Lever, Pulley & Mechanical Advantage Calculator
Work out the effort, the load or the size for the simple machines. Solve levers of all three classes, pulley systems and block and tackle, wheel and axle, ramps and screw jacks, with efficiency, and see each one drawn.
How to Use
- Pick the machine: Lever, Pulley, Wheel & axle, Ramp or Screw.
- Choose what to solve for: the effort, the load, or a size such as an arm length, the number of ropes, a radius or the ramp length.
- Enter the other values with their units. Loads can be in newtons, kilonewtons, pound-force or kilogram-force (1 kgf is the weight of 1 kg).
- For pulleys, ramps and screws, enter the efficiency if you know it; leave it at 100% for an ideal machine with no friction.
- Read the answer in its highlighted field and the first readout, with the mechanical advantage beside it, and press a preset to load an example.
Worked Example
A crowbar. The pivot is 0.15 m from an 800 N load and your hand is 1.2 m from the pivot. Moments balance when E × a = L × b, so E = 800 × 0.15 ÷ 1.2 = 100 N. The mechanical advantage is 1.2 ÷ 0.15 = 8, and the pivot has to carry both forces, 900 N.
A screw jack. One turn of a 300 mm handle moves your hand 2π × 0.3 = 1.885 m and lifts the load one 6 mm pitch, an ideal advantage of 314.2. Real jacks lose a lot to thread friction; at 30% efficiency the advantage is 94.25 and lifting 1,000 kg (9,806.65 N) takes 104.1 N, rather than the 31.22 N a frictionless screw would need.
The common mistake: counting the rope you pull. In a block and tackle only the rope sections holding up the lower block count. A tackle with 4 supporting ropes, pulled down from the top block, shows 5 rope sections; counting all 5 gives 1,961.33 ÷ (5 × 0.9) = 435.9 N for a 200 kg load, when the real pull is 1,961.33 ÷ (4 × 0.9) = 544.8 N. The rope you pull down from a fixed pulley only changes direction.
Show Work
Formulas
Archimedes, Hero and the Simple Machines
Archimedes of Syracuse proved the law of the lever in the 3rd century BC: weights balance at distances in inverse proportion to their size. Plutarch tells how he showed King Hiero what that meant by pulling a loaded ship up the beach on his own with a compound pulley, and the boast “give me a place to stand and I will move the Earth” is credited to him.
Hero of Alexandria, in the 1st century AD, described five machines for moving a weight with a small force: the lever, the wheel and axle, the pulley, the wedge and the screw. Renaissance writers added the inclined plane to make the six classical simple machines.
Around 1600 Galileo Galilei’s Le Meccaniche made the point every machine obeys: what you gain in force you lose in distance, so no machine creates work. That idea grew into the conservation of energy, and efficiency became the measure of how much of the work put in comes out.
About This Tool
This calculator covers the simple machines in one place: levers of all three classes, pulleys from a single fixed wheel to a block and tackle, the wheel and axle, the ramp and the screw. In each one you can solve for the effort, the load or a size, such as the arm length that makes a push enough or the number of ropes a lift needs. Efficiency can be added where friction matters, and every unit can be mixed. The diagram redraws each machine to your numbers.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Friction & Inclined Plane Calculator, Torque Calculator, and Work & Power Calculator.
Frequently Asked Questions
What is mechanical advantage?
It is how many times a machine multiplies your force: MA = load ÷ effort. A crowbar 1.2 m from your hand to the pivot and 0.15 m from the pivot to the load has MA = 1.2 ÷ 0.15 = 8, so a 100 N push lifts an 800 N load. Your hand moves 8 times as far as the load.
What are the three classes of lever?
In a first-class lever the pivot is in the middle (a seesaw or crowbar); in a second-class lever the load is in the middle (a wheelbarrow or nutcracker); in a third-class lever the effort is in the middle (tweezers, or your forearm). A wheelbarrow with 60 kg 0.4 m from the wheel and handles at 1.4 m needs a lift of 168.1 N, about 17.14 kg.
How much does a block and tackle reduce the pull?
Divide the load by the number of rope sections holding the lower block, then by the efficiency. A 200 kg load on 4 supporting ropes at 90% efficiency needs 1,961.33 ÷ (4 × 0.9) = 544.8 N, against 490.3 N for a perfect tackle. You pull 4 m of rope for every metre the load rises.
What is the mechanical advantage of a screw jack?
Ideally 2πR ÷ pitch, the distance your hand travels in one turn over the distance the load rises. A 300 mm handle on a 6 mm pitch thread gives 2π × 300 ÷ 6 = 314.2. At 30% efficiency that drops to 94.25, so lifting 1,000 kg takes a push of 104.1 N.
Do simple machines save work?
No. They trade force for distance, and friction only adds to the work. Pushing 100 kg up a 3 m ramp to a height of 0.6 m takes 196.1 N over 3 m, which is 588.4 J, exactly the 588.4 J it takes to lift it 0.6 m straight up with 980.7 N.
How do I use the Lever, Pulley & Mechanical Advantage Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Prying and lifting
A crowbar with an 8:1 arm ratio lets a 100 N push lift 800 N, and the pivot carries 900 N.
Hoists and rigging
Lifting 200 kg on a 4-rope block and tackle at 90% efficiency takes 544.8 N; to stay under 400 N you need 6 supporting ropes.
Winches and windlasses
A 0.4 m handle turning a 0.08 m axle has an advantage of 5: a 150 N bucket needs a 30 N push, and each turn winds 0.5027 m of rope.
Ramps
A 6 m ramp rising 0.5 m has an ideal advantage of 12, so moving 100 kg up it takes 81.72 N plus whatever the wheels lose to friction.
Car and screw jacks
A 6 mm pitch screw turned by a 300 mm handle needs 1.667 turns per centimetre of lift and 104.1 N to raise 1,000 kg at 30% efficiency.
Biology and sport
The forearm is a third-class lever: holding 5 kg 35 cm from the elbow with a muscle attached about 4 cm from it takes about 429 N of muscle force.
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