Simple Machines Calculator
Calculate mechanical advantage, effort force and distance for levers, pulleys, inclined planes, wheels, screws and gear trains, with friction losses accounted for separately.
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A machine trades force for distance and never creates energy
Every simple machine reduces the force needed by increasing the distance over which it acts, and the product of the two is unchanged apart from losses. Lifting 100 kilograms with a mechanical advantage of four takes a quarter of the force over four times the distance. Nothing is gained except convenience, and understanding that a machine cannot reduce the work done is the whole of the topic.
Ideal and actual mechanical advantage differ by friction
The ideal figure comes from geometry alone: the ratio of lever arms, the number of supporting rope sections, the ratio of slope length to height. The actual figure is always lower, because friction consumes some of the input. Efficiency is the ratio between them, and it varies from above 90 percent for a good pulley to below 20 percent for a screw thread, where nearly all the input becomes heat. Quoting an ideal advantage as though it were achievable is the standard error.
Screws and wedges are inclined planes in disguise
A screw is a ramp wrapped around a cylinder, and its mechanical advantage is the circumference divided by the pitch, which is why a fine thread lifts more for the same effort. The same low efficiency that wastes energy also makes a screw self-locking: friction holds the load when the effort stops, which is why a jack does not run back down and a pulley system does.
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Frequently Asked Questions
Does a machine reduce the work needed?
No. It reduces the force and increases the distance by the same factor, so the work is unchanged apart from friction losses. A machine converts a large force over a short distance into a small force over a long one.
What is the difference between ideal and actual mechanical advantage?
Ideal comes from geometry alone; actual accounts for friction and is always lower. Their ratio is the efficiency, which ranges from above 90 percent for a good pulley to below 20 percent for a screw.
Why does a fine screw thread lift more?
Because mechanical advantage is the circumference travelled by the handle divided by the pitch, so a smaller pitch means a larger ratio. The load rises more slowly for the same turning effort.
Why is a screw jack self-locking?
Because its efficiency is low, which means friction is large relative to the load. When the effort stops, friction holds the load in place. A high-efficiency pulley system does the opposite and runs back.
How does a pulley system multiply force?
By the number of rope sections supporting the moving block. Four supporting sections means each carries a quarter of the load, and the rope must be pulled four times the distance the load rises.
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How to Use
Choose a machine and enter its dimensions to find the force and distance trade.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.