Simple Machine Mechanical Advantage Calculator
Calculate the mechanical advantage of levers, inclined planes, screws, pulleys, and wheel-and-axle systems.
Select a machine type to get started.
Mechanical advantage (MA) is the factor by which a simple machine multiplies force. A MA of 5 means you apply 1 N of force to move a 5 N load.
MA = Output force / Input force = Load / Effort
Formulas by machine type:
Lever: MA = effort arm length / load arm length The three classes differ in where the fulcrum, effort, and load are placed.
Inclined Plane (ramp): MA = length / height = 1/sin(θ) A gentle ramp has high MA — you push less force over a longer distance.
Screw: MA = 2π × radius / pitch The pitch is the distance the screw advances per full rotation. A finer pitch = higher MA.
Pulley: MA = number of rope segments supporting the load A single fixed pulley has MA = 1 (just changes direction). A movable pulley has MA = 2.
Wheel and Axle: MA = wheel radius / axle radius Used in steering wheels, wrenches, and door handles.
Important note: MA is the theoretical (ideal) advantage. Real machines have efficiency < 100% due to friction: Actual MA = Theoretical MA × efficiency (e.g., 80%)
The work-energy theorem ensures: input work = output work (ideal), so force × distance is conserved. High MA → more force, but less distance of movement.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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