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.