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Lever calculator: how much force do you need?

Calculate the effort needed to lift a load with a lever, its mechanical advantage and the balance of moments around the fulcrum.

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Results

Effort needed

50.0

Mechanical advantage

4.00

Force is multiplied: you push less but further
Weight of the load (force)
200.0
Moment of the load about the fulcrum
200.0
Distance the effort must travel
8.0 in

The oldest machine

A lever is a rigid bar that turns around a fixed point, the fulcrum. Pushing on the long side of the bar lets you lift a load far heavier than you could lift by hand. Archimedes worked out the rule in the third century BC, and every crowbar, pair of pliers and wheelbarrow still relies on it.

The law of the lever

The bar balances when the turning effects, or moments, on each side of the fulcrum are equal:

Effort × effort arm = load × load arm

So the effort needed is

Effort = load × load arm ÷ effort arm

The ratio effort arm ÷ load arm is the mechanical advantage. A mechanical advantage of 4 means you push with a quarter of the load’s weight.

Worked example

You want to lift a 200 lb rock with a bar. You place a block as a fulcrum 1 ft from the rock and push 4 ft from the fulcrum:

  • Mechanical advantage: 4 ÷ 1 = 4.
  • Effort: 200 ÷ 4 = 50 lbf.
  • Moment of the load about the fulcrum: 200 lbf × 1 ft = 200 lbf·ft, balanced by 50 lbf × 4 ft.
  • To raise the rock 2 inches, your end of the bar must travel 8 inches.

That last line is the price of the advantage: a lever trades force for distance. The work you do, force times distance, is the same as the work done on the load, minus friction.

The three classes

  • First class: fulcrum between effort and load. Crowbar, seesaw, scissors.
  • Second class: load between fulcrum and effort. Wheelbarrow, nutcracker, bottle opener. The mechanical advantage is always above 1.
  • Third class: effort between fulcrum and load. Tweezers, broom, fishing rod, and most of the muscles in your body. The mechanical advantage is below 1, which gives speed and range of motion instead of force.

In every class, measure each arm from the fulcrum to the point where the force acts.

Practical tips

  • Move the fulcrum closer to the load to cut the effort; each halving of the load arm halves the force.
  • A longer bar does the same job, but it also bends more. Use a bar rated for the load.
  • The calculator ignores the bar’s own weight and friction at the fulcrum, so real effort is slightly higher.
  • Lift with your legs, keep your back straight and never put hands or feet under a raised load.

Frequently asked questions

What is the law of the lever?

Effort × effort arm = load × load arm. A lever balances when the moments on each side of the fulcrum are equal. Archimedes stated the principle in the third century BC and is credited with saying that, given a place to stand, he could move the Earth.

What are the three classes of levers?

In a first-class lever the fulcrum sits between the effort and the load, as in a seesaw or a crowbar. In a second-class lever the load is in the middle, as in a wheelbarrow or a nutcracker. In a third-class lever the effort is in the middle, as in tweezers, a fishing rod or your forearm. The formula is the same for all three.

Why does the effort have to travel further?

Work is conserved. If a lever with a mechanical advantage of 4 cuts the force to a quarter, your hand must move four times as far as the load. In the example, lifting the load 2 inches takes 8 inches of travel at the end of the bar.

What does the calculator leave out?

The weight of the bar itself and friction at the fulcrum. A heavy bar adds its own moment, and a bar that bends stores some of your effort. For heavy loads, use a bar rated for the job and keep your back straight.

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Results are estimates provided for information purposes. They do not replace professional advice.

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