Torque Calculator: Find Rotational Force Instantly

How to use the torque calculator

1. Enter the force you are applying and select its unit (newtons or pounds-force).
2. Enter the lever arm distance from the pivot point and choose meters, centimeters, feet, or inches.
3. Set the angle between the force vector and the lever arm. Use 90 degrees for a perpendicular push, which gives maximum torque.
4. Read the calculated torque instantly in newton-meters, foot-pounds, and inch-pounds.

How Torque Is Calculated

Torque is the rotational equivalent of linear force. The formula used by this torque calculator is:

τ = F × r × sin(θ)

Where F is the applied force, r is the lever arm distance from the pivot, and θ is the angle between the force direction and the lever arm. When you push exactly perpendicular to the lever (90 degrees), sin(90°) = 1, giving the maximum possible torque.

For example, if you apply 50 newtons of force at the end of a 0.3 meter wrench held perfectly perpendicular, the calculation is 50 × 0.3 × 1 = 15 N·m. If you push at a 45 degree angle instead, the effective torque drops to 50 × 0.3 × 0.7071 = 10.61 N·m.

Common Torque Unit Conversions

The standard SI unit for torque is the newton-meter (N·m). In the United States, foot-pounds (lbf·ft) and inch-pounds (lbf·in) are more common in automotive and mechanical work. Here are the exact conversion factors:

These conversions rely on exact definitions: 1 pound-force equals 4.4482216152605 newtons, and 1 foot equals exactly 0.3048 meters.

Practical Applications

Understanding rotational force matters across many fields. Mechanics use a torque calculator to verify that bolts are tightened to manufacturer specifications. Under-tightening can cause parts to loosen under vibration, while over-tightening can stretch or snap the fastener.

In physics and engineering education, calculating torque helps students understand static equilibrium, where the sum of all torques around a pivot must equal zero for an object to remain stationary. This principle governs everything from seesaws to bridge supports.

Cyclists and automotive engineers analyze torque at the crankshaft or pedals to determine how effectively power transfers through gears. A longer crank arm increases leverage, producing more torque for the same pedal force.

Why the Angle Matters

A common mistake is assuming that any force applied to a lever produces the full F × r torque. Only the component of force acting perpendicular to the lever arm contributes to rotation. The parallel component simply pushes or pulls along the lever toward or away from the pivot, creating no rotation.

This is why the sine function appears in the formula. At 0 degrees (pushing directly toward the pivot), sin(0°) = 0 and no rotation occurs. At 90 degrees, the entire force contributes to turning. At angles beyond 90 degrees, the sine value decreases again, meaning pushing past perpendicular wastes effort.

When using wrenches or levers in practice, always try to pull or push at right angles to the handle to maximize your mechanical advantage.

Torque vs. Work

Torque and mechanical work share the same base units (newton-meters), but they describe fundamentally different things. Torque is a vector quantity representing a twisting force that may or may not cause movement. Work is a scalar quantity representing energy transferred when a force moves an object through a distance.

To avoid confusion, the scientific community typically writes torque as newton-meters (N·m) and energy as joules (J), even though dimensionally they are identical. You cannot convert torque directly into energy without knowing the angular displacement: Work = Torque × angle in radians.

Worked examples

Each result below was produced by the same code the tool runs, so you can check your own numbers against them.