Mechanical Advantage vs. Efficiency: Why No Real Machine Hits Ideal

Mechanical advantage describes a machine's geometry: the ratio of arm lengths, rope segments, radii, or turns that determines how much a simple machine could multiply force in a perfect world. Efficiency describes what happens when that geometry meets the real world — friction, flex, and heat that quietly eat into the ideal number every single time. No machine on this site, or anywhere else, ever reaches 100% efficiency, and understanding why the shortfall differs so much from one machine to another is as useful as knowing the ideal formulas in the first place.

What efficiency actually measures

For every machine on this site, mechanical efficiency comes down to the same ratio: the ideal effort force a frictionless version of the machine would need, divided by the actual effort force a real one demands, expressed as a percentage. A 100% efficient machine needs no more force than the ideal calculation predicts; anything less than that means friction is quietly demanding some of your effort before it ever reaches the load. This isn't a separate law from the conservation-of-energy idea running through every article on this site — it's the same idea, just admitting that some of the input work turns into heat and noise at the machine's moving contact points instead of useful output work.

The screw: the least efficient machine here, for a specific reason

A screw jack lifting a 9,000 N load with a 0.35 m handle and an 8 mm pitch has an ideal effort of about 32.7 newtons at 100% efficiency, but a realistic 30% efficiency — typical for a threaded screw jack — pushes the actual effort up to about 109.1 newtons, more than triple the ideal figure. The reason a screw loses so much more than the other machines here comes down to contact geometry: a screw thread stays in continuous, tightly wedged sliding contact across its entire mating surface throughout every turn, unlike a lever's brief pivot point or a pulley's rolling wheel. That same friction is doing double duty, though — it's also what makes a screw self-locking, holding a raised jack or a clamped joint in place without a separate brake. Low efficiency and self-locking are two faces of the identical friction, not two separate properties.

The pulley: friction at every wheel, but no self-locking payoff

A 4-part block and tackle lifting an 800 N load has an ideal effort of exactly 200 newtons, and a realistic 85% efficiency (a well-maintained system with decent bearings) brings the actual effort to about 235.3 newtons — a much smaller gap than the screw's, because a pulley's rope-over-wheel contact is rolling and brief at each sheave rather than continuously wedged. Unlike a screw, though, a pulley system offers nothing in return for that friction loss: let go of the rope and the load falls, friction or not, which is why real hoists and cranes need a separate ratchet, brake, or cleat to hold a raised load, something a self-locking screw jack doesn't require.

The inclined plane: efficiency that depends entirely on the surfaces involved

A ramp doesn't come with a single, fixed efficiency the way a well-made pulley or screw roughly does — it depends entirely on what's sliding or rolling across what. Push a load up that same familiar 5 m/1 m ramp with a friction coefficient of 0.15 (a hand truck's wheels on rough wood) and the ideal 200 newtons becomes about 347 newtons, an efficiency-equivalent of roughly 58%. Improve the surface to a friction coefficient of 0.05 (smoother wheels, a slicker ramp material) and the actual force drops to about 249 newtons, pushing the efficiency-equivalent up to about 80%. The lesson generalizes past ramps: efficiency is often less a fixed property of a type of machine and more a property of the specific materials and surface finish involved, which is exactly why "add wheels" or "smooth the surface" are such reliable ways to improve a ramp's real-world performance without changing its geometry at all.

The lever and wheel-and-axle: modeled as ideal here, but not perfect in reality

The lever and wheel-and-axle calculators on this site report the ideal, frictionless case only, with no efficiency parameter to adjust. That's not because real levers and axles are perfectly efficient — a rusty hinge or a dry bearing absolutely costs some of your effort — but because a well-made pivot or axle bearing typically loses only a small percentage to friction, often in the 90–99% efficiency range for decent hardware, compared to a screw's 25–40% or a rough pulley system's lower efficiencies. A pivot's contact area is small and often rolls or barely slides at all, especially with a proper bearing, which is the structural reason levers and wheel-and-axle machines tend to run closer to their ideal numbers than screws or dragging-contact ramps do.

Gears: small per-stage losses that compound

A single well-machined, well-lubricated gear pair typically loses only a few percent of input power to friction between the meshing teeth and in the supporting bearings — often comparable to a good lever or axle bearing. The catch is that gear trains rarely stop at one stage: chain three such pairs together, each losing even a modest few percent, and the losses compound multiplicatively rather than adding up gently, so a three-stage gearbox's overall efficiency can run noticeably lower than any single stage's efficiency alone would suggest. This is the flip side of the "multi-stage vs. single-stage" design trade-off covered in the gear-ratio articles on this site: more stages generally means more compounded friction loss, even when each individual stage is well made.

Why "ideal" is still worth calculating

None of this makes the ideal, frictionless formulas on this site useless — quite the opposite. The ideal calculation is the honest ceiling: no real machine will ever need less effort than its frictionless ideal predicts, so it tells you the best possible outcome before a single real material or bearing gets involved. Efficiency then tells you how close a specific, real build is likely to come to that ceiling, and comparing the two numbers is what turns "this doesn't feel like the calculator said it would" from a confusing mismatch into an expected, explainable gap.

A rule of thumb across all six machines

Continuous sliding contact under load (a screw thread, a dry ramp surface) tends to produce the largest efficiency losses; rolling or briefly-pivoting contact (a ball-bearing pulley, a lever's pivot pin, a lubricated axle, a well-cut gear tooth) tends to produce the smallest. When you're choosing between two ways to build the same mechanical advantage — a screw jack versus a lever-and-ratchet arrangement, say — that contact-type distinction is often a better efficiency predictor than the specific numbers on any single machine's spec sheet.

Where the lost effort actually goes

Efficiency losses aren't a mysterious accounting error — the "missing" work becomes heat and, to a lesser extent, sound, generated right at the points of sliding or rolling contact. A screw thread turning under load genuinely warms up slightly at the contact surfaces between the male and female threads; a pulley bearing running for an extended lift can be noticeably warmer to the touch afterward than a bearing that's been sitting idle. This is the same energy-conservation principle behind every article on this site, just tracked one level further: the work you put in either becomes useful output work moving the load, or it becomes heat at a friction surface. Nothing vanishes, and nothing appears from nowhere — it just isn't all put to the use you intended.

Estimating your own build's efficiency

If you've built a simple machine for a project (see the companion article on science-fair builds), you can measure your own efficiency directly rather than assuming a textbook figure: calculate the ideal effort force from your measured dimensions using the relevant calculator, then measure the actual effort force with a spring scale, and divide the ideal figure by the actual one to get your own efficiency percentage. A homemade pulley system built with plastic hardware-store pulleys and cotton string might come in well below the 85% figure used in the examples above — and that's a genuinely interesting, reportable result in its own right, not a sign that something went wrong with the build.

Efficiency and holding a load: not the same question

It's worth keeping "how much effort does this take" separate from "will this stay put once I let go," since the two don't always track together. A screw's low efficiency comes with a genuine safety benefit — it self-locks and holds a raised load without your hand on it. A pulley system's comparatively higher efficiency comes with no such benefit — the moment you release the rope, gravity takes back over, efficiency or not, which is exactly why cranes, hoists, and elevators need a dedicated brake or ratchet mechanism that has nothing to do with the pulley's own mechanical advantage or efficiency figure. Never assume a mechanism holds a load safely just because it was hard to lift in the first place.

See it across all six machines at once

The Simple Machines Reference runs a worked example for the lever, pulley, inclined plane, wheel and axle, gear pair, and screw side by side, computed directly from the same functions behind each calculator. To dig into any one machine's efficiency behavior more closely, try the pulley calculator, the inclined plane calculator, or the screw calculator directly, each with its own efficiency or friction input to experiment with.