Facit C1-13 Mechanical Calculator | How to Use

Watch how basic calculations are performed on a vintage Facit C1-13 mechanical calculator. Also watch a futile attempt to divide by zero.

A little bit of history
Before the advent of electronic computers in businesses, mechanical calculators like these were used, either hand-cranked or driven by an electric motor. The Facit C1-13 was made by the company Åtvidaberg-Facit of Sweden sometime in the late 1950 or early 1960s and is a masterpiece of mechanical engineering, and it is very smooth and reliable in operation.

Until the early 1970s Sweden had a profitable and prosperous calculator industry employing thousands of employees in factories and in sales agents' offices around the world and countless service technicians until it all collapsed in the matter of a mere two years in the beginning of the 1970s. Electronic calculators quickly took over, and mechanical calculators, with their 1-2,000 mechanical parts simply could not be made at prices that were competititive with silicon-based calculators. Facit tried to adapt to the new technological reality, but were unsuccessful, and the company went from high profitability to collapse within just a couple of years. Facit's failure was so sudden and astounding that its story is today used a common business case in the Swedish business curriculum, and the once-profitable company's sudden collapse due to failure to adapt is colloquially known as the Facit Trap .

How does it work
These mechanical calculators basically work by applying addition or subtraction using a variable amount of protruding pins on wheels that interact with a counting mechanism. Turning the crank forward (clockwise) adds a chosen number to an accumulation register, and turning the crank in reverse causes the number to be subtracted. Since multiplication basically consists of repeated addition, and since division is simply repeated subtraction and keeping track of a final remainder, these calculators were also capable of multiplication and division, especially because special mechanisms allow adding or subtracting the operand in multiples of 10, 100, 1000, etc., greatly speeding up the computations.

A professional tool
In today's money these calculators were not cheap instruments. They cost approximately the modern equivalent of an office desktop computer and required regular servicing by a technician for smooth and reliable operation of the several hundred mechanical parts inside the calculator. Nowadays you may see them sold in poor condition at bargain prices at flea markets, but if you find a good, functional one it can be lots of fun to play with and be reminded of simple mathematical facts that you learned in school but have long-since forgotten.

Mechanical calculators vs Slide rules
Now you might ask: Weren't slide rules the typical tool for doing calculations before the electronic calculators? Good question! And the answer is yes and no .

Yes for engineering applications where small inaccuracies (down to approximately one part in 1000) could be tolerated slide rules were powerful instruments and also allowed more computation of more advanced functions such as logarithms, exponentiation (including exponentiation with an arbitrarily chosen exponent), arbitrary roots, and trigonometric functions.

But no for financial computations. Here accuracy down to the final digit is important, and thus the mechanical calculator which offers extreme precision was the the only option, except from resorting to doing calculations entirely by hand.

How about more advanced mathematical functions?
Running businesses rarely required functions more advanced than addition, subtraction, multiplication and division. But, given the fact that exponentiation is just repeated multiplication, and multiplication is repeated addition, you could do exponentiation with integer exponents on these calculators. Square root extraction is also possible (perhaps surprisingly easily in fact), and with some mechanical calculators the documentation included model-specific tricks to speed up the computation of square roots. However, for advanced financial functions such as computation of compound interest, books with lookup tables where simply used instead. Given that square roots could be computed, logarithms could also be computed using Euler's method, although I wouldn't bother doing it if a table of logarithms was available. I've tried Euler's method for computing logarithms a few times just for fun, and while very educational it's also very, very tedious.

How about trignometric functions? No, not a chance. Well, technically yes, you could turn the trignometric functions into Taylor polynomials and compute those, but now we have moved into territory where advanced slide rules reigned supreme until the electronic scientific calculators took over the scene. Use the right tool for the right job...

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