Mechanical Advantage Calculator
Mechanical advantage measures how much a simple machine multiplies your effort. Pick your machine (lever, pulley, screw, wedge, ramp, wheel and axle) or work straight from forces, then add an efficiency to see the real-world (actual) advantage and the effort force needed to move a given load.
Formula
Worked example
A crowbar with a 1.2 m effort arm and a 0.3 m load arm: MA = 1.2 ÷ 0.3 = 4. At 90% efficiency the actual MA is 3.6, so lifting a 1000 N rock needs about 1000 ÷ 3.6 = 278 N of effort.
What mechanical advantage means
Mechanical advantage (MA) is the factor by which a simple machine multiplies an input force. It is defined as the output force divided by the input force, or equivalently as the load divided by the effort. A value greater than one means the machine lets you move a heavier load than you could push directly, which is the whole point of levers, pulleys, gears, ramps, and screws. The trade-off, dictated by conservation of energy, is distance: a machine that doubles your force also requires you to move the input through twice the distance the load travels. Because MA is a pure ratio it has no units, so you can mix newtons with pounds-force or metres with inches as long as both values in a pair share the same unit.
A formula for every simple machine
Each classic simple machine has its own geometry-based shortcut for the ideal mechanical advantage. For a lever it is the effort arm divided by the load arm, both measured from the fulcrum, which follows from balancing torques. For a block and tackle the ideal MA equals the number of rope segments supporting the moving block. For a wheel and axle it is the wheel radius divided by the axle radius. For a ramp it is the slope length divided by the rise, equal to 1 divided by the sine of the incline angle. For a screw it is π times the effort-circle diameter divided by the thread pitch (lead). For a wedge it is the slope length divided by the width of the thick end. Pick the matching machine in this calculator and it applies the right formula automatically.
Ideal versus actual mechanical advantage
The geometry formulas give the ideal mechanical advantage (IMA), what you would get if the machine were frictionless and weightless. Real machines also have an actual mechanical advantage (AMA), measured from the forces you really observe, which is always smaller because friction, flexing, and the weight of the machine itself consume part of the input. The ratio of actual to ideal mechanical advantage is the machine efficiency. Set the efficiency below 100 percent and this calculator reports the actual MA alongside the ideal value. A well-oiled pulley system might reach 90 percent efficiency, while a rusty screw jack converts far less of your effort into useful lifting.
Solving the effort and the distance trade-off
Knowing the mechanical advantage lets you answer the practical question: how hard do I have to push to move this load? Turn on "Solve the effort for a load", enter the weight or resistance you want to move, and the calculator divides it by the (actual) mechanical advantage to give the effort force needed. The same ratio governs distance: with an MA of 4 your hand must travel four times as far as the load rises, because the machine cannot create energy, only redistribute it between force and distance. The distance multiplier output makes that trade-off explicit so you can check that the throw of your lever or the run of your rope is long enough.
How to use this calculator
Choose your machine from the menu. Forces mode takes the output (load) force and the input (effort) force directly. Each geometry mode takes the lengths, radii, counts, or angle that define that machine, with unit switches so you can enter metres, centimetres, millimetres, feet, or inches and let the tool convert. The advanced section adds an efficiency input for the real-world actual MA and a toggle to solve the effort needed for a chosen load. Defaults are set to a worked crowbar example so a sensible result appears the moment the page loads.
Mechanical advantage formula by machine
| Machine | Inputs | Ideal MA formula |
|---|---|---|
| Lever | Effort arm, load arm | effort arm ÷ load arm |
| Pulley (block and tackle) | Supporting rope segments | number of rope segments |
| Wheel and axle | Wheel radius, axle radius | wheel radius ÷ axle radius |
| Inclined plane (ramp) | Slope length, rise (or angle) | length ÷ rise = 1 ÷ sin θ |
| Screw | Effort-circle diameter, pitch | π × diameter ÷ pitch |
| Wedge | Slope length, thick-end width | length ÷ width |
Ideal (frictionless) mechanical advantage for each classic simple machine.
Frequently asked questions
What is mechanical advantage?
Mechanical advantage is the ratio of the output force a machine produces to the input force you apply. A mechanical advantage of 4 means the machine multiplies your effort fourfold, so a 100 N push delivers a 400 N load force. It is a dimensionless number because it compares two forces, and it quantifies the force-multiplying benefit of levers, pulleys, ramps, gears, and screws.
How do you calculate mechanical advantage for different machines?
Each simple machine uses a geometry shortcut. A lever uses effort arm divided by load arm. A pulley uses the number of rope segments supporting the load. A wheel and axle uses the wheel radius divided by the axle radius. A ramp uses slope length divided by rise (or 1 divided by the sine of the angle). A screw uses pi times the effort-circle diameter divided by the pitch, and a wedge uses its length divided by its width. Select the machine in this calculator and it applies the right formula.
What is the difference between ideal and actual mechanical advantage?
Ideal mechanical advantage (IMA) comes from the geometry alone and assumes no friction. Actual mechanical advantage (AMA) is measured from the real forces and is always lower because friction and the machine weight waste some input. Their ratio is the efficiency. Set an efficiency below 100 percent in this calculator and it shows the actual MA next to the ideal value.
Can mechanical advantage be less than 1?
Yes. A mechanical advantage below 1 means the input force is larger than the output force, so the machine trades force for speed or range of motion instead of multiplying force. Your forearm, a fishing rod, and a third-class lever all work this way: the muscle applies a large force over a short distance to move the hand quickly over a long arc. It is still a useful machine, just optimized for distance rather than strength.
How much effort do I need to lift a given load?
Divide the load by the mechanical advantage. With an MA of 4 a 1000 N load needs about 250 N of effort in the ideal case. Account for friction by using the actual MA instead: at 90 percent efficiency the actual MA is 3.6, so the same load needs about 278 N. Toggle "Solve the effort for a load" in this calculator to do this automatically.