Couple and Torque Calculator

Torque is calculated using the formula τ = r × F × sin(θ), where r is the lever arm (distance from pivot to force application point), F is the applied force, and θ is the angle between the force vector and the lever arm. For maximum torque, apply force at 90° to the lever arm. For example, a 120 N force applied at 0.5 m with a 90° angle produces 60 N·m of torque.

The SI unit of torque is the Newton-meter (N·m). It represents the product of a force in Newtons and a distance in meters. Although dimensionally equivalent to Joules (the unit of energy), N·m is used specifically for torque to distinguish rotational tendency from energy.

The dimensional formula for torque is [M¹ L² T⁻²], where M is mass, L is length, and T is time. This is derived from the product of force ([M L T⁻²]) and distance ([L]), giving [M L² T⁻²]. While this matches the dimensions of energy, torque is a vector quantity representing rotational tendency, not work done.

To convert Newton-meters to pound-force feet, multiply the N·m value by 0.7376. For example, 60 N·m × 0.7376 ≈ 44.26 lbf·ft. Conversely, to go from lbf·ft back to N·m, multiply by 1.3558. This calculator automatically shows the torque in all common units simultaneously.

A 90° angle between the force vector and the lever arm gives the maximum torque, because sin(90°) = 1. At any other angle, the effective component of force acting perpendicularly to the lever arm is reduced. For instance, at 30°, only sin(30°) = 0.5 of the force contributes to torque, meaning the torque is halved compared to applying the same force at 90°.

A couple in mechanics is a pair of equal, opposite, and parallel forces separated by a perpendicular distance (called the moment arm). Unlike a single force, a couple produces pure rotation with no net translational force. The torque (moment) of a couple is calculated as the product of one of the forces and the perpendicular distance between them: τ = F × d.

Torque is the rotational tendency produced by a single force acting at a distance from a pivot point, while a couple consists of two equal and opposite forces producing pure rotation. The key difference is that a couple's torque is the same about any point in the plane, making it a 'free vector,' whereas regular torque is measured relative to a specific pivot point.

Torque appears in countless everyday situations: opening a door (force applied at the handle creates torque about the hinge), tightening a bolt with a wrench (longer wrench = more torque for the same force), a seesaw (children's weights at different distances create torques about the pivot), and car engines (rated in N·m or lbf·ft to describe their rotational power output).