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Torque

τ=rFsin⁡θ\tau = r F \sin\theta
sig figs

Worked example: 100 N perpendicular on 0.3 m wrench → 30 N·m. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Torque fits

Your answer feeds
Rotational Power (P = τω)
In this toolkit

See also

Torque with a Lever Arm (τ = rF sin θ): Both use applied torque and lever arm length.Rotational Power (P = τω): Both use applied torque.Impulse (J = FΔt): Both use applied force.Power from Force and Velocity (P = Fv): Both use applied force.Pressure (P = F/A): Both use applied force.Work (W = Fd cos θ): Both use applied force.
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Torque explained

Fθτr

Torque is the rotational cousin of force: how hard something is twisted about a pivot. Push a 0.3 m wrench with 100 N perpendicular to the handle and you apply 0.3 × 100 × sin 90° = 30 N·m. Only the force component perpendicular to the lever arm turns the bolt: pushing along the handle (θ = 0°) accomplishes nothing, which is exactly what sin θ encodes. Archimedes understood the leverage half of this over two millennia ago: "give me a place to stand and I will move the Earth".

The practical lesson is in the trade-off: a longer wrench delivers the same torque with less force, which is why breaker bars exist and why door handles sit far from the hinges. When solving for θ, the arcsin returns only the principal branch, angles up to 90°; the supplementary angle 180° − θ produces the identical torque, so check which geometry matches your setup.

Torque formula

τ=rFsin⁡θ\tau = r F \sin\theta
Where
  • τ\tau= Torque (N·m)
  • rr= Lever arm length (m)
  • FF= Applied force (N)
  • θ\theta= Angle between arm and force (°)
In this toolkit

The rotational equations of motion

13 formulasThe angular twins of the linear equations — θ, ω and α in place of d, v and a, and torque, moment of inertia and Iω in place of F, m and p.

Revised 16 October 2026
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formula.expert. (2026, October 16). Torque Formula & Calculator. https://formula.expert/solvers/torque

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