Mechanical Advantage Calculator

Mechanical advantage (MA) is the factor by which a machine multiplies your input force: MA = F_out / F_in. For an ideal (frictionless) machine it also equals the distance ratio d_in / d_out — you trade force for distance, never get energy for free. Worked example (lever): effort arm 2 m, load arm 0.5 m, so MA = 2 / 0.5 = 4. A 50 N effort then produces F_out = 50 x 4 = 200 N at the load.

Divide the effort arm by the load arm: MA = L_in / L_out, both measured from the fulcrum. Worked example: 2 m effort arm, 0.5 m load arm -> MA = 4. Class matters for direction: a class-1 lever (fulcrum between effort and load, like a crowbar) reverses direction; class-2 (load between fulcrum and effort, like a wheelbarrow) and class-3 (effort between fulcrum and load, like tweezers) keep the same direction. The formula MA = L_in / L_out holds for all three classes.

Friction, rope stretch, and deformation eat part of the work. The real relation is F_out = F_in x MA_ideal x eta, where eta is efficiency (0-1). Worked example: 50 N effort, ideal MA 4, eta = 0.85 -> F_out = 50 x 4 x 0.85 = 170 N, not 200 N. Equivalently the actual MA is 4 x 0.85 = 3.4... precisely 3.40. Enter your best efficiency estimate in the calculator; the Ideal vs Actual columns show both.

Count the rope segments supporting the moving block (including the free end if it pulls up on the load): MA = n. Worked example: n = 4, 100 N effort, eta = 0.85 -> F_out = 100 x 4 x 0.85 = 340 N. Ideal (eta = 1) with n = 6 gives 600 N from 100 N. The trade-off is rope: to lift the load 2 m with n = 4 you must pull 8 m of rope (distance ratio = n). Each sheave loses roughly 4% (eta ~0.96 per sheave); a 3-sheave lashing tackle with 80 N effort gives 80 x 3 x 0.96^3 = 212.34 N.

MA = L / h: slope length divided by vertical rise. Worked example: a 3 m ramp rising 0.6 m -> MA = 3 / 0.6 = 5, so 200 N of push up the slope lifts F_out = 200 x 5 = 1,000 N (about 101.97 kgf). The slope angle is arcsin(0.6/3) = 11.54 degrees. With rolling/sliding efficiency eta = 0.95, lifting 1,000 N needs F_in = 1,000 / (5 x 0.95) = 210.53 N. A longer, shallower ramp always means less force but a longer push.

One turn of the handle moves your hand through a circumference 2 x pi x r while the load advances one lead: MA = 2 x pi x r / lead. Worked example: handle radius r = 0.2 m, lead = 5 mm -> MA = 2 x pi x 0.2 / 0.005 = 251.33. With 50 N at the handle and a sliding-screw efficiency of 0.35: F_out = 50 x 251.33 x 0.35 = 4,398.23 N (ideal eta = 1 would be 12,566.37 N). A finer thread multiplies harder: r = 150 mm with a 2 mm lead gives MA = 471.24, turning 30 N into 5,654.87 N at eta = 0.4.

Yes — then the machine is a speed/distance multiplier instead of a force multiplier. Worked example: effort arm 0.75 m, load arm 1.5 m -> MA = 0.75 / 1.5 = 0.5, so 10 N of effort moves a 5 N load, but the load travels twice as far and twice as fast as your hand. Class-3 levers (tweezers, fishing rods, the human forearm) and overdrive gears live in this regime. The same force equations apply unchanged; the calculator handles MA < 1 in every mode.

Rearrange to F_in = F_out / (MA_ideal x eta) and use the Effort solver tab. Worked example: you must lift 1,000 N with a screw of MA 251.33 at eta = 1 -> F_in = 1,000 / 251.33 = 3.98 N at the handle. Lever check: to get 200 N out of a 4:1 lever at eta = 1 you need 200 / 4 = 50 N in — the inverse of the anchor example. Always include efficiency: ignoring it underestimates the required effort.

Honest defaults: lever and fulcrum 0.95-1.0 (pivot friction is tiny); pulley about 0.96 per sheave, so eta_total ~ 0.96^n — four sheaves give ~0.85, which is why the worked n = 4 example uses eta = 0.85; inclined plane 0.85-0.95 depending on rollers vs sliding friction and lubrication; screw: ball screw 0.85-0.95, sliding/Acme lead screw 0.3-0.5 (self-locking but lossy). When unsure, derate one step: the calculator shows ideal and actual side by side so you can see the cost of optimism.

This tool covers simple machines — levers, pulleys, ramps, screws — where a human-scale effort force is the input and geometry sets the ideal MA. Powered actuators start from pressure or motor torque instead: for hydraulic/pneumatic cylinders (F = P x A, push and pull) and electric screw actuators (F = 2 x pi x T x eta / lead), use the companion Linear Actuator Force Calculator. The screw mode here and the screw actuator there share the same physics; the difference is whether your input is hand force at a handle or motor torque at a shaft.