Calculate the rotational force applied to an object around an axis or pivot point.
Last updated: March 2026 | By Summacalculator
90° produces maximum torque
Torque is the rotational equivalent of linear force. It measures the tendency of a force to rotate an object around an axis, fulcrum, or pivot point. In physics and engineering, torque (represented by the Greek letter tau, τ) is fundamental to understanding rotational motion, just as force is fundamental to linear motion. When you turn a wrench, push a door open, or spin a steering wheel, you are applying torque. The effectiveness of that torque depends not just on how hard you push, but on where you push and at what angle. A longer wrench makes it easier to loosen a bolt because the increased lever arm (radius) amplifies the rotational effect of the same applied force.
Torque is essential across countless applications: mechanical engineers design gear systems and motor shafts around torque specifications, automotive technicians use torque wrenches calibrated in Newton-meters to tighten fasteners to exact specifications (critical for engine safety and performance), aerospace engineers calculate wing torques during flight maneuvers, and roboticists must balance torque output with motor selection. The relationship between torque, force, radius, and angle is expressed mathematically as τ = r × F × sin(θ), where the sine function accounts for the directional component of the applied force. Only the perpendicular component of force (relative to the lever arm) contributes to rotation; force applied parallel to the lever arm produces zero torque.
Step 1: Enter the force magnitude in Newtons. This is the amount of push or pull being applied (e.g., 100 N for a typical hand force on a wrench).
Step 2: Enter the lever arm length in meters. This is the perpendicular distance from the axis of rotation to the point where force is applied (e.g., 0.5 m for a typical wrench length).
Step 3: Enter the angle in degrees between the force vector and the lever arm. 90 degrees (perpendicular) produces maximum torque; 0 degrees (parallel) produces no torque.
Step 4: The calculator displays torque in Newton-meters (N·m). Use this result to verify fastener tightness specifications, motor performance requirements, or structural load analysis.
A mechanic uses a wrench to loosen a bolt on an engine block. The wrench is 0.4 meters long, and the mechanic applies a perpendicular force of 150 Newtons at 90 degrees to the wrench handle. What is the torque applied to the bolt?
90 degrees (perpendicular) produces maximum torque. At this angle, sin(90°) = 1.0, so all the applied force contributes to rotation. At 0° or 180° (parallel to lever arm), sin(0°) = 0, producing zero torque. At 45°, sin(45°) ≈ 0.707, so only ~70.7% of the force contributes to rotation.
Torque is directly proportional to the lever arm length. Doubling the lever arm doubles the torque for the same force. This is why a longer wrench makes it easier to loosen a tight bolt—the increased mechanical advantage amplifies your applied force. Engineers exploit this principle in gear ratios, door handles, and crowbars.
Force causes linear (straight-line) motion and is measured in Newtons. Torque causes rotational motion and is measured in Newton-meters. A force of 100 N applied to a 1 m lever at 90° produces 100 N·m of torque. Both are fundamental quantities in physics, but torque specifically measures rotational tendency.
Torque specifications ensure fasteners (bolts, nuts, screws) are tightened to the correct tension. Under-tightening leaves connections loose and prone to failure; over-tightening strips threads or breaks fasteners. Engine bolts, wheel nuts, and pressure vessel seals all have precise torque specs measured in N·m. Professional mechanics use calibrated torque wrenches.
Torque depends on sin(θ), where θ is the angle between force and lever arm. At 90°, sin(90°) = 1.0 (maximum). At 30°, sin(30°) = 0.5 (half torque). At 0°, sin(0°) = 0 (no torque). This is why door hinges are designed to open and close perpendicular to the hinge axis—maximum torque efficiency. Applying force parallel to the lever arm wastes effort.
The direction of torque (clockwise vs. counterclockwise) depends on the direction of the applied force. If force points downward on a wrench, torque rotates counterclockwise. If force points upward, torque rotates clockwise. This is captured by the right-hand rule in physics: curl your right hand fingers in the direction of rotation; your thumb points along the torque vector direction (into or out of the page).
Yes. Negative torque simply indicates rotation in the opposite direction. For example, if a wrench produces +60 N·m (counterclockwise), applying force in the opposite direction produces −60 N·m (clockwise). In engineering, negative torque represents braking or opposing rotation, like engine braking in vehicles or resistance in motors.
Motors and engines produce rotational force (torque) at their shafts. A motor spec of 50 N·m means the motor shaft develops 50 Newton-meters of rotational force. An engine with high torque accelerates quickly and can pull heavy loads. An electric motor with high torque can lift heavy objects. Torque and rotational speed (RPM) together determine power output: Power (watts) = Torque (N·m) × Angular velocity (rad/s).