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Abacus
The abacus stores a number as the positions of movable markers, with each rod or row standing for a place value, so the frame is a memory and the fingers are the processor. Its forms vary, from the Chinese suanpan with two beads above the bar and five below to the Japanese soroban with one above and four below, but the principle is the same.
It is no museum piece. In a 1946 contest in Tokyo, a postal worker using a soroban beat an American soldier with an electric calculator in four of five rounds. Start here to see why place value, not gears, is the real foundation of every machine further down this list. Even the shop counter is named after the counting boards that sat on it.
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Antikythera mechanism
Divers recovered the corroded remains of this bronze device from a Roman-era shipwreck off the Greek island of Antikythera in 1901. It is the oldest known scientific calculator, and it is about 2,000 years old.
Turn a handle and more than 30 interlocking gears model the heavens: the device could show the positions of the sun, moon and planets, predict eclipses and track the dates of the Olympic Games. That precision changed what historians believed ancient Greek craftsmen could make. It is also the clearest early case of an analogue computer, where the shape of the mechanism itself embodies the mathematics rather than counting in digits.
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Napier's bones
John Napier described his rods in 1617, the year he died, as a way to turn multiplication into addition. Each rod carries a multiplication table split into squares, and every square is cut by a diagonal with the tens digit of the product above it and the units digit below.
Lay rods for each digit of a number side by side, read across the row for the multiplier, and add the digits that fall between neighbouring diagonals. No mechanism is involved, yet the trick is a real algorithm made physical, and the best sets were carved in ivory, hence the name. Their influence was direct: Wilhelm Schickard built a set of these rods into his calculating machine within a few years.
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Slide rule
William Oughtred is widely credited with inventing the slide rule in the 1620s, and his first design was circular. It turns logarithms into distance: because the scales are logarithmic, sliding one bar along another adds lengths, and adding lengths multiplies numbers.
Aligning different scales gives trigonometry as well as multiplication. The answer is only as precise as the reader's eye, but that was good enough for generations of engineers, and slide rules stayed in wide use through the 20th century. It belongs here as the longest-lived analogue computer in everyday hands, and the clearest way to understand what "analogue" actually means.
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Wilhelm Schickard
Schickard's calculating machine, about 1623
Wilhelm Schickard, a university professor, minister, astronomer and engraver, built two calculators around 1623 and described one in a letter to his friend Johannes Kepler. His design combined a set of Napier's rods for multiplication and division with a toothed-wheel adder for addition and subtraction, which makes it the earliest known mechanical four-function calculator.
Neither machine survives: Kepler's was destroyed by fire and the other is lost. The design was known only from sketches and letters that stayed lost until 1935. It earns its place as the first attempt to make gears do the carrying a human clerk would otherwise do in their head.
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Pascaline
Blaise Pascal invented this adding machine in the 1640s to help his father, a tax collector, with endless sums. You entered a digit by putting a stylus into a toothed wheel at that number and turning until it hit a stop, and the machine carried into the next wheel by itself.
That carry was the hard part. Pascal's mechanism used falling weights rather than linked gears, and it was complicated and unreliable, so a handsome exterior hid a fragile heart. Even so, he built about 50, making it the first adding machine produced in any quantity, though only about 15 sold. It shows the problem every later designer had to solve: carrying a one across many digits at once.
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Stepped reckoner
Gottfried Wilhelm Leibniz's Step Reckoner of 1673 is often called the first true four-function calculator. Its secret is the stepped drum, a cylinder whose teeth run partway along its length in graded steps, so that sliding a small gear along it chooses how many teeth it meets. One revolution can enter any digit from 0 to 9, and repeated turns of the crank multiply.
That drum-shaped gear underpinned calculator designs for roughly 275 years, an unbroken record for a single mechanism, and it reappears in the arithmometer and the Curta further down this list. Leibniz spent about 45 years building versions of the machine and only one survives.
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Jacquard machine
Joseph Marie Jacquard's loom of 1801 did not calculate anything, yet few machines matter more to this story. It wove patterned textiles by following a chain of large punched cards bound together: where a card had a hole, a hooked rod passed through and lifted its thread, and where it had none, the thread stayed down.
That chain of cards is a program in all but name, stored outside the machine and swapped to change what it made. Change the cards and the same loom weaves a different picture. Charles Babbage saw the point, and his Analytical Engine was designed to be programmed with punched cards borrowed from the loom. Herman Hollerith's census machines later made punched cards the working medium of data processing.
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Arithmometer
Thomas de Colmar's Arithmometer, first produced in 1820, is where the calculator became a product rather than a curiosity. Inside, it borrowed Leibniz's stepped drums; outside, it was built to be made in numbers, the first calculator to take advantage of industrial manufacturing.
Early models were driven by pulling a silk ribbon, later ones by turning a crank, and the operator set digits with sliders before cranking to add, or cranking repeatedly to multiply. Nearly 2,000 were sold and it stayed in production into the 20th century. If the Pascaline proved a machine could add, this proved people would pay for one that kept working.
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Difference engine
Charles Babbage's Difference Engine No. 2
Babbage wanted to end the errors in printed mathematical tables, and the method of differences let him compute a whole table of polynomial values using nothing but addition, which gears do well. He worked on his first engine from 1821, but the project halted in 1832 after a dispute with his engineer, Joseph Clement, leaving a demonstration piece of about 2,000 parts.
His improved design of 1848, Difference Engine No. 2, has 8,000 parts, weighs five tons and is 11 feet long. It was never built in his lifetime. In London its calculating section was finished in 1991, for the bicentenary of his birth, and the printer in 2002. The completed machine works as Babbage intended.
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Analytical engine
Babbage's Analytical Engine, conceived in 1834, is arguably the first design for a programmable computer, and the leap from his Difference Engine is enormous. It separated memory, which he called the Store, from the processor, the Mill, and it took its instructions from punched cards, an idea borrowed from the Jacquard loom.
It could also branch, choosing what to do next depending on a result, which is the step from calculator to computer. It was never completed. Ada Lovelace contributed to and documented the work, and her writing on it is still read today. Read this entry to see the architecture of a modern computer laid out in brass a century before electronics.
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Per Georg Scheutz
Born
The Scheutz difference engines, 1853 and 1859
Babbage designed difference engines; Per Georg Scheutz and his son Edvard actually delivered working ones. Inspired by an account of Babbage's work in 1834, they built a prototype in 1843 that produced the first tables calculated and printed by machinery, followed by full metal engines completed in Stockholm in 1853 and in London in 1859.
Babbage welcomed their success. The results were sobering, though: the first engine went to the Dudley Observatory in Albany, New York, and sat largely unused, while the second computed the 1864 English Life Table but proved temperamental. It is the honest counterpoint to Babbage's story, showing that building the machine was only half the problem.
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Tide-predicting machine
William Thomson's tide-predicting machine, 1872
Tides matter to every harbour, and Thomson, later Lord Kelvin, treated them as a sum of regular astronomical rhythms. His machine gave each component its own shaft, crank and pulley, and a wire running over the pulleys added their motions together, so a pen traced the combined tidal curve.
This first working machine of his design combined ten components and could draw a year of tides for one harbour in about four hours. Nothing in it counts: the answer is the curve itself, which makes it the purest example here of harmonic analysis done in metal and a clear forerunner of the analogue machines that later solved equations.
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Odhner Arithmometer
Willgodt Odhner, a Swedish immigrant living in Russia, designed this calculator in 1873 around the pinwheel, a thin gear from which zero to nine teeth stick out depending on where a lever is set. It does the stepped drum's job in a sliver of the space, so the whole machine could shrink to a compact desktop box worked by a crank.
That compactness is why it mattered. Several manufacturers built machines on the Odhner pattern and millions were sold worldwide, which made the pinwheel one of the most widely used calculating mechanisms ever made. Frank Baldwin in the United States built a pinwheel machine in 1872, so the idea arrived from two directions at almost the same time.
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Comptometer
Patented in 1887 by Dorr E. Felt, then 24, the Comptometer was the first commercially successful keyboard adding machine, and its trick was speed. There was no crank and no separate setting step: pressing a key drove the mechanism and added the digit at once, so adding a column of figures became a matter of typing them.
Felt's first model was improvised from a wooden pasta box, meat skewers and rubber bands. More than 6,500 were built between 1886 and 1903. Choose this entry to see how the interface, not just the arithmetic, became part of the engineering, and why the keyboard became the way people talk to machines.
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Tabulating machine
Herman Hollerith's tabulating machine for the 1890 United States census
Officials feared that counting the 1890 census by hand would not be finished before 1900. Hollerith's answer was electrical: each person's details were punched as holes in a card, and when the card was pressed, pins passed through the holes into cups of mercury, completing circuits that advanced counting dials.
Some 60 million cards were punched for that census, and an operator could handle about 7,000 a day, at least ten times faster than manual methods. Hollerith founded the Tabulating Machine Company in 1895, and punched-card data processing grew from here. This is the moment computing became about data as well as arithmetic.
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The Millionaire (calculator)
Otto Steiger's Millionaire solved the slowest part of mechanical multiplication. Most machines before it multiplied by repeated addition, one turn of the crank per unit of each digit. The Millionaire held the multiplication table itself, up to 9 x 9, as metal pins of different heights, so a single turn of the crank multiplied by a whole digit at once.
The first series was made in Munich in 1896, mass production moved to Zurich in 1898, and it was built there for about 40 years. It earns its place for an idea that later computing reused constantly: when a result is needed again and again, store it in a table and look it up rather than work it out each time.
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Differential analyser
Vannevar Bush's differential analyser, MIT, 1931
Bush built his machine to model electrical power networks, problems described by differential equations that were painful to solve on paper. Its heart was the wheel-and-disc integrator: a small wheel resting on a spinning disc turns faster the further it sits from the centre, so its rotation adds up a changing quantity over time, which is exactly what integration means.
Six integrators were linked through 18 long rotating shafts, and each new problem had to be set up laboriously by reconnecting them. Once running, the machine solved the equation by acting it out. It shows analogue computing at its most ambitious, and why reprogramming by spanner made the case for stored programs.
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Z3 (computer)
Konrad Zuse completed the Z3 on 12 May 1941, and it is widely regarded as the world's first working programmable, fully automatic digital computing machine. It used no valves at all: more than 2,000 electromechanical relays clicked open and shut to hold and process its numbers, and its program was read from holes punched in film.
That makes it the clearest answer to anyone who assumes a real computer had to wait for electronics. The original was destroyed by bombing in Berlin in December 1943, and a replica was built in the 1960s. Set it beside the Harvard Mark I, completed three years later, to see two very different routes to automatic computation arriving at almost the same moment.
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Harvard Mark I
Howard Aiken proposed a large automatic calculator in 1937, IBM and Harvard agreed to build it, and the Harvard Mark I was completed in 1944. Its scale is the point: switches, relays and counting wheels were all kept in step by a single rotating shaft some 50 feet long, so the whole machine ran like one vast piece of clockwork driven electrically.
It read its instructions from punched paper tape and worked through long calculations unattended, including work that helped design America's atomic bomb. Grace Hopper was among its first programmers. It is where the electromechanical tradition reached its largest size, just as electronic machines arrived.
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Curta
Curt Herzstark refined the design of this pepper-grinder-shaped calculator while imprisoned in Buchenwald concentration camp, where he was sent in 1943. Inside its cylinder sits a modified version of Leibniz's stepped drum: set the digits with sliders on the side, turn the crank on top, and the single drum serves every column in turn.
With more than 600 parts in a body that fits in one hand, it is the smallest all-mechanical four-function calculator ever built. Rally navigators kept using it well into the age of electronic calculators. Hold it beside the Step Reckoner and you can see one idea refined over nearly three centuries.
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Phillips Machine
The New Zealand economist Bill Phillips built this machine in 1949 and computed with water. Pink-dyed water pumped into a top reservoir stood for income, then flowed down through clear tanks and pipes, draining away as saving and taxes and flowing back in as investment and government spending, with valves set to represent economic choices. Change a valve and the levels settled into a new balance, showing the effect on the whole economy.
Phillips presented it at a seminar at the London School of Economics late in 1949 and built 14 of these machines. It is the most vivid analogue computer on this list: the equations of a national economy acted out in plumbing that anyone in the room could watch.
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