From Archimedes' lever to the star label on your AC: how people learned that force times distance is something you can measure, sell and pay for.
For two thousand years people used levers and pulleys without a word for what they traded. Galileo saw that a machine gains force only by losing distance, engineers measured horses and water wheels, and in 1829 Coriolis and Poncelet gave the idea its name: work. Joule showed that work and heat are the same stuff, the watt and the joule became units, and meters began to charge homes for every kilowatt-hour.
Greek engineers explain the lever and the pulley, and Galileo sees the catch: what a machine gains in force it loses in distance.
250 BCE
c. 250 BCE
The law of the lever
ArchimedesSyracuse, Sicily
In On the Equilibrium of Planes, Archimedes proved that weights balance on a lever when weight times distance from the pivot is the same on both sides. A later writer, Pappus, credits him with the boast: give me a place to stand and I will move the Earth.
Why it mattered. It is the first exact rule for trading a small force for a big one.
Hero's Mechanics lists five devices for moving heavy loads: the lever, the windlass, the pulley, the wedge and the screw. He explained them with balanced forces, but had no idea yet of work.
Why it mattered. These are still the simple machines taught in school today.
Teaching at Padua, Galileo wrote Le Mecaniche, a short book on levers, pulleys, screws and ramps. He showed they all follow one rule: a machine that lets a small force lift a big weight makes that force move much further. Marin Mersenne printed it in French in 1634.
Why it mattered. It is the first clear statement that machines transform effort but never create it.
In a letter explaining machines to Constantijn Huygens, Descartes wrote that lifting 100 pounds one foot twice is the same as lifting 200 pounds one foot, or 100 pounds two feet. The effort of a job is weight multiplied by height.
Why it mattered. It measures a machine's job the way we measure work today.
Engineers selling pumps and mills compare them with horses and measure weight raised times height, per minute.
1702
As many horses as it replaces
Thomas SaveryLondon, England
In The Miner's Friend, Savery sold his steam pump for draining mines by saying how many horses it could replace. Mine owners paid for horses, so a horse was a unit they understood.
Why it mattered. Comparing engines with horses led to the horsepower.
Smeaton spent seven years testing model water wheels and windmills and reported how much weight each could raise, how high, in a given time. He showed that an overshot wheel, fed from the top, does far more work than an undershot one. The Royal Society gave him its Copley Medal.
Why it mattered. Measuring weight raised times height per minute is measuring power.
Watt watched mill horses turn a wheel of 12 ft radius 144 times an hour, pulling with about 180 pounds-force. That came to about 32,600 foot-pounds a minute. In 1783 he and Boulton rounded it up to 33,000: one horsepower, today 745.7 W.
Why it mattered. It gave buyers a number for how fast an engine could work.
French engineers call force times distance 'travail', and Joule shows that work and heat are two faces of one thing.
1824
The motive power of fire
Sadi CarnotParis, France
Carnot asked how much work a steam engine could possibly get from its fuel. He found a limit set by how hot and how cold its two ends are, so no heat engine can turn all its heat into work.
Why it mattered. It explains why a petrol engine is only about 30% efficient.
In Du calcul de l'effet des machines, Coriolis called force times distance moved 'travail', work. He also put the half into ½ m v², showing that the work done on a body equals the change in its energy of motion. He even proposed a unit, the dynamode, 1,000 kilogram-metres, which never caught on.
Why it mattered. Work became a precise, measurable quantity for engineers.
Teaching engineers and workers at Metz, Poncelet used 'mechanical work' as the key idea for judging machines, independently of Coriolis. His Introduction à la mécanique industrielle came out in 1829, and he also designed better water wheels.
Why it mattered. He made work the everyday language of engineering.
Joule let falling weights spin a paddle wheel in an insulated can of water and measured how much the water warmed. The same amount of work always gave the same amount of heat: 819 foot-pounds per British thermal unit in 1845, refined to about 772 by 1850.
Why it mattered. It proved that work and heat are both energy, which is why the unit of work is the joule.
Working for Westinghouse, Shallenberger noticed a loose spring turning in the magnetic field of an AC lamp. He turned the idea into a meter that measured how much alternating current a customer used. About 120,000 were sold within ten years.
Why it mattered. Homes could now be charged for the energy they used, not a flat fee per lamp.
Meeting during the Paris World's Fair, the congress adopted the joule for work and the watt, one joule per second, for power. Joule died in October that year, weeks after his unit became official.
Why it mattered. Scientists and engineers everywhere could now use the same words for work and power.
Bláthy's induction meter, shown at the Frankfurt Fair, used a spinning disc to add up power over time and show kilowatt-hours. The same principle ran most electricity meters for the next hundred years.
Why it mattered. The kilowatt-hour became the unit on every electricity bill.
11th General Conference on Weights and MeasuresSèvres, France
The new International System of Units, the SI, made the joule (a newton times a metre) its unit of energy and work, and the watt (a joule per second) its unit of power.
Why it mattered. One set of units now serves physics, engineering and your electricity bill.
At the National Physical Laboratory, Kibble designed a balance that compares mechanical power, a mass moving in gravity, with electrical power in a coil. It was called the watt balance.
Why it mattered. Power became precise enough to define the kilogram itself.
Bryan Allen, Paul MacCready's teamFolkestone, England to Cap Gris-Nez, France
Cyclist Bryan Allen pedalled the Gossamer Albatross 35.7 km across the English Channel in 2 hours 49 minutes, producing about 300 W, just enough to keep the ultralight plane in the air.
Why it mattered. It shows how much a fit person can do with a few hundred watts.
Under the Energy Conservation Act 2001, the BEE launched its star labels: one to five stars showing how many units a year an appliance needs. From 7 January 2010 labels became mandatory for frost-free fridges, room ACs, tube lights and distribution transformers.
Why it mattered. Families could compare the energy bill before buying, not after.
General Conference on Weights and MeasuresSèvres, France
The kilogram stopped being a metal cylinder in a vault. It is now fixed by the Planck constant, and Kibble balances, renamed after Bryan Kibble in 2016, realise it by balancing mechanical and electrical power.
Why it mattered. A unit of mass now rests on measuring watts.
Watt measured about 32,600 foot-pounds a minute for a mill horse, then rounded up to 33,000, perhaps so that buyers of his engines would never feel short-changed.
Europe and India often quote engines in metric horsepower (PS), 735.5 W, about 1.4% smaller than Watt's 745.7 W.
One kilowatt-hour, a single unit on your bill, is 3.6 million joules: enough to lift a 1,000 kg car about 367 m.
Joule died on 11 October 1889, weeks after the unit named after him was officially adopted.
Coriolis also proposed a unit of work, the dynamode, 1,000 kilogram-metres. Nobody used it.
The people
Who figured it out
A
Archimedes
c. 287 – c. 212 BCE · Mathematician and engineer · Syracuse, Sicily
Proved the law of the lever.
HA
Hero of Alexandria
c. 10 – c. 70 CE · Engineer and mathematician · Egypt
Listed the five machines for moving loads.
GG
Galileo Galilei
1564 – 1642 · Physicist and astronomer · Italy
Showed that every simple machine gains force only by losing distance.
JS
John Smeaton
1724 – 1792 · Civil engineer · England
Measured the work of water wheels and windmills by experiment.
JW
James Watt
1736 – 1819 · Engineer and inventor · Scotland
Defined the horsepower; the unit of power is named after him.
SC
Sadi Carnot
1796 – 1832 · Engineer and physicist · France
Found the limit on how much work a heat engine can give.
GC
Gaspard-Gustave Coriolis
1792 – 1843 · Mathematician and engineer · France
Named work 'travail' and wrote kinetic energy as ½ m v².
JP
Jean-Victor Poncelet
1788 – 1867 · Engineer and mathematician · France
Made mechanical work the language of industrial engineering.
JP
James Prescott Joule
1818 – 1889 · Physicist and brewer · England
Measured how much heat a given amount of work makes.
OB
Oliver B. Shallenberger
1860 – 1898 · Electrical engineer · United States
Invented the AC electricity meter for Westinghouse.
OB
Ottó Bláthy
1860 – 1939 · Electrical engineer · Hungary
Built the induction kilowatt-hour meter.
BK
Bryan Kibble
1938 – 2016 · Metrologist · England
Invented the watt balance that now helps define the kilogram.