Lever Mechanical Advantage Calculator
Lever advantage, output force, and load travel from arms.
What it does
Levers trade force for travel at a fixed ratio. A 4 meter effort arm over a 1 meter load arm multiplies 100 N into 400 N while the load creeps a quarter of the push: 0.5 m from a 2 m stroke. Crowbars, wheelbarrows, and pliers all run this exchange.
The tool above runs both unit systems. Enter effort with both arms and the push distance, and it prints advantage, output force, and load travel. Defaults give 4:1 with 400 N out; imperial mirrors at 25 lbf with 12 ft and 3 ft arms for 100 lbf out.
OpenStax states the law for levers generally: output over input equals input arm over output arm, with a 45 kg wheelbarrow working 32.4 N at 13.6:1. Torque balances on both sides of the fulcrum, so energy is conserved across the trade.
Ratios under 1 run the exchange backward. Shovels and tweezers move loads farther and faster than the hand for less force, which suits speed over strength. Fulcrum friction keeps a real-world cut everywhere; this page stays ideal.
How to use
- Pick metric (N, m) or imperial (lbf, ft).
- Enter the effort force.
- Enter both arm lengths.
- Enter the push distance.
- Read advantage first, then output.
- Read load travel for the stroke.
Formula
- effort
- Input force: N or lbf by system.
- effort arm
- Fulcrum to effort line, same units as load arm.
- load arm
- Fulcrum to load line.
- push
- Effort travel setting load travel.
Torque balance (effort x arm = load x arm) per OpenStax simple machines. Arms share units; the ratio is unitless.
Worked example
Example: 100 N, 4:1 arms
Metric defaults: 100 N with 4 m / 1 m arms, 2 m push. Imperial mirrors in ft.
- Inputs: 100 N effort, 4 m effort arm, 1 m load arm, 2 m push.
- Advantage: 4 / 1 = 4:1.
- Output: 100 x 4 = 400 N.
- Load travel: 2 / 4 = 0.5 m.
- Torque checks: 400 = 400. Tool shows 4:1, 400 N, 0.5 m.
Reference table
| Arms | MA | Out / Travel |
|---|---|---|
| 4.0 / 1.0 m | 4.0 | 400 N / 0.25 m |
| 3.0 / 0.5 m | 6.0 | 600 N / 0.167 m |
| 1.02 / 0.075 m | 13.6 | 1360 N / 0.074 m |
| 1.0 / 2.0 m | 0.5 | 50 N / 2.0 m |
Limits
- Ideal static only. Fulcrum friction excluded.
- Straight perpendicular arms assumed.
- Dynamic and impact loading differ.
- Arm flex under heavy loads ignored.
Common mistakes
- Dividing load arm by effort arm.
- Expecting force and travel to grow together.
- Mixing arm units across the ratio.
- Forgetting friction on real levers.
- Reading shovel ratios as force gains.
Try it yourself
Quick checks. Answers sit tucked under each question.
50 N, 3 m / 0.5 m arms, 1.2 m push?
MA 3 / 0.5 = 6. Output 50 x 6 = 300 N. Travel 1.2 / 6 = 0.2 m.
200 N, 2.5 m / 0.5 m arms, 1.0 m push?
MA 2.5 / 0.5 = 5. Output 200 x 5 = 1000 N. Travel 1.0 / 5 = 0.2 m.
Questions
How is advantage figured?
Effort arm over load arm. Here 4 / 1 = 4:1.
How is output force figured?
Effort times advantage. Here 100 x 4 = 400 N.
How far does the load move?
Push over advantage. Here 2 / 4 = 0.5 m for the load.
Does torque balance check?
Yes. Torque balances: 100 x 4 equals 400 x 1 on both sides.
What does advantage under 1 mean?
Below 1, like a shovel: faster load motion for less force. Arms 1 m over 2 m give 0.5:1.
Does friction count?
No. Friction at the fulcrum keeps a cut; this page is ideal and static.
Sources
- OpenStax College Physics 9.5: Simple Machines (lever law)
- LibreTexts College Physics 9.5: Simple Machines