How this instrument works
Mechanical advantage grades a machine rather than describing one: divide force it delivers by force you supply, and out drops a bare number. Newtons cancel newtons, so this quantity has SI dimension 1 and carries no unit whatsoever — which is why an advantage quoted "in newtons" reliably signals that somebody has divided the wrong pair of things. Hero of Alexandria set out the family around 60 CE in his Mechanics, naming five members — windlass, lever, pulley, wedge and screw — and describing the baroulkos, a train of toothed wheels built to haul burdens far past anything its crew could raise bare-handed.
Two different numbers answer to that one name, and mistaking either for its twin is where estimates quietly fail. Ideal advantage falls out of geometry alone: count rope falls supporting a load, or divide piston areas in jacks, and arithmetic hands you that figure before anything is built. Actual advantage is what two gauges report, and it always lands lower, because pin friction, seal drag, thread rubbing and rope stiffness each take their cut before your burden so much as stirs. Divide actual by ideal and efficiency drops out. This sheet returns actual advantage, since both figures you type are measurements.
Two limits sit inside that simple division. First, it is a statics quantity, defined at balance or at constant speed; snatch a load into motion and part of your effort goes into accelerating mass rather than resisting it, so gauges read lower than what your machine can truly manage. Second, it says nothing at all about travel, speed, or whether anything stays put once you let go. Worm drives and screw jacks running near thirty-fold advantage are frequently under half efficient, and that very wastefulness is what stops them unwinding beneath load. Somebody specifying one is buying friction deliberately.
- Enter what your machine delivers into Output (load) force — newtons, kilonewtons or pounds-force, whichever your gauge or rating plate reports.
- Enter what you supply into Input (effort) force. Mixing units across both boxes is safe, since conversion runs before any division happens.
- Read Mechanical advantage. It is a bare ratio carried to six figures, and it never wears a unit.
- Above 1 means force multiplied; exactly 1 means direction turned and nothing more; below 1 means force traded away for speed or reach.
- Zero effort is refused. Machines delivering something on nothing supplied signal a broken measurement, not infinite advantage.
Worked example — a windlass raising 102 kg of mortar
A hand windlass lifts material up the builder's shaft. Its crank swings through 300 mm of throw while its cable winds onto 50 mm of drum, so geometry promises six-fold multiplication. Hooked between cable and hook, a dynamometer reads 1000 N — near enough 102 kg of bucket and mortar together. A second gauge strapped to that crank handle reads 200 N. Type 1000 into Output (load) force and 200 into Input (effort) force, and Mechanical advantage returns exactly 5.
Five, where geometry offered six. Nothing was wrong with your arithmetic: a dry bronze bearing and stiff galvanised wire claimed that missing sixth, about 33 N of your pull spent warming an axle instead of raising mortar. Measuring rather than counting teeth is precisely why this sheet asks for forces. Note too what 5 does not buy you. Your hand still sweeps six times as far as that bucket climbs, because travel follows geometry whether or not friction taxes the force, which is how 200 N through 6 metres of crank path delivers 1000 N through 1 metre of lift and loses the remainder as warmth.
Questions
What unit does mechanical advantage have?
None whatsoever. Dividing newtons by newtons cancels dimension entirely, leaving a bare number whose coherent SI unit is 1 — the same status NIST SP 811 gives to any ratio of like quantities. Only one rule applies: both figures must be expressed alike before you divide. A 1000 N load over a 45 lbf pull is not 22; convert first, and this sheet does that for you.
What is the difference between ideal and actual mechanical advantage?
Ideal advantage comes from geometry — falls of rope, gear teeth, piston areas, crank and drum radii — and describes a machine with no friction anywhere. Actual advantage comes from two force measurements on real hardware and is invariably smaller. Their quotient is efficiency: measure 5 where geometry promised 6 and your machine is running at roughly five sixths. Design with the ideal figure, size your motor or your crew with the actual one.
Can mechanical advantage be less than 1?
Often, and deliberately. Sculling oars, a bicycle in top gear, and a badminton racket all supply more force than they deliver, buying tip speed and sweep in exchange. Enter such a case normally — 100 N out against 400 N in reads 0.25, meaning your effort is quartered at the working end while that end moves four times faster. Force and speed are the two currencies every machine exchanges between.
Does high mechanical advantage mean a machine is efficient?
No, and the two are almost independent. A worm drive multiplying force forty-fold may pass under a third of its energy onward, dumping the rest into sliding tooth contact. Engineers pick such drives for exactly that reason: any machine under 50% efficient cannot be back-driven, so hoists hold their load when a crank is released. Efficiency and advantage answer separate questions — how much of your energy survives, and how much of your force is amplified.
Why does my measured advantage change with the load?
Because friction is not purely proportional. Seal drag in hydraulic rams, preload in ratchet pawls, and stiffness in rope bent round a sheave all cost roughly the same regardless of what hangs beneath, so at light loads that fixed toll swallows a large share of your input and the ratio reads poorly. Push toward rated capacity and the same toll becomes a small fraction, so measured advantage climbs toward its geometric ceiling. Always quote load alongside any measurement.
How does mechanical advantage relate to velocity ratio?
Velocity ratio is input travel divided by output travel, fixed entirely by geometry, and it equals ideal advantage exactly. Efficiency is measured advantage divided by that velocity ratio. On the windlass above, velocity ratio is 6 because a hand sweeps 6 metres per metre of lift, measured advantage is 5, and the machine therefore returns five sixths of what it is fed. Velocity ratio never shifts; only the force ratio degrades as bearings age.