Torque Calculator

Use τ = rF sin θ and convert newton-meters to pound-feet and pound-inches.

Force

Lever arm

Angle between r and Fdegrees

—N·m

—lb·ft

—lb·in

—sin θ factor

—τ = rF sin θ. Torque is not labeled as joules even though N·m has the same dimensions.

These are idealized classical-physics calculations. Real systems can differ because of air resistance, friction, deformation, measurement uncertainty, non-constant forces, or other effects not included in the selected model.

Physics model preflight

Check the governing model before trusting the number

single-force moment about an axis

τ = rF sinθ

Reading the current native inputs…

Lever-arm magnitude is non-negative; sign/direction requires an axis convention beyond this magnitude-oriented UI. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

Torque reverse solve & geometry verification

The primary τ = rF sin θ calculator remains first. This optional layer reuses its force, lever-arm and angle values, then solves torque, required force, required lever arm, or the principal angle for a target torque while exposing the sine factor, maximum possible torque and supplementary-angle ambiguity.

Solve forTarget torqueTarget torque unit

Torque handoff evidence

Magnitude model only; rotation sign, distributed loads, friction and structural safety factors remain outside this ideal point-force calculation.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

τ = rF sinθ — single-force moment about an axis.

How to verify the result

At 90° the torque magnitude should reach rF; at 0° or 180° it should be zero for this single-force model.

Domain and assumption boundary

Lever-arm magnitude is non-negative; sign/direction requires an axis convention beyond this magnitude-oriented UI. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.

Practical guide and verification

Use the tool first, then apply these checks to verify inputs, interpret the result, and hand it off without displacing the primary workflow.

Use the angle between the lever arm and force vectors

The sine term uses the included angle between r and F, not automatically the angle drawn from a horizontal page or the orientation of a wrench. A perpendicular force uses 90 degrees and produces maximum magnitude for fixed force and radius. A force directed along the lever arm produces zero torque about the pivot even when the force itself is large.

Keep moment-arm distance distinct from straight-line distance

Torque can also be understood as force times the perpendicular moment arm. When entering r in the rF sin theta form, use the distance from the pivot to the force application point and supply the included angle. Do not also shorten r to a perpendicular distance and then multiply by sine again, because that applies the geometry correction twice.

Reverse solutions can have geometry constraints

Solving for force or lever arm requires nonzero sine of the angle. Solving for angle requires the requested torque magnitude to be no greater than r times F. Because sine is symmetric, an acute principal angle can have a supplementary angle with the same torque magnitude. Keep the physical layout and rotation direction visible instead of treating a single numeric angle as the complete vector solution.

Check units, signs, and real-system assumptions before handoff

Convert force and distance to a consistent unit basis before comparing results. The calculator reports torque magnitude; clockwise or counterclockwise sign depends on the chosen coordinate convention. Real fasteners, shafts, tools, joints, and structures can involve friction, preload, distributed forces, deformation, dynamic effects, and safety factors that are not represented by the ideal point-force model.