What is mechanical advantage?

Mechanical advantage (MA) is how many times a machine multiplies your force: output force ÷ input force. In an ideal machine it also equals the distance the effort moves ÷ the distance the load moves, because the work in equals the work out.

How do you find the mechanical advantage of a pulley system?

Count the rope segments that hold up the moving block and the load. That count is the ideal mechanical advantage. A single fixed pulley has an MA of 1: it only changes the direction of the pull.

What is the mechanical advantage of an inclined plane?

The length of the slope divided by its height. A 15 ft ramp rising 3 ft has an MA of 5, so pushing a 30 lb box up it takes about 6 lb of force, ignoring friction.

Free tool · OAR Mechanical Comprehension

Mechanical advantage calculator

Three simple machines, one idea: trade distance for force. Get the mechanical advantage and the effort needed for a pulley system, a ramp or a wheel and axle.

Pulley system

MA = supporting rope segments · effort = load ÷ MA

Result

Effort needed: 100 lb
Mechanical advantage: 4 : 1
Rope you pull: 12 ft of rope

Inclined plane (ramp)

MA = length ÷ height · effort = load × height ÷ length

Result

Effort needed: 6 lb
Mechanical advantage: 5 : 1

Wheel and axle

MA = wheel radius ÷ axle radius · effort = load × axle radius ÷ wheel radius

Result

Effort needed: 50 lb
Mechanical advantage: 6 : 1

One rule behind every simple machine

An ideal machine cannot create energy, so the work you put in equals the work you get out: effort × effort distance = load × load distance. A machine that cuts the force you need makes you push or pull over a longer distance. That ratio is the mechanical advantage.

Pulleys: with 4 rope segments holding a 400 lb load, each carries a quarter of it, so you pull 100 lb, but you pull 4 ft of rope for every foot the load rises (12 ft of rope to lift it 3 ft).
Inclined plane: pushing a 30 lb crate up a 15 ft ramp that rises 3 ft takes 6 lb (MA 5 : 1), but over 15 ft instead of a 3 ft lift.
Wheel and axle: turning a 12 in handle on a 2 in axle multiplies your force by 6, so a 300 lb load needs 50 lb.

Wedges and screws are inclined planes too: a wedge is two ramps back to back, and a screw is a ramp wrapped around a cylinder. For the remaining simple machine, see the lever calculator.

Test yourself: an OAR-style question

A 30-lb crate is pushed up a frictionless ramp that is 15 feet long and 3 feet high. What is the minimum effort force needed to push the crate up the ramp?

9 lb
6 lb
11 lb
1 lb

Show answer

B. 6 lb

For an inclined plane, effort = load × height ÷ length = 30 × 3 ÷ 15 = 6 lb.

Questions like this come up on the Mechanical Comprehension section of the OAR. The 2,604 questions in the app each come with a written explanation.

FAQ

What is mechanical advantage?: Mechanical advantage (MA) is how many times a machine multiplies your force: output force ÷ input force. In an ideal machine it also equals the distance the effort moves ÷ the distance the load moves, because the work in equals the work out.
How do you find the mechanical advantage of a pulley system?: Count the rope segments that hold up the moving block and the load. That count is the ideal mechanical advantage. A single fixed pulley has an MA of 1: it only changes the direction of the pull.
What is the mechanical advantage of an inclined plane?: The length of the slope divided by its height. A 15 ft ramp rising 3 ft has an MA of 5, so pushing a 30 lb box up it takes about 6 lb of force, ignoring friction.

Sources

Checked against these sources on October 24, 2026. Ideal machines: no friction and weightless ropes and pulleys, so real efforts are a little higher. For OAR preparation only; not affiliated with or endorsed by the U.S. Navy. Calculations run in your browser.