Torque Calculator

Torque is the result of multiplying the lever arm length by the force acting on it, perpendicular to that arm. The full formula is τ = F × r × sin(θ), where F is the applied force, r is the lever arm (radius), and θ is the angle between the force and the lever arm — when the force is applied at a right angle (θ = 90°), sin(θ) = 1, so the formula simplifies to τ = F × r.

Torque is calculated by multiplying the applied force by the length of the lever arm and the sine of the angle between the force vector and the lever arm: τ = F · r · sin(θ). For example, a 50 N force applied at the end of a 0.3 m wrench, perpendicular to the handle (θ = 90°), produces τ = 50 × 0.3 × sin(90°) = 15 N·m. If the force isn't perpendicular, only the component of force acting at a right angle to the lever arm contributes to rotation, which is why the sine term is included.

The formula is τ = F · r · sin(θ), where τ (tau) is torque in newton-meters (N·m), F is the applied force in newtons (N), r is the length of the lever arm or radius from the pivot point to where the force is applied in meters (m), and θ is the angle between the force vector and the lever arm in degrees. When the force is applied exactly perpendicular to the lever arm (θ = 90°), sin(θ) = 1 and the formula simplifies to τ = F · r.

Torque is measured in newton-meters (N·m) in the SI system, since it is the product of force (newtons) and distance (meters). In the US customary system, torque is often measured in pound-feet (lb-ft) or inch-pounds (in-lb). One newton-meter equals approximately 0.7376 pound-feet. Despite sharing units with energy (joules = newton-meters), torque and energy are different physical quantities — torque is a vector describing rotational force, while energy is scalar.

Torque depends only on the component of force that acts perpendicular to the lever arm, because that's the component that actually causes rotation. When a force is applied at 90° to the lever arm, all of it contributes to turning, giving maximum torque. As the angle decreases toward 0° (force applied parallel to the lever arm, such as pushing or pulling straight along a wrench handle), the sine of the angle approaches zero and the torque produced drops toward zero, even though the same force is being applied.

Force is a push or pull that causes linear (straight-line) acceleration, measured in newtons. Torque is a rotational force that causes angular acceleration around a pivot point or axis, measured in newton-meters. A large force applied very close to the pivot point (small r) can produce less torque than a smaller force applied farther away, which is why longer wrenches and lever arms make it easier to loosen a tight bolt — they increase r without needing more force.

Torque wrenches are calibrated to apply a precise, specified torque (in N·m or lb-ft) to bolts and fasteners so they're tight enough to hold securely without being over-tightened and stripped or sheared. Car and motorcycle engines are rated by peak torque output, which determines how much rotational force the engine can deliver to the wheels — higher torque generally means better acceleration and towing capability. Door handles, bicycle pedals, and steering wheels are all everyday examples of levers designed to maximize torque for a given input force by increasing the lever arm length.