Torque Calculator
Torque (N·m)100.0000
Force (N)50.0000
Lever Arm (m)2.0000
The Torque Calculator works out the turning effect of a force about a pivot using τ = F × r × sin(θ). Choose whether to solve for torque, the applied force, or the lever-arm length, and the tool rearranges the equation for you. The angle θ between the force and the moment arm is included, so a force pushing straight along the arm produces no torque while a perpendicular force produces the maximum.
Formula
τ = F × r × sin(θ)
- τ
- Torque, the moment of force (newton-metres)
- F
- Magnitude of the applied force (newtons)
- r
- Lever arm — distance from pivot to force (metres)
- θ
- Angle between the force and the lever arm (degrees)
How it works
- Pick the variable to solve for: torque, force, or lever arm (the moment-arm distance from the pivot).
- Enter the two known quantities plus the angle θ between the force direction and the lever arm (90° for a perpendicular push).
- The calculator evaluates τ = F × r × sin(θ), or the rearranged form, and reports the result in newton-metres or the matching unit.
Worked example
A 50 N force applied 2 m from a bolt, perpendicular to the wrench.
- F = 50 N, r = 2 m, θ = 90° so sin(θ) = 1.
- τ = 50 × 2 × sin(90°).
- τ = 50 × 2 × 1 = 100 N·m.
Torque = 100 N·m.
Frequently asked questions
- Why does the angle matter for torque?
- Only the component of force perpendicular to the lever arm twists the object. The sin(θ) term captures this: a perpendicular force (θ = 90°) gives full torque, while a force aimed straight along the arm (θ = 0°) gives zero.
- What units does the calculator use?
- Torque is reported in newton-metres (N·m) when force is in newtons and the lever arm is in metres. The same equation works in any consistent unit system, such as pound-feet, as long as you keep inputs consistent.
- Is torque the same as the moment of a force?
- Yes. In statics and mechanics "moment of a force" and "torque" describe the same quantity — the tendency of a force to rotate a body about a point or axis.
- How is this different from a gear-ratio calculator?
- A gear-ratio calculator multiplies an input torque by the ratio of gear teeth to find output torque and speed. This tool computes torque directly from a force and lever arm using τ = F × r × sin(θ).