turning, which is why the sin(θ) term appears — equivalently, r × sin(θ) is the perpendicular (effective) lever arm. With SI units of newtons and metres the result is in newton-metres (N·m).

When θ = 90° the force is square to the arm and torque is maximised (sin 90° = 1); as the force lines up with the arm (θ → 0° or 180°) the turning effect vanishes. The tool also reports the same torque in pound-feet (÷ 1.3558) and kilogram-force metres (÷ 9.80665) for convenience. This is the fundamental single-force moment — distinct from a bolt's tightening torque (driven by preload and thread friction) and from rotational shaft torque (derived from power and speed).

Worked example

250 N on a 0.4 m spanner, pushed square to the handle. A worker pushes with F = 250 N at the end of a spanner r = 0.4 m long, at θ = 90° (perpendicular). Torque T = 250 × 0.4 × sin(90°) = 100 N·m (≈ 73.756 lb·ft, ≈ 10.1972 kgf·m). If instead the push were at 60° to the handle, the effective lever arm drops to 0.4 × sin(60°) = 0.3464 m and the torque falls to about 86.603 N·m — a clear reason to keep the force square to the arm.

Common mistakes

Forgetting the angle: if the force is not perpendicular to the lever arm you must include sin(θ). Using θ = 90° when the real push is angled overstates the torque.
Mixing units — entering the radius in millimetres or centimetres instead of metres, or the force in kilograms-force instead of newtons. Keep F in N and r in m to get N·m (1 kgf ≈ 9.80665 N).
Confusing this basic moment with bolt tightening torque or shaft torque. This tool gives F × r × sin(θ) about a pivot, not clamp-load-based bolt torque or power-÷-speed shaft torque.

Frequently asked questions

What is the difference between this and the Bolt Torque Calculator?

This tool gives the basic turning moment of a single force at a radius from a pivot, T = F × r × sin(θ). The Bolt Torque Calculator instead works out the tightening torque needed to reach a target clamp-load (preload) in a bolt, using the nut factor / thread and head friction (T = K × d × F). They answer different questions.

Why does the angle matter?

Only the force component perpendicular to the lever arm produces torque. At 90° the whole force turns the arm (sin 90° = 1) and torque is greatest; as the force aligns with the arm the turning effect drops to zero. The sin(θ) term captures this, and r × sin(θ) is the effective lever arm shown in the results.

How do I convert the result to pound-feet?

Divide the torque in newton-metres by 1.3558179 to get pound-feet (1 lb·ft = 1.3558179 N·m). The calculator shows the lb·ft and kgf·m equivalents automatically, so 100 N·m ≈ 73.756 lb·ft ≈ 10.1972 kgf·m.

Tip: Enter any known values to calculate the remaining results.

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