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Mechanical Advantage Calculator

Physics

Forces and losses

Lever

Force multiplier

Class 1 — fulcrum between effort and load

Ideal MA
4
Actual MA
4
Efficiency
100 %
Velocity ratio
4
Effort force
75 N
Load force
300 N
Effort travels
0.6 m
Load travels
0.15 m
fulcrumeffortloadeffort armload arm

Ideal against actual

IMA 4

AMA 4

The gap is the friction penalty — efficiency 100 %. High — very little work is lost.

Where the work goes

Work in 45 J (33.1903 ft·lb)

Useful work out 45 J

Lost to friction 0 J

Force in every unit

ForceNkNkgflbf
Effort750.0757.647916.8607
Load3000.330.591567.4427

Cross-checks

Each quantity is computed a second, independent way. Agreement is the best guard against an arithmetic slip.

CheckRoute ARoute BAgree
EfficiencyAMA ÷ IMA = 1 W_out ÷ W_in = 1
Agree
Torque balanceF_effort(ideal) × effort arm = 180 N·mF_load × load arm = 180 N·m
Agree
Ideal work balanceF_effort(ideal) × d_effort = 45 JF_load × d_load = 45 J
Agree
StepFormulaSubstitutionResult
Ideal mechanical advantageIMA = effort arm ÷ load armIMA = 2.4 m ÷ 0.6 mIMA = 4
Ideal effortF_effort(ideal) = F_load ÷ IMAF_effort(ideal) = 300 N ÷ 475 N
Velocity ratioVR = d_effort ÷ d_load = IMAd_effort = 0.15 m × 40.6 m
Work outputW_out = F_load × d_loadW_out = 300 N × 0.15 m45 J
Work inputW_in = F_effort × d_effortW_in = 75 N × 0.6 m45 J
Torque balanceτ_effort = τ_load75 N × 2.4 m vs 300 N × 0.6 m180 N·m = 180 N·m

About This Tool

Mechanical Advantage Calculator – Simple Machines, Effort and Efficiency

Mechanical advantage is the factor by which a machine multiplies the force you put into it. Push a 200 kg crate straight up and you fight its full weight; roll it up a five-metre ramp that rises a metre and a quarter and you only fight a quarter of it. Nothing is created in that bargain. The machine simply trades force for distance under the rule that governs every one of them, F_effort × d_effort = F_load × d_load. This calculator covers all six classical simple machines — lever, pulley system, wheel and axle, inclined plane, wedge and screw — plus compound machines built by chaining them together.

Ideal advantage comes from geometry alone

The ideal mechanical advantage (IMA) is what a frictionless version of the machine would deliver, and it can be read straight off the dimensions. For a lever it is effort arm ÷ load arm; for a pulley system it is the number of rope strands supporting the movable block; for a wheel and axle it is R ÷ r; for a ramp it is L ÷ h, which is the same statement as 1 ÷ sin θ; for a wedge it is L ÷ t; and for a screw it is 2πR ÷ P. A crowbar with a 2.4 m effort arm against a 0.6 m load arm has an IMA of 4, so a 300 N load yields under 75 N of effort — and the torques balance at 180 N·m on both sides.

Actual advantage comes from measured force

The actual mechanical advantage (AMA) is simply F_load ÷ F_effort with real forces on a real machine. It is always smaller than the IMA, because friction takes its cut. The ratio between the two is the efficiency: η = AMA ÷ IMA = W_out ÷ W_in. A block and tackle with four supporting strands has an IMA of 4, but at 85 % efficiency lifting 800 N costs 200 ÷ 0.85 = 235.29 N of pull rather than 200 N, giving an AMA of 3.4. Check it the other way and the numbers close: the load rises 0.5 m for 400 J of output while you haul 2 m of rope for 470.59 J of input, and 400 ÷ 470.59 is 0.85 again.

AMA can never exceed IMA
If your measurements imply an actual advantage larger than the geometry allows, the measurement is wrong — a machine cannot beat its own shape. Usually the effort force was read at the wrong point, or friction has been subtracted twice. The calculator flags this case explicitly rather than quietly reporting an efficiency above 100 %.

Advantage below 1 is a feature, not a fault

A Class 3 lever puts the effort between the fulcrum and the load, so the effort arm is the shorter one and the advantage drops below 1. Your forearm is the standard example: the biceps inserts about 0.05 m from the elbow while the hand sits 0.35 m out, giving an MA of 0.1429. Holding 50 N in your palm therefore costs 350 N of muscle tension. What you buy is speed and range — a small, strong contraction near the joint sweeps the hand a long way, quickly. Tweezers, fishing rods and the human jaw all make the same trade.

Friction, ramps and why screws leak energy

When a coefficient of friction is known, efficiency follows from first principles rather than from a guess. On a ramp the useful component of weight is W·sin θ while friction adds μ·W·cos θ, so η = sin θ ÷ (sin θ + μ·cos θ). A 5 m ramp rising 1.25 m sits at 14.4775°, and at μ = 0.20 it runs at only 56.35 % efficiency: a 200 kg crate needs 870.14 N to push rather than the ideal 490.33 N. Screws are worse still. A jackscrew with a 0.40 m handle and a 5 mm lead has an IMA of 502.65, but the effort travels 2.51 m of circumference for every 5 mm of lift, sliding thread on thread the whole way. At 30 % efficiency a 120 N push still delivers 18.1 kN — enormous, yet most of the work became heat.

Compound machines multiply both ways

Chain machines in series and the ideal advantages multiply — but so do the efficiencies. Two stages of IMA 4 give a total IMA of 16, and two stages at 85 % give 0.85 × 0.85 = 0.7225, or 72.25 %. A 50 N effort therefore delivers 578 N rather than the ideal 800 N. Losses compound rather than average, which is why practical hoists and gear trains use the fewest stages that will do the job.

Count strands, not wheels
A pulley system's advantage equals the number of rope segments that actually support the movable block. Two double blocks contain four sheaves and give an IMA of 4 — but the count comes from the four supporting strands, not from the four wheels. Counting wheels is the most common mistake in pulley problems.

Whichever machine you choose, the calculator reports the IMA, the AMA, the efficiency, the required effort or delivered load, the velocity ratio and the full work ledger, then verifies the answer a second way through torque balance or conservation of work. When both routes agree, the result is sound.

Frequently Asked Questions

Is the Mechanical Advantage Calculator free?

Yes, Mechanical Advantage Calculator is totally free :)

Can I use the Mechanical Advantage Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Mechanical Advantage Calculator?

Yes, any data related to Mechanical Advantage Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

How does this mechanical advantage calculator work?

Pick one of the six classical simple machines — lever, pulley, wheel and axle, inclined plane, wedge or screw — or build a compound machine from several stages. Enter its geometry and the calculator returns the ideal mechanical advantage (IMA) from that geometry alone, then applies either a stated efficiency, a measured counterpart force, or a coefficient of friction to give the actual mechanical advantage (AMA) and the effort or load force in your chosen unit. Every result comes with a step-by-step derivation and a cross-check panel that computes the same answer a second way, through the work ledger, so you can see the two routes agree.

What is the difference between ideal and actual mechanical advantage?

IMA comes from geometry and assumes no friction: it is the effort arm over the load arm, the number of supporting rope strands, the slope length over the rise, and so on. AMA comes from real measured forces, AMA = F_load / F_effort. Because friction always eats some of the input work, AMA is always less than IMA in a real machine, and their ratio is exactly the efficiency: η = AMA / IMA = W_out / W_in. If your measurements make AMA exceed IMA, something is wrong with the measurement — no machine can beat its own geometry.

Why is a mechanical advantage below 1 not an error?

A machine trades force for distance, and the trade can run either way. A Class 3 lever such as your forearm has the effort applied between the fulcrum and the load, so the effort arm is shorter than the load arm and the mechanical advantage falls below 1. You pull harder than the load weighs, but the load moves further and faster than your muscle does. That is the whole point of the arrangement, so the calculator reports it as a speed multiplier rather than flagging it as a mistake.

How do I count the rope segments in a pulley system?

Count only the strands that actually support the movable block — the ones that carry the load upward — not the number of sheaves or wheels. A block and tackle with two double blocks has four supporting segments and therefore an IMA of 4, even though it contains four wheels. Whether the segment you pull on counts depends on which way it runs: if you pull down over a fixed pulley it does not support the load, but if you pull up on a strand attached to the movable block it does. Miscounting here is the single most common error in pulley problems.

Why are screws and jackscrews so inefficient?

A screw has an enormous ideal mechanical advantage — 2πR divided by the lead, often several hundred — because the effort travels a whole circumference for every few millimetres of axial advance. But that same long travel is spent sliding thread against thread under the full load, so friction acts over a very long distance and consumes most of the input work. Real jackscrews commonly run at 20–40 % efficiency, and a screw that is self-locking (one that will not unwind under its load) is under 50 % efficient by definition. The huge IMA still leaves a very useful actual advantage.

Why do two 85 % efficient stages give only 72 % overall?

In a compound machine the stages are in series, so the ideal advantages multiply and the efficiencies multiply too. Two stages of IMA 4 give a total IMA of 16, but two efficiencies of 0.85 give 0.85 × 0.85 = 0.7225, or 72.25 %. Each stage only ever passes on a fraction of what it receives, so losses compound rather than average. This is why long gear trains and multi-stage hoists gain force cheaply but lose energy expensively, and why designers keep the number of stages as low as the required advantage allows.