Mechanical advantage is how many times a machine multiplies your force: MA = load force ÷ effort force. The ideal mechanical advantage (IMA) ignores friction and equals effort distance ÷ load distance — for a lever, effort arm ÷ load arm. A lever with a 4:1 arm ratio lets 25 N lift 100 N.
This calculator gives the ideal and actual mechanical advantage and efficiency of levers, wheels and axles, inclined planes, wedges, pulleys and screws, using the formulas in OpenStax Physics.
How to use this calculator
- Choose the machine: lever, wheel and axle, inclined plane, wedge, pulley system or screw.
- Enter the two dimensions it asks for, in the same unit (for a pulley, just the number of supporting rope segments).
- Read the ideal mechanical advantage.
- Optional: enter the measured load force and effort force, in the same unit, to get the actual mechanical advantage and the efficiency.
How it's calculated
OpenStax Physics §9.3 starts from work, W = F × d. A simple machine can't create work; it trades force for distance. That gives two ways to write the ideal mechanical advantage:
IMA = Fr ÷ Fe = de ÷ dr
where Fr is the resistance (load) force, Fe the effort force, de the distance the effort moves and dr the distance the load moves. Friction means the real output is lower, so:
AMA = load force ÷ effort forceefficiency (%) = Wout ÷ Win × 100 = AMA ÷ IMA × 100
IMA formulas
| Machine | IMA | Example |
|---|---|---|
| Lever | effort arm ÷ load arm | 0.4 m ÷ 0.1 m = 4 |
| Wheel and axle | wheel radius ÷ axle radius | 30 cm ÷ 5 cm = 6 |
| Inclined plane | length ÷ height | 5 m ÷ 2 m = 2.5 |
| Wedge | length ÷ thickness | 10 cm ÷ 2 cm = 5 |
| Pulley | number of supporting ropes | 4 ropes = 4 |
| Screw | 2π × handle length ÷ pitch | 0.25 m, 5 mm = 314.2 |
The screw formula and efficiency = AMA ÷ IMA are derived from OpenStax's definitions (IMA = effort distance ÷ load distance; efficiency = work out ÷ work in). For the screw, one full turn moves the handle end 2π × handle length while the screw advances one pitch.
Worked examples
Lever (OpenStax Physics §9.3)
A lever with a 0.4 m effort arm and a 0.1 m load arm has IMA = 0.4 ÷ 0.1 = 4. If it takes 11 N of effort to lift a 40 N load, AMA = 40 ÷ 11 = 3.636 and efficiency = 3.636 ÷ 4 × 100 = 90.9%.
Pulley system with 4 supporting ropes
IMA = 4. Ideally, lifting a 400 N load takes 100 N of pull. If you actually need 125 N, AMA = 3.2 and efficiency is 80%. Either way, you pull 4 m of rope to raise the load 1 m.
Loading ramp
A 5 m ramp rising 2 m has IMA = 2.5. Pushing a 500 N crate up it ideally takes 200 N instead of lifting 500 N straight up — but over 5 m instead of 2 m.
Your forearm (a third-class lever)
With the biceps attached about 1.5 in from the elbow and a load in the hand 13 in away (Davis, Body Physics §6.2), IMA = 1.5 ÷ 13 = 0.115. The muscle must pull about 8.7 times the load, in exchange for moving the hand much farther and faster than the muscle contracts.
The three classes of lever
| Class | What's in the middle | Examples | Typical IMA |
|---|---|---|---|
| First | Fulcrum | Crowbar, seesaw | Above, equal to or below 1, depending on arm lengths |
| Second | Load | Nutcracker, wheelbarrow | Above 1 (effort arm is longer) |
| Third | Effort | Sugar tongs, your forearm | Below 1 (effort arm is shorter) |
Lever classes and examples follow the University of Illinois Physics Van and Davis's Body Physics. The IMA column follows directly from IMA = effort arm ÷ load arm: in a second-class lever the load sits between the fulcrum and the effort, so the effort arm is always the longer one.
Common mistakes
- Counting every rope in a pulley system. Only the segments that support the moving load count. The free end you pull down on a fixed pulley just changes direction.
- Measuring lever arms from the wrong point. Both arms are measured from the fulcrum — to where the effort is applied and to where the load sits.
- Using the horizontal run of a ramp. The incline formula uses the sloped length, not the horizontal distance.
- Mixing units. A 0.25 m handle and a 5 mm pitch must both be in meters (0.005 m) or both in millimeters.
- Getting an efficiency over 100%. That means a measurement is off — usually the effort force was read too low, or the IMA inputs are swapped.
Why mechanical advantage matters
OpenStax lists everyday simple machines: levers such as seesaws and wheelbarrows, pulleys in flag systems and construction cranes, and inclined planes, wedges, wheels and axles and screws. Every one of them makes the same trade: less force, more distance. Knowing the IMA tells you the best a design can do; measuring the AMA tells you how much friction is costing you. For another ratio-based physics tool, try the current divider calculator, which splits current in inverse proportion to resistance.
Frequently asked questions
What is the formula for mechanical advantage?
Ideal mechanical advantage (IMA) is the effort distance divided by the load distance. For a lever it is effort arm ÷ load arm; wheel and axle, wheel radius ÷ axle radius; inclined plane, length ÷ height; wedge, length ÷ thickness; pulley system, the number of rope segments supporting the load (OpenStax Physics §9.3).
What is the difference between IMA and actual MA?
Actual mechanical advantage is load force ÷ effort force, which friction makes smaller than the IMA. Efficiency is AMA ÷ IMA × 100%. In OpenStax's lever example, IMA = 4 and AMA = 3.636, so efficiency is 90.9%.
How do you calculate efficiency of a machine?
Efficiency = work output ÷ work input × 100%. Because work is force × distance and the distance ratio is the IMA, this is the same as AMA ÷ IMA × 100%. Real machines are always below 100% because some work is lost as heat through friction.
What is the mechanical advantage of a pulley?
The IMA of a pulley system equals the number of rope segments that hold up the load. With 4 supporting segments, a 400 N load needs about 100 N of effort (ignoring friction), but you pull 4 m of rope for every meter the load rises.
What is the mechanical advantage of an inclined plane?
IMA = slope length ÷ vertical height. A 5 m ramp rising 2 m has an IMA of 2.5.
What is the mechanical advantage of a screw?
IMA = 2π × handle length ÷ pitch, derived from the distance the effort travels in one turn versus the distance the screw advances. A 0.25 m handle on a 5 mm pitch screw gives 314.2.
What are the three classes of lever?
First class: the fulcrum is between effort and load (crowbar, seesaw). Second class: the load is in the middle (nutcracker, wheelbarrow). Third class: the effort is in the middle (sugar tongs), so the mechanical advantage is below 1 — your forearm, with the biceps about 1.5 in from the elbow and a load 13 in away, has an IMA of about 0.12.
Can mechanical advantage be less than 1?
Yes. An MA below 1 means you apply more force than the load, but the load moves farther and faster than your effort. Third-class levers work this way; the forearm example has an IMA of 0.12.
Does a machine reduce the work you do?
No. Simple machines reduce the force you need but increase the distance over which you apply it. Work (force × distance) stays the same in an ideal machine, and friction makes the real work input a bit larger.
What units does mechanical advantage use?
None. It is a ratio of two forces or two distances, so the units cancel. Just use the same unit for both inputs — meters and meters, or newtons and newtons.
Sources & method
- OpenStax Physics, §9.3 — simple machines (IMA formulas, work, efficiency)
- OpenStax College Physics 2e, §9.5 — simple machines (MA = Fo/Fi)
- Davis, Body Physics 2e, §6.2 — body levers (lever classes, forearm example)
- University of Illinois Physics Van — Q&A 295, classes of levers
Results are estimates for general information. Found an error? It helps everyone — see our methodology.