Torque Calculator

Torque is the rotational effect of a force applied at a distance.

How the Math Works

The Torque Calculator uses the fundamental formula τ = F × r × sin(θ) to determine rotational force. This equation multiplies the applied force (F) by the lever arm length (r) and the sine of the angle (θ) between the force vector and the lever arm. When the force acts perpendicular to the lever arm (θ = 90°), sin(θ) equals 1, making torque simply force times distance. For other angles, the sine function reduces the effective torque, reflecting how pushing at an angle wastes some of your effort. The result tau (τ) represents the rotational effect in newton-meters (Nm).

Practical Applications

To use this calculator practically, first identify the applied force in newtons and measure the perpendicular distance from the rotation axis to where the force is applied. Determine the angle between the force direction and lever arm. Input these three values into the calculator to find torque. This calculation is essential for selecting appropriate fasteners, designing mechanical systems, sizing motors, and ensuring bolts and screws achieve proper tightness without over-torquing. Engineers use it to verify that machinery components can handle expected rotational loads.

Day-to-Day Use

Understanding torque helps with everyday tasks like properly tightening a car's lug nuts, assembling furniture with correct bolt tension, or using power tools effectively. When you adjust a bicycle wheel, open a jar lid, or turn a screwdriver, you're applying torque — knowing the right amount prevents stripped threads, damaged fasteners, or loose assemblies. It also explains why using a longer wrench provides more turning power and helps you choose the right tool for the job, making DIY projects more successful and saving you from costly mistakes.

Worked example

50 N at 0.3 m, 90° → 15 N·m.

FAQ