Torque Calculator

Torque describes the rotational effect of a force about a pivot or axis. A force can be large yet produce little torque if it acts close to the pivot or points along the lever arm. Conversely, the same force creates a greater turning effect when applied farther from the axis and more nearly perpendicular to the arm. The SI unit is the newton metre, written N·m, and the vector symbol is commonly the Greek letter tau. The magnitude formula is τ = Fr sin(θ). Here F is force in newtons, r is the distance from the axis to the point where the force acts, and θ is the angle between the position vector and force direction. Only the component perpendicular to the arm contributes to rotation. At 90 degrees, sine is one and torque reaches Fr. At zero or 180 degrees, the force line passes through the axis and torque is zero. Moment arm can also mean the shortest perpendicular distance from the axis to the force's line of action. If that perpendicular distance is already known, multiply it directly by force and use a 90-degree angle in this calculator. Be careful not to combine a perpendicular moment arm with the sine correction a second time. The distance entered here is the radial distance to the application point, so the angle determines its effective perpendicular component. Torque has direction as well as magnitude. In planar problems, counterclockwise torque is often positive and clockwise torque negative, although a course or engineering standard may choose another convention. This calculator preserves the sign of the entered force and of the sine function, allowing directional calculations when signed values or angles are used. For several forces, calculate each torque with a consistent sign convention and add them to obtain net torque. Torque appears in wrenches, hinges, shafts, motors, pedals, structural supports, and rotational dynamics. Static equilibrium requires the net torque and net force to be zero. In dynamics, net torque equals moment of inertia times angular acceleration for a rigid body about a fixed axis. Do not confuse torque with energy: both can be dimensionally expressed using newtons and metres, but torque is a vector-like rotational moment while work is force integrated through displacement. The calculator provides a clear ideal result for mechanics exercises, preliminary design, and checking hand calculations.