Calculate ideal and actual mechanical advantage for all six simple machines: lever, pulley, wedge, screw, wheel & axle, and inclined plane. Includes efficiency and work analysis.
Mechanical advantage (MA) quantifies how much a simple machine multiplies force: MA = Load / Effort. The six classical simple machines — lever, pulley, wedge, screw, wheel & axle, and inclined plane — all trade force for distance, and each has a different formula for calculating ideal MA. Real machines always have friction and other losses, so the actual MA is lower than the ideal.
This Mechanical Advantage Calculator covers all six simple machines with a single interface. Select a machine type, enter its geometric parameters, set the efficiency, and see both ideal and actual MA, the effort required to lift a given load, and the work input vs output. Presets demonstrate real-world examples from crowbars to screw jacks, and the reference table summarizes all six machines.
Engineering students, physics learners, and makers use this calculator to quickly size simple machines, verify homework solutions, and understand how efficiency affects real mechanical systems.
Each simple machine has its own MA formula — this calculator consolidates all six into one tool, applies efficiency corrections, and computes the actual effort needed. The visual comparison of ideal vs actual MA and the work-energy analysis make it clear where energy is lost and how much force you really need.
Mechanical Advantage: MA_ideal = (varies by machine, see table) MA_actual = MA_ideal × efficiency Effort Required: F_effort = F_load / MA_actual Velocity Ratio: VR = d_effort / d_load = MA_ideal Efficiency: η = Work_out / Work_in = MA_actual / MA_ideal Machine Formulas: Lever: d_effort / d_load Pulley: # supporting ropes Wedge: length / width Screw: 2πr / pitch Wheel & Axle: R_wheel / R_axle Inclined Plane: 1 / sin θ
Result: Ideal MA = 15, Actual MA = 12.75, Effort = 118 N
A crowbar with 0.9 m effort arm and 0.06 m load arm gives an ideal MA of 15. At 85% efficiency, the actual MA is 12.75, requiring about 118 N of effort to lift a 1500 N load — turning a heavy prying task into a one-hand job.
Renaissance scientists identified six fundamental simple machines from which all mechanical devices are composed. While modern physics recognizes only two independent types (the lever and the inclined plane — all others are variants), the six-machine classification remains the standard framework for teaching mechanical advantage and is universally used in engineering education.
Most real machines are compound — combinations of simple machines working in series. A bicycle combines wheel & axle (pedals, wheels), levers (brake handles), and pulleys (chain and sprockets). The total MA is the product of individual MAs, but the total efficiency is the product of individual efficiencies, which can result in surprisingly low overall efficiency for complex mechanisms.
Engineers optimize machine efficiency through material selection (low-friction bearings), lubrication (reducing Coulomb and viscous friction), geometry optimization (minimizing sliding contact), and precision manufacturing (reducing alignment losses). Modern CNC-machined components with ball bearings can achieve >98% efficiency per stage, enabling compact, high-performance mechanisms.
Ideal MA is the theoretical maximum based on geometry alone, assuming no friction. Actual MA accounts for real-world losses (friction, deformation) and is always lower: MA_actual = MA_ideal × efficiency.
Yes — a Class 3 lever or a speed-multiplying gear has MA < 1, meaning you apply more force but gain distance/speed. This is useful when range of motion or speed matters more than force.
No. Conservation of energy means work out ≤ work in. A machine trades force for distance (or vice versa). With friction, some input work becomes heat, so work out < work in.
The screw converts rotation over a large circumference (2πr) into linear advance of just one pitch. This large distance ratio creates very high MA (often 50–200), which is why screw jacks can lift tons with a small handle force.
Efficiency η = useful work out / total work in = (F_load × d_load) / (F_effort × d_effort). It is always ≤ 100% due to friction and other losses.
Friction is the primary factor: bearing quality, surface roughness, lubrication, and alignment. Material deformation and air resistance also contribute. Well-designed machines can exceed 90% efficiency; screws are typically 25–40% due to thread friction.