An illustrated history of the calculator
A heterodox take on the prehistory, the golden years, and the future of general-purpose calculating machines.
I find it difficult to talk about the history of the computer. The actual record is dreadfully short: almost nothing of consequence happened before the year 1935. We keep looking for a better story, but we inevitably end up grasping at straws.
Just look at what we’ve done so far. The “father of the computer” is no longer Konrad Zuse (Z1, 1938) or John Mauchly (ENIAC, 1943). Somehow, we pivoted to Charles Babbage — a 19th century polymath who never constructed such a device, and had no luck inspiring others to try. Not content with this injustice, we also turned “computing” into a meaningless word. On Wikipedia, the timeline of computer hardware includes mechanical clocks, dolls, weaving looms, and a miniature chariot from 910 BCE. It’s historical synthesis run amok.
To me, the calculator is a particularly regrettable casualty of this expansionist approach. Of course, the development of the calculator is intertwined with the history of the computer, but it deserves to be treated as a story of its own.
The ancient art of tallying goods
We know that sophisticated trade-based economies go back at least 5,000 years. Even in their early days, this required merchants to maintain accurate inventories, tally the proceeds, and keep track of debt.
There is ample archeological evidence of specialized tools used to accomplish these tasks. For addition and subtraction, the implements included notched sticks and bones, rope tied with knots, and — later — rudimentary manually-operated “registers” such as the abacus:
For multiplication, it was common to rely on lookup tables. The earliest known Babylonian multiplication table is 4,000 years old. The first decimal tables discovered in China date back to around 300 BC:
Both the abacus and the multiplication table remained in common use well into the 20th century — largely unchanged, but sometimes “updated” in wacky ways. For example, the following contraption from the early 1900s allows the multiplication of any two integers between 1 and 12 by aligning the legs of a monkey-shaped mechanical linkage:
Such novelties notwithstanding, the first “modern”, commercially successful mechanical calculation aid was the slide rule. The device, developed in the early 17th century, exploited the fact that any two positive numbers can be expressed as exponents of a common base n; for example, if we choose base n = 2, we can write 16 as 24, while 42 is equal to approximately 25.3924.
It can be trivially shown that multiplication of numbers written in this form boils down to the addition of exponents:
For example, in the earlier case of base 2, we can find the result of 16 · 42 by adding the exponents for the two operands — 4 + 5.3924 = 9.3924 — and then calculating 29.3924 ≈ 672.
To implement this scheme in hardware, we just need two sticks with uniformly-spaced markings annotated with numbers that represent constant increments of the exponent of some common base. Again, choosing n = 2 for illustration purposes, we could notch the sticks at one-inch intervals and then mark the subsequent notches as ¼, ½, 1, 2, 4, 8, 16, and so forth. Once we have this, we can easily sum exponents, as shown below:
To calculate 4 · 8, we align the marked reference point (1) on the top scale with the first operand (4) on the lower scale. We then read the value directly below the second operand (8). This operation effectively sums the linear distances on the scales — i.e., sums the exponents. The result works out to 32.
In practice, most slide rules had had two fixed elements (stators), a sliding portion in the middle, and a moveable cursor to facilitate precise readouts on a number of overlapping scales.
The slide reigned supreme well into the 1970s, an indispensable fashion accessory for every engineer worth a dime. It was manufactured in a variety of form factors, including some fairly unusual designs, such as this double-sided “pocket watch” design:
The slide rule depended on human eyesight to align the values and read out the result, so small devices weren’t particularly accurate. One ingenious workaround was to wrap a very long scale around a more compact Bakelite tube. “Tube-style” slides include the Otis King calculator and the Fuller calculator:
The carry mechanism
Although the slide rule has revolutionized engineering, it was more or less a one-trick pony. It could only tackle a specific subset of computations, required user training and care to avoid mistakes, and provided only approximate results.
The next major breakthrough in automation arrived with the invention of the carry mechanism. A counting device equipped with carry solved one of the most significant hurdles of using the abacus: the need to manually zero the column and add one to the next decimal position on overflow.
The first functional design of an adding machine with carry is conventionally credited to Blaise Pascal in 1642, although some historians give primacy to Wilhelm Schickard, who sketched a more questionable mechanism in a letter dating back to 1623. Either way, it wasn’t until the 19th century that simplified, portable adding machines started cropping up in trade. The most rudimentary device of this type in my collection is an early Webb adder:
The Webb adder is operated with a stylus. The large rotating disk on the right has a series of holes vis-a-vis numbers stamped on a fixed outer shroud. The numbers start at 3 o’clock and increase in the counterclockwise direction; the 3 o’clock position also features a protruding stylus stop. If you place the stylus in the position marked “5” and turn the disk clockwise toward the stop, you advance the number shown in the sight window (at 9:00) by five.
The operation can be repeated, with each stylus-entered value having a cumulative effect on the number shown in the sight window. This, in itself, is a simple addition mechanism. But crucially, on overflow — that is, right before the large disk completes a full turn and wraps back from “99” to “00” — an internal pawl advances the smaller disk on the left by one. The small disk has 50 positions (“0” to “49”), so the resulting range of the Webb adder is 0-4,999.
Many of the early attempts to improve the adder turned out to be evolutionary dead ends; for example, the Adix calculator traded the clunky stylus for a keyboard, with ten keys that advanced the rightmost disk in a three-disk carry mechanism. Alas, this only allowed single-digit values — 0 to 9 — to be added in each step:
An improvement over the Adix design was to provide nine keys per each decimal position in the output register. Alas, this input method made the mechanism bulky and remarkably complicated, so its use was limited to expensive adders sold to the accounting departments of big firms; a noted example is the Comptometer, patented in 1887. For a ten-digit adder, you needed 90 keys:
To build a more portable and affordable device for household and small business use, one could settle for a “half-keyboard” that only included digits from 1 to 5. In this design, any digits greater than five needed to be entered in two steps (e.g., 9 = 5 + 4):
Another approach was to stick to the disk-and-stylus input method, but use one disk per each decimal digit, keeping the device simple and small. Desktop adders of this sort continued to sell well into the 1970s:
A number of other inexpensive 20th century designs relied on vertically-mounted disks, chains, or sliding bars, but the fundamental principle was the same:
The accumulator
Adders, as the name implies, were good for adding and not much more. Using them for multiplication or division was theoretically possible, but required the user to repeatedly re-enter the same operand. This wasn’t any faster nor more reliable than performing the same calculation with pen and paper.
The next major invention, credited to Gottfried Wilhelm Leibniz (1672), is the separation of the input register and the output register (the “accumulator”). In Leibniz’s design, modifying the input register had no immediate effect on the displayed output value. The number would be added to (or subtracted from) the output only after the operator turned a crank, thanks to a fairly simple coupling mechanism known as the stepped drum. A modified version of the mechanism entered mass-production around 1851 with the Arithmometer; this was quickly followed by a wide range of other crank-operated desktop calculating machines.
Because the entered value persisted in the input register, multiplication and division could be accomplished by simply spinning the crank a desired number of times. Further, a separate turn counter could be furnished to keep track of the process; and a movable coupling between the registers could be used to permit rapid addition of the original number multiplied by a chosen power of ten.
A sophisticated mechanical calculator with all these features is shown below. The input register is visible on top, with the main crank to the right and a rapid clearing lever on the left. The output register is on the bottom right, next to the rotation counter (bottom left). Two lever-like buttons in front move the output carriage left and right in relation to the input register:
To calculate 79 · 123, one could enter “79” by manipulating small levers on top of the input register. The operator would turn the main crank three times to calculate 79 · 3 = 237; shift the carriage left, effectively shifting the input register by one decimal position in relation to the output register, and then turn the crank two times to add 790 · 2 = 1,580. Finally, the carriage would be shifted left again and the calculator would be cranked once to enter 7,900 · 1. In the following clip, I demonstrate the process using a similar machine:
If you’re unsure why this calculation technique works, note that adding 790 · 2 to the output register is functionally the same as adding 79 · 20. Similarly, the final 7,900 · 1 calculation can be restated as 79 · 100. In effect, we have calculated 79 · (100 + 20 + 3), or 79 · 123. The procedure is quite similar to the pen-and-paper long multiplication algorithm that’s sometimes taught in school.
Although all desktop calculators of that era had their charm, the most sought-after variation of the theme is the palm-sized Curta: an incredibly complex clockwork-like pocket calculator envisioned by Curt Herzstark in the late 1930s. A well-preserved specimen will usually fetch $1,500, compared to maybe $300-$400 for a desktop device:
The Curta isn’t fundamentally different from the desktop models showcased earlier, but its sheer level of miniaturization is the source of its lasting appeal. It is also relatively delicate; more than 100,000 have been made, but relatively few survived to this day in good shape.
All kinds of fully-featured mechanical calculators continued to be made well into the second half of the 20th century. The designs were simplified, cranks were replaced with smaller buttons or levers, metal enclosures gave way for injection-molded plastics. Further, spring-actuated auto-advance couplings allowed numbers to be entered sequentially using ten digit keys:
One would expect the electronic calculator to be the immediate next step in the evolution of counting devices. Not so: it was simpler to fit mechanical calculators with a motor in the place of a lever or a crank. Here’s an example of another Belgium-made Bohn calculator that appears strikingly similar to the model shown above, except for an extra power cord:
The digital age
Compact electromechanical calculating machines, such as bombsights, started appearing around the time of WWII; the first pocket-sized transistor radios shipped in 1955. It might be surprising, then, that we needed to wait another fifteen years for electronic calculators to take hold. A major reason for the holdup was the lack of a suitable display technology.
A handful of early digital calculators were equipped only with a printer; a delightful example was the Mathatronics Mathatron, circa 1963. Some other designs used hundreds of incandescent lamps to highlight the currently-active digit for each decimal position, as seen in the desk-sized, relay-based Casio 14-A (1957).
Naturally, all of these designs were rather cumbersome to use. To remedy this, several manufacturers experimented with cathode ray tube (CRT) displays, but the added bulk and the high cost made their devices a tough sell:
This particular specimen from my collection is the first transistor-based calculator to be mass-manufactured. It dates back to 1964, features reverse Polish notation, weighs over 40 lbs, and had an original price tag comparable to that of a nice car. The design uses acoustic (magnetostrictive) delay line memory and contains no integrated circuits whatsoever; all the CRT digit drawing was done with discrete components. It’s a marvel of engineering, but it wasn’t a good direction to follow.
Instead, the answer turned out to be the nixie tube: a gas-filled vial containing a stack of intricately-shaped wires. With around 180 V applied to the terminals, the gas emitted a pleasant orange glow in the immediate vicinity of the currently-energized wire:
Nixie tubes were used on what can be described as the first “electronic” calculator: Sumlock Anita Mk VII / VIII, sold in Europe starting in the late 1961. The Anita traded electromechanical (relay) switching of Casio 14-A for nearly two hundred gas-discharge tubes, about a dozen vacuum tubes, and several hundred solid-state (diode-like) selenium rectifiers. Interestingly, it retained the clunky, ten-keys-per-decimal-position input scheme of the mechanical Comptometer.
The case of the Anita aside, the first truly successful nixie tube calculators of the era were mains-powered and used a mix of discrete transistors and low-complexity, general-purpose integrated circuits. It follows that they took up quite a bit of desk space — although nowhere near as much as the CRT monstrosities mentioned earlier in the article.
A distinctive feature of these early designs was their rather leisurely computation speed. This was especially evident for more complex operations, such as multiplication and division; as well as premium “scientific” features such as square roots, logarithms, and trigonometry. In the following video, I demonstrate the processing speed of Compucorp 110:
For cost-saving reasons, the devices lacked many of the convenience features we now take for granted. For example, many calculators had no power-on-reset circuitry, so the equipment booted to an unpredictable state and had to be manually zeroed before use. In the same vein, many units had no floating point capabilities (although it was common to see a fixed decimal point that could be moved with a knob). Finally, a good number of devices lacked true support for negative numbers, requiring the operator to keep track of signs.
Because of its cost and complexity, a nixie tube calculator would be an unusual sight in a private home, but the technology enjoyed substantial adoption in the world of business and science.
The portable calculator
As hinted earlier, calculator displays continued to be a significant limiting factor even after the adoption of the nixie tube. Bulky, high-voltage tubes were difficult to integrate into battery-operated circuits. The situation improved slightly after the arrival of streamlined “Panaplex” displays that used a similar operating principle, but came in the form of more rugged, self-contained 7-segment display modules:
Nevertheless, to fully realize the dream of the handheld calculator, the industry needed a different approach. The answer turned out to be the vacuum fluorescent display, or VFD.
The new technology, pioneered by Sharp, relied on a heated cathode in a vacuum to emit electrons that would then strike a phosphorescent material and produce visible, blue-green glow. Because the emission of electrons was aided by thermal energy, the design required a much lower operating voltage — around 15 V — and offered better contrast than neon tubes.
The following photo shows one of the earliest portable calculators, Sharp EL-8. The device tipped the scales at 1.5 lbs and was too big to fit in a typical pocket. Still, it heralded a new era of calculating on the go:
Note the unusual 8-segment digit pattern of eight individual “Itron” display tubes. The calculator also used a fairly peculiar multi-function key layout. This was likely a cost-saving measure, as the keypad relied on costly (but superbly reliable) magnetic Reed switches. Internally, the circuitry was still rather bespoke: the device used four general-purpose logic chips, a timing IC in a metal can, and nine driver chips for the display itself.
Novelties such as the wacky Itron display tube soon went the way of the dodo, the industry converging on the more familiar multi-digit 7-segment approach. These new displays combined low cost, high reliability, and excellent legibility:
Note the neatly stylized “4” on the display of this Panasonic calculator. The internals of this generation of devices were simplified too; this particular unit features a Texas Instruments TMS0100 series chip that combines ROM, RAM, timing, and arithmetic logic on a single silicon die.
Vacuum fluorescent displays were a massive leap forward, but the technology still had marked disadvantages. For one, as noted earlier, it needed a heated cathode and a modestly elevated voltage to trigger the emission of a sufficient number of electrons. This wasted electricity and required internal DC-DC conversion circuitry in most battery-operated gear.
Because of these shortcomings, VFDs were eventually ditched in favor of another nascent display technology: the light-emitting diode. LED displays, initially available only in red, weren’t nearly as pretty as VFDs, but they still had some charm:
The first commercially successful LED calculator was the rather ugly Busicom LE-120; that device also earned the distinction of being the first calculator to use a dedicated “all-in-one” calculator chip: Mostek MK6010.
My favorite design of this era is probably the wildly impractical Calcu-Pen, running off a single “N” type cell:
The final chapter in the evolution of calculator form factors is the development of liquid crystal displays (LCDs). LCDs don’t emit their own light; instead, they exploit the fact that the optical properties of certain organic substances change if subjected to an external electric field. Sharp was arguably the first to successfully commercialize the tech in 1973:
Reflective LCDs aren’t nearly as pretty as nixie tubes, VFDs, or LEDs, but they draw virtually no current in their steady state. Because of this, a new breed of calculators could be powered with solar cells or watch batteries. Heck, with the advances in chip design, you could even put a calculator in a wristwatch if you wanted to!
Readers old enough to remember the 1990s probably recall the nerdy fashion accessory that was the calculator watch. Here’s a particularly wacky design from Casio — a flip-top watch face that revealed a numerical keypad and an LCD:
The future lost
For a while, it seemed that counting devices were destined to become the hubs of our digital lives. In the 1980s and in the early 1990s, there was an explosion of "personal assistant” devices developed by calculator makers, keeping the traditional calculator functionality in the forefront. The units included features such as phone books, calendars, and “to do” lists. Casio was once again ahead of the pack:
Of course, that future wasn’t meant to be. The calcu-assistant ended up getting upstaged by the cell phone. Today, you can still buy a calculator — but why would you ever carry one?
👉 For a followup article on the history of RAM, click here. A catalog of other articles on this site can be found on this page.
I write well-researched, original articles about geek culture, electronic circuit design, algorithms, and more. This day and age, it’s increasingly difficult to reach willing readers via social media and search. If you like the content, please subscribe!
Your collection is incredible. I think that was my dad's sliderule. 😂 Really enjoyed reading this, thank you.
Awesome article and an impressive collection :)