Enter your force, lever arm length, and the angle between them to calculate torque using the formula τ = r × F × sin(θ). Choose your preferred units for both force and distance, and the calculator returns the torque value in N·m, lbf·ft, and other common units so you can use the result directly in your application.
Torque (N·m)
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Torque (lbf·ft)
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Torque (lbf·in)
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Torque (kgf·m)
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Torque (mN·m)
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Torque is calculated using the formula τ = r × F × sin(θ), where r is the lever arm length (distance from the pivot to the point of force application), F is the applied force, and θ is the angle between the force vector and the lever arm. When the force is applied perpendicular to the lever arm (θ = 90°), sin(90°) = 1, giving maximum torque.
The SI unit of torque is the newton-meter (N·m). It represents a force of one newton applied at a perpendicular distance of one meter from the pivot point. Other common units include lbf·ft (pound-force feet) and lbf·in (pound-force inches) in the imperial system.
A 90° angle between the force vector and the lever arm produces the maximum torque, because sin(90°) = 1. Any deviation from 90° reduces the effective torque. For example, at 45° the torque is only about 70.7% of the maximum, and at 0° or 180° the torque is zero.
The dimensional formula for torque is [M¹ L² T⁻²], which is the same as energy (joules). However, torque and energy are different physical quantities — torque is a vector quantity representing rotational force, while energy is a scalar. This is why torque uses the unit N·m rather than J, even though they are dimensionally equivalent.
To convert from N·m to lbf·ft, multiply by 0.7376. For example, 60 N·m × 0.7376 = 44.26 lbf·ft. To go the other way, multiply lbf·ft by 1.3558 to get N·m. This calculator automatically displays your result in N·m, lbf·ft, lbf·in, and kgf·m simultaneously.
Force is a linear push or pull acting on an object, measured in Newtons (N) or pound-force (lbf). Torque, by contrast, is the rotational equivalent of force — it measures how effectively a force causes an object to rotate around a pivot point. Torque depends on both the magnitude of the force and the distance from the pivot (lever arm length).
The lever arm length directly multiplies the force to produce torque. A longer lever arm means the same force creates more torque. This is why a longer wrench makes it easier to tighten a bolt — you apply the same force but at a greater distance, producing higher torque. Doubling the lever arm length doubles the torque.
Torque appears in many everyday situations: tightening a bolt with a wrench, opening a door (you push near the edge, far from the hinge, to maximize torque), pedaling a bicycle, and engine output measured in lbf·ft or N·m. In automotive engineering, engine torque determines how effectively a vehicle can accelerate or tow loads.