What this calculator does
A lever trades distance for force. Pushing down with a small force over a long distance lifts a large load over a short one, and the ratio between the two arms sets exactly how favourable that trade is.
Nothing is gained for free. The work done is the same on both sides, so whatever is saved in force is paid for in distance moved. That is the constraint every simple machine operates under.
The formula
At balance the load force times the load arm equals the effort force times the effort arm. Rearranging gives the effort required, and the mechanical advantage is the ratio of effort arm to load arm.
| Term | Meaning |
|---|---|
| Mechanical advantage | The factor by which the lever multiplies force, equal to the ratio of effort arm to load arm. |
| Fulcrum | The pivot point the lever turns about. |
| Moment | Force times distance from the pivot. At balance the moments on both sides are equal. |
The inputs explained
| Field | What to enter |
|---|---|
| Load (resistance) force (N) | The load force to be moved, in newtons. For a mass, multiply kilograms by 9.81. |
| Load arm (fulcrum to load) (m) | The distance from the fulcrum to the load, in metres. |
| Effort arm (fulcrum to effort) (m) | The distance from the fulcrum to where the effort is applied, in metres. A longer effort arm means less force needed. |
When to use it
Sizing a lever for a job
Knowing the load and the force available determines how long the effort arm needs to be.
Understanding a crowbar or wheelbarrow
Both are levers, differing only in where the fulcrum sits relative to the load and the effort.
Checking a balance condition
A seesaw balances when the moments match, which is this same calculation with the effort force known instead.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does a longer effort arm reduce the force needed?
The same load with the effort applied at increasing distances.
| Effort arm | Effort force required | Mechanical advantage |
|---|---|---|
| 0.6 m | 250.00 N | 2.000× |
| 1.2 m | 125.00 N | 4.000× |
| 2.4 m | 62.50 N | 8.000× |
Questions
Does a lever create energy?
No. The work done is identical on both sides: a force four times smaller has to move four times as far. Levers redistribute effort rather than reducing the total work.
What are the three classes of lever?
They differ in what sits in the middle. First class has the fulcrum between effort and load, like a seesaw. Second class has the load in the middle, like a wheelbarrow. Third class has the effort in the middle, like a fishing rod, and gives mechanical advantage below 1 in exchange for speed and range.
Why would anyone want an advantage below 1?
To gain speed and distance rather than force. Your forearm is a third-class lever: the muscle pulls hard over a short distance so the hand can move quickly over a long one, which is far more useful for throwing than raw force would be.
Does the lever's own weight matter?
This calculation ignores it, which is fine when the lever is light compared with the load. For a heavy beam its own weight adds a moment that has to be accounted for separately.
For the turning moment in a rotational context, see the torque calculator. For work and energy generally, see the work, power and efficiency calculator.