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Mechanical advantage (MA) quantifies how much a simple machine multiplies an input force. A machine with MA = 5 means a 100 N effort produces a 500 N output force — but the effort must move 5 times farther than the load. This trade-off between force and distance is a direct consequence of energy conservation: machines can multiply force but cannot create energy.
This Mechanical Advantage Calculator computes both the actual mechanical advantage (AMA = output force / input force) and the ideal mechanical advantage (IMA = input distance / output distance). The ratio AMA/IMA gives the machine's efficiency, accounting for friction and other losses. These calculations apply to all six classical simple machines: levers, pulleys, inclined planes, wedges, screws, and wheel-and-axle systems. Engineers, physicists, and technicians use these metrics to design and evaluate mechanical systems from bicycle gears to hydraulic jacks.
Two definitions of mechanical advantage are used:
Actual MA (AMA): $$MA = \frac{F_{out}}{F_{in}}$$
This measures the real force multiplication, including friction losses.
Ideal MA (IMA): $$IMA = \frac{d_{in}}{d_{out}}$$
This is the theoretical maximum based on geometry — the ratio of distances moved by effort and load. Efficiency relates them: $$\eta = \frac{AMA}{IMA} \times 100\%$$. Work input is $$W_{in} = F_{in} \times d_{in}$$ and work output is $$W_{out} = F_{out} \times d_{out}$$. In an ideal (frictionless) machine, $$W_{in} = W_{out}$$ and AMA = IMA.
An MA greater than 1 means the machine amplifies force (at the cost of distance). An MA less than 1 means the machine amplifies distance/speed instead (at the cost of force). Efficiency below 100% indicates energy lost to friction, deformation, or other dissipative processes. Real machines typically achieve 30–95% efficiency depending on design and lubrication.
Inputs
Results
An ideal lever with MA = 5: 100 N effort moves 2 m to lift 500 N load by 0.4 m. Work in = work out = 200 J (100% efficient).
Inputs
Results
Pushing 300 N up a 5 m ramp to raise 980 N by 1 m. AMA = 3.27, IMA = 5, efficiency = 65.3% due to friction.
The six classical simple machines are the lever, pulley, inclined plane, wedge, screw, and wheel and axle. Each provides mechanical advantage by trading force for distance. Complex machines combine multiple simple machines.
Yes. Machines with MA < 1 sacrifice force to gain speed or distance. A baseball bat has MA < 1 at the tip — you apply more force than the bat delivers, but the tip moves much faster than your hands. Similarly, a fishing rod amplifies distance, not force.
Friction, air resistance, material deformation, and heat generation all convert some input energy into unusable forms. No real machine is perfectly frictionless. Well-lubricated machines approach but never reach 100% efficiency.
For an ideal pulley system, the MA equals the number of rope segments supporting the load. A single fixed pulley has MA = 1 (changes direction only). A single movable pulley has MA = 2. A block-and-tackle with 4 supporting segments has MA = 4.
No. Mechanical advantage multiplies force but not energy. The input work (force × distance) always equals or exceeds the output work. What you gain in force, you pay for in distance. Energy is always conserved.
The ideal MA of an inclined plane is $$IMA = \frac{L}{h}$$ where $$L$$ is the ramp length and $$h$$ is the height. A 5 m ramp to a 1 m platform has IMA = 5, meaning you need only 1/5 the force compared to lifting vertically (ignoring friction).
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