Mechanical Advantage Calculator
Calculate the mechanical advantage of any simple machine by comparing output force to input force. Use it to evaluate levers, pulleys, ramps, and other force-multiplying devices.
About this calculator
Mechanical advantage (MA) quantifies how much a machine multiplies an applied force. The formula is: MA = Output Force / Input Force. An MA greater than 1 means the machine amplifies force — you exert a small input force to move a large output load, as with a crowbar or a block-and-tackle pulley system. An MA less than 1 means the machine trades force for speed or distance — useful in applications like a fishing rod, where a small movement of the handle produces a larger movement of the tip. An MA exactly equal to 1 means the machine simply redirects force without amplifying it, like a single fixed pulley. Note that no machine creates energy: when MA > 1, the input must move a proportionally greater distance than the output, conserving energy (work = force × distance). Real machines always have an MA slightly lower than theoretical due to friction.
How to use
A worker uses a lever to lift a 600 N rock, pushing down with only 150 N of force. Using the formula: MA = Output Force / Input Force = 600 / 150 = 4.0. The lever provides a mechanical advantage of 4, meaning the machine multiplies the worker's force by a factor of 4. To achieve this, the input end of the lever must travel 4 times the distance that the rock moves. For example, if the rock rises 0.1 m, the worker's hand must push down 0.4 m — consistent with conservation of energy.
Frequently asked questions
What is the difference between theoretical and actual mechanical advantage?
Theoretical mechanical advantage (TMA) is calculated purely from geometry — the ratio of output to input distances or, equivalently, output to input force in a frictionless machine. Actual mechanical advantage (AMA) is the measured ratio of output force to input force in a real machine, and it is always lower than TMA because friction converts some input work into heat. The ratio of AMA to TMA gives the machine's efficiency as a percentage. A well-designed pulley block might achieve 85–90% efficiency, while a rusted or poorly lubricated mechanism could drop to 50% or lower.
How do I use mechanical advantage to choose the right pulley system for lifting heavy loads?
First determine the maximum force your workers or motor can comfortably apply (input force), then divide the load weight (output force) by that input force to find the minimum MA required. For example, a 2000 N load with a maximum input of 500 N requires an MA of at least 4. A 4-strand block-and-tackle pulley system provides a theoretical MA of 4, making it a suitable choice. Remember to account for friction losses — if the system is 80% efficient, the actual MA drops to 3.2, meaning you would need a 5-strand system to lift the load comfortably. Always include a safety factor of at least 1.5–2× for the rope or chain rating.
Why can't mechanical advantage be used to get more energy out of a machine than you put in?
Mechanical advantage amplifies force but never energy. This follows directly from the law of conservation of energy: work input must equal work output plus any friction losses. Work is force multiplied by distance, so if a machine doubles the output force (MA = 2), the input must move twice as far as the output to keep the work equal. In other words, you pay for the extra force with extra distance. A machine with MA = 4 and 100% efficiency would require the input to travel 4 metres for every 1 metre the output moves. Friction losses mean real machines always deliver less output work than input work — you can never 'win' energy from a simple machine.