# Torque Calculator (τ = rF sinθ) Compute torque, force, or lever arm from τ = r·F·sin(θ), with the perpendicular force component shown > Canonical page: https://elysiatools.com/en/tools/torque-calculator - **Category:** Math & Numbers - **Keywords:** torque, moment of force, lever arm, force, angle, rotation, rotational, wrench, physics, mechanics, statics ## Overview Torque (moment of force) is the rotational analog of force. Equations (three-way solver, θ in degrees): - Torque: τ = r · F · sin(θ) (N·m) - Force: F = τ / (r · sin(θ)) - Lever arm: r = τ / (F · sin(θ)) Only the perpendicular component F·sinθ produces torque. Maximum torque is at θ = 90°. ## Inputs - **Solve For** (select) - **Torque (τ, N·m)** (number): leave blank when solving for torque - **Force (F, N)** (number): leave blank when solving for force - **Lever arm (r, m)** (number): leave blank when solving for lever arm - **Angle (θ, °)** (number): angle between lever arm and force (0–180) ## When to use - When designing mechanical systems, linkages, or structural joints that involve rotational forces. - When calculating the required force or wrench length needed to tighten a bolt to a specific torque specification. - When solving physics homework problems or engineering statics equations involving moments of force at non-perpendicular angles. ## How it works - Select the variable you want to solve for: Torque (τ), Force (F), or Lever arm (r). - Enter the values for the other two known variables in their respective fields (Newton-meters, Newtons, or meters). - Input the angle (θ) in degrees between the lever arm and the direction of the applied force. - Click calculate to compute the result and display the perpendicular force component (F · sinθ). ## Use cases - Determining the torque applied to a bolt when using a wrench at an angle. - Calculating the required force to lift a load using a lever of a specific length. - Finding the minimum lever arm length needed to achieve a target torque with a limited force capacity. ## Frequently asked questions ### What units are used in this calculator? Torque is measured in Newton-meters (N·m), force in Newtons (N), lever arm in meters (m), and the angle in degrees (°). ### How does the angle affect the torque? Torque is maximized at 90° where sin(90°) = 1. At 0° or 180°, no torque is generated because the force is parallel to the lever arm. ### Can I calculate the lever arm length if I know the torque and force? Yes, select 'Lever arm (r)' from the dropdown, enter the torque, force, and angle, and the tool will calculate the length. ### What is the perpendicular force component? It is the portion of the force acting at a right angle to the lever arm (F · sinθ), which is the only component that produces rotation. ### Does this calculator support angles in radians? 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