About the Mechanical Advantage Calculator
This mechanical advantage calculator covers all six classical simple machines — the lever, pulley, wheel and axle, inclined plane, wedge and screw. Choose a machine, enter its dimensions, and it returns the ideal mechanical advantage (IMA) from geometry, the actual mechanical advantage (AMA) once you allow for efficiency, and the effort force needed to move a given load.
It is built for physics and technology classes studying simple machines, and for practical questions such as how much force a jack, ramp, block and tackle or vice will need. Comparing machines side by side shows the trade-off they all share: a larger mechanical advantage means less force but more distance.
Ideal mechanical advantage assumes no friction. Real machines lose energy, especially screws and wedges, which often have efficiencies well below 50%. Enter an efficiency to get a realistic effort; at 100% the actual and ideal values are equal. Lengths can be in any unit as long as each pair uses the same one.
With the default inputs, the ideal mechanical advantage (ima) is 4 ×. Change any value above to recalculate instantly.
How to use the mechanical advantage calculator
- 1Pick the simple machine.
- 2Enter its dimensions — arms, radii, ramp size, wedge size, strands or thread pitch.
- 3Enter the load you need to move, in newtons.
- 4Set the efficiency (100% for an ideal machine).
- 5Read the ideal and actual mechanical advantage and the effort force.
Formula and method
Ideal mechanical advantage comes from geometry alone: it is the ratio of the distance the effort moves to the distance the load moves. For a lever that is the effort arm over the load arm; for a pulley system it is the number of rope segments holding up the moving block; for a wheel and axle, the wheel radius over the axle radius; for a ramp, the slope length over the height; for a wedge, its sloping length over its thickness; and for a screw, the circumference traced by the handle (2πR) over the thread pitch.
Friction means real machines deliver less. Actual mechanical advantage equals the ideal value times the efficiency η, and the effort needed is the load divided by the actual mechanical advantage. Because energy is conserved, the effort always travels IMA times farther than the load, whatever the efficiency.
- IMA
- Ideal mechanical advantage (no friction)
- AMA
- Actual mechanical advantage (load ÷ effort)
- η
- Efficiency as a fraction
- n
- Rope segments supporting the moving block
- p
- Screw thread pitch (advance per turn)
Worked examples
Lever with a 2 m effort arm and 0.5 m load arm
IMA = 2 ÷ 0.5 = 4. With no friction, a 1,000 N load needs 250 N of effort — about the weight of 25.5 kg — but your hand moves four times as far as the load.
Block and tackle with 4 strands at 80% efficiency
Four supporting strands give an IMA of 4. Friction in the sheaves cuts the AMA to 4 × 0.8 = 3.2, so lifting 1,000 N takes 1,000 ÷ 3.2 = 312.5 N.
Screw jack: 200 mm handle, 5 mm pitch, 30% efficient
One turn moves the handle 2π × 200 = 1,256.6 mm while the load rises 5 mm, so IMA ≈ 251.3. At 30% efficiency the AMA is about 75.4, so 1,000 N needs only about 13.3 N on the handle.
5 m ramp rising 1 m
IMA = 5 ÷ 1 = 5, so pushing a 1,000 N load up the frictionless ramp takes 200 N — but you push it 5 m to raise it 1 m.
Frequently asked questions
What is mechanical advantage?+
Mechanical advantage is the factor by which a machine multiplies the input force: load force ÷ effort force. A mechanical advantage of 5 means you can move a 500 N load with 100 N of effort, ignoring friction.
What is the difference between ideal and actual mechanical advantage?+
Ideal mechanical advantage is calculated from the machine’s dimensions and assumes no friction. Actual mechanical advantage is measured from real forces (load ÷ effort) and is always lower; the ratio AMA ÷ IMA is the efficiency.
What are the six simple machines?+
The six classical simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge and the screw. The screw is an inclined plane wrapped around a cylinder, and the wedge is a moving inclined plane.
Can mechanical advantage be less than 1?+
Yes. A class 3 lever or a wheel driven at the axle has a mechanical advantage below 1. It needs more force than the load but moves the load farther and faster, which is useful for speed and reach.
Why are screws so inefficient?+
A screw thread slides under heavy pressure, so friction is large; typical lead screws are 20–40% efficient. That friction is also useful: it stops a screw jack from unwinding under load.