Simple Machine Mechanical Advantage Calculator

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, so 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 gives more force but less distance of movement.

Nothing is free, and the distance is what you pay with

This is the part people skip. A machine with MA of 10 lets you lift ten times the load, and every centimetre the load rises costs you ten centimetres of pull. Energy in equals energy out. A car jack with MA around 50 lifts a tonne on a comfortable handle force, and that is exactly why you pump it thirty times to gain a few centimetres of clearance.

Where the trade becomes awkward is speed. A high-MA winch is slow by construction, so if you need both force and speed you need a bigger power source, not a cleverer machine.

Efficiency is where the theory leaks

The figures above are ideal. Real machines lose energy to friction, and the losses are not evenly spread: a good pulley block runs at 90% or better per sheave, but stack four sheaves and the compounding leaves you nearer 65%. A screw is worse again. A typical square-thread screw jack converts perhaps 30 to 40% of the input work, with the rest going to heat in the threads.

That inefficiency is not always a fault. A screw jack with 40% efficiency is self-locking: the friction that wastes your effort on the way up is also what stops the load driving the screw backwards when you let go. An ideal frictionless jack would drop the car the moment you released the handle. Multiply the ideal figure by a realistic efficiency before sizing anything that matters.