How to use it
- Choose what to find: the torque, the force or the lever arm.
- Enter the two known values and pick their units.
- Enter the angle between the lever and the force: 90° when you push straight across the handle.
- Read the result, the torque in N·m and lbf·ft, the turning part of the force and the effective arm.
Formula
- Torque: τ = r × F × sin θ
- Force for a given torque: F = τ ÷ (r × sin θ)
- Arm for a given torque: r = τ ÷ (F × sin θ)
- Turning force and effective arm: F⊥ = F × sin θ, r⊥ = r × sin θ, so τ = r × F⊥ = r⊥ × F
Worked example
A 50 N push at the end of a 30 cm wrench, straight across the handle: τ = 0.3 × 50 × 1 = 15 N·m, which is 11.0634 lbf·ft.
Push the same 100 N at 30° to a 0.5 m lever: sin 30° = 0.5, so τ = 0.5 × 100 × 0.5 = 25 N·m. Only 50 N of the force turns the lever, and the effective arm is 0.25 m.
To tighten a bolt to 40 N·m with a 25 cm wrench you need F = 40 ÷ 0.25 = 160 N.
Tips
- Measure the arm from the centre of the bolt to where your hand pushes, not the full length of the tool.
- Push at right angles. Any other angle wastes part of the force.
- Use the right units. A torque spec in lbf·ft entered as N·m comes out about 26 % too low; pick the unit instead of converting by hand.