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Compute torque, force, or lever arm from τ = r·F·sin(θ), with the perpendicular force component shown
Details
Torque (moment of force) is the rotational analog of force.
Equations (three-way solver, θ in degrees):
Only the perpendicular component F·sinθ produces torque. Maximum torque is at θ = 90°.
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Torque Calculator is a physics and mechanics utility designed to compute torque, force, or lever arm length using the formula τ = r · F · sin(θ). By entering any three known variables and the angle of force application, you can instantly solve for the missing value and view the perpendicular force component.
Background
A technician needs to tighten a bolt to a specific torque but must pull the wrench at a 60-degree angle due to tight engine bay clearance.
Problem
Determine the torque generated when applying 50 N of force to a 0.3-meter wrench at a 60° angle.
How to use
Set 'Solve For' to Torque, enter 50 for Force, 0.3 for Lever arm, and 60 for Angle.
Outcome
The tool calculates a torque of approximately 12.99 N·m.
Background
A student is analyzing a static equilibrium problem where a torque of 20 N·m must be generated using a 0.25-meter lever arm at a perpendicular angle.
Problem
Calculate the exact force required to achieve the target torque.
How to use
Set 'Solve For' to Force, enter 20 for Torque, 0.25 for Lever arm, and 90 for Angle.
Outcome
The tool calculates that a force of 80 N is required.
Torque is measured in Newton-meters (N·m), force in Newtons (N), lever arm in meters (m), and the angle in degrees (°).
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.
Yes, select 'Lever arm (r)' from the dropdown, enter the torque, force, and angle, and the tool will calculate the length.
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.
No, the calculator expects the angle input to be in degrees (0 to 180).