Lever Arm Torque Calculator
Find torque from perpendicular force and lever arm length.
What it does
Torque twists bolts, shafts, and doors. Pushing 100 newtons at half a meter from the pivot gives 50 newton meters. The same twist comes from 50 newtons at one meter, since only the product matters at right angles.
The tool above takes perpendicular force and arm and returns torque, small unit torque, and arm in small units. The defaults 100 N with 0.5 m match the worked example, so the page opens showing 50 N-m. Switch to imperial for pounds and feet.
The right angle form is tau = r times F. Angled pushes use r times F times sine of the angle, with 90 degrees giving sine 1. Wrenches grow torque with cheaters for the same reason: longer r at the same hand force.
Use N-m for specs and datasheets, N-cm for small fasteners, lbf-ft for US engines and lug nuts, lbf-in for small US hardware. Keep torque apart from energy: same dimensions, different physics.
This page shows the formula, one full hand checked example at 100 N on 0.5 m, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (N, m) or Imperial (lbf, ft).
- Type force square to the lever.
- Type arm from pivot to push point.
- Read Torque as the main result.
- Read small unit torque for shop wrenches.
- For angled pushes, enter the square component first.
Formula
- F
- Perpendicular force in N or lbf.
- r
- Arm in m or ft from pivot.
- tau
- Twist in N-m or lbf-ft.
Conversions use 1 lbf = 4.448221615 N and 1 ft = 0.3048 m, so 1 N-m = 0.737562 lbf-ft. For other angles multiply by sine of the angle first.
Worked example
Example: 100 N on 0.5 m
Push 100 N square at half a meter from a bolt. Find torque.
- Write F = 100 N, r = 0.5 m.
- Multiply: 100 x 0.5 = 50 N-m.
- Small: 50 x 100 = 5000 N-cm.
- Arm: 0.5 x 100 = 50 cm.
- Imperial mirror: 22.5 lbf on 1.64 ft gives 36.9 lbf-ft.
- Check: 50 x 0.737562 = 36.88 lbf-ft.
Reference table
| Push | Arm | Torque |
|---|---|---|
| 100 N | 0.5 m | 50 N-m |
| 200 N | 0.3 m | 60 N-m |
| 50 N | 1.2 m | 60 N-m |
| 22.5 lbf | 1.64 ft | 36.9 lbf-ft |
Limits
- 90 degrees only. Angled pushes need sine factor.
- Static twist only. Dynamic spin adds inertia terms.
- Rigid arm assumed. Flex bends change effective r.
- No friction model. Thread friction eats much of wrench torque.
Common mistakes
- Using diameter instead of radius for wheels.
- Mixing N with feet without converting.
- Reading N-cm as N-m, off by 100 times.
- Pushing at an angle but using full force.
- Adding torque N-m into energy joules.
Try it yourself
Quick checks. Answers sit tucked under each question.
200 N on 0.3 m?
Torque 60 N-m, 6000 N-cm, arm 30 cm.
50 N on 1.2 m?
Torque 60 N-m, 6000 N-cm, arm 120 cm.
Questions
What is torque?
Force times arm at right angle. 100 N on 0.5 m is 50 N-m.
N-m or lbf-ft?
Same twist, different units. Multiply N-m by 0.737562 for lbf-ft.
Longer wrench why?
Same hand force times longer r gives more torque.
Angled push?
Use square component: F times sine of angle, then times r.
Torque vs energy?
Same dimensions, different physics: twisting versus spending.
What is 50 N-m in lbf-ft?
About 36.88 lbf-ft.