Lever Calculator
Find the effort force and mechanical advantage of a lever
Result
How it is calculated
A lever is in balance when the turning effect (moment) on both sides of the fulcrum is equal: Effort × Effort arm = Load × Load arm. The tool solves this for the effort: Effort = Load × Load arm ÷ Effort arm. The mechanical advantage is Effort arm ÷ Load arm. Each arm is the distance from the fulcrum to where the force acts, measured along the lever, and both arms must use the same length unit. The effort comes out in the same force unit as the load (newtons, pounds-force, kilograms-force) and the advantage has no unit. Arms must be above zero and the load cannot be negative. Results are rounded to two decimals. Friction and the weight of the lever itself are ignored, and the forces are assumed to act at right angles to the lever.
Worked example
You want to lift a load of 600 with a bar that has its load 0.5 from the fulcrum, while you push at 2 from the fulcrum. Effort = 600 × 0.5 ÷ 2 = 300 ÷ 2 = 150.00. Mechanical advantage = 2 ÷ 0.5 = 4.00. The lever multiplies your force by four, so you need a quarter of the load, but your end must move four times farther than the load does.
Common mistakes
- Measuring the arms from the wrong point. They must run from the fulcrum, not from the end of the bar or from the load to the effort.
- Mixing units, for example one arm in centimetres and the other in metres, which breaks the ratio.
- Swapping the two arm fields. The result is then the load multiplied by the inverse ratio: for the same bar a load arm of 2 and effort arm of 0.5 gives an advantage of 0.25 and an effort four times larger than the load.
- Entering the mass in kilograms and reading the result as newtons. The effort is in the same unit as the load you typed; multiply by about 9.81 to turn kilograms into newtons yourself.
- Ignoring that the tool assumes a perpendicular push or pull. A force applied at an angle is less effective than the result suggests.
About this calculator
A lever balances around its fulcrum according to the principle of moments — first formalized by Archimedes — where the torque applied by the effort force equals the torque needed to support the load: Effort force × Effort arm = Load force × Load arm. Rearranging gives the effort force required for a given load, while the ratio of the two arm lengths, Mechanical advantage = Effort arm / Load arm, tells you how much the lever multiplies (or reduces) force.
This exact torque-balance relationship governs everything from a crowbar prying up a nail to a see-saw, wheelbarrow, or bottle opener — first-class, second-class, and third-class levers all follow the same equation, differing only in where the fulcrum, effort, and load sit relative to each other.
Mechanical engineering students learning simple machines, tool designers positioning a fulcrum for maximum leverage, and DIYers figuring out whether a given pry bar or lever arrangement can move a heavy object all use this relationship to size the force and arm lengths needed for the job.
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