Potentiometer Calculator

published 2026-01-07

by Christopher Howard

When two potentiometers are chained together, the fractional voltages are multiplied. I.e., if you set the two potentiometers each to output 50% of their input voltage, the final output would be 25% of the first input voltage, or hopefully something close to that depending on several actual engineering details, in particular:

An interesting question to explore is how useful such a calculator would be in practice, especially compared to a slide rule. Decades ago, there were several educational computer kits — I think I've seen at least two different brands on ebay — which allowed users to experiment with this basic idea. I do not own one of these kits, but I spent some time studying the instruction manual for the Edmund Analog Computer Kit.

PDF Edmund Analog Computer Instruction Manual

This system is a simple design, with a 1000 Ω potentiometer and two 50 Ω potentometers. The pots are mounted on a panel that has three identical semi-circular dials printed on it — with each dial having four scales. The main scale is the linear scale — 0.0 to 1.0, but there is also a log scale, a sine/cosine scale, and a tangent/cotangent scale.

Rather than measuring the output voltage directly, a current meter is used, which is connected between the last two potentiometers. Potentiometer A is fed to pot. B, and the current meter is placed between pot. B and C. The basic idea is that you set up a multiplication problem on A and B. Then you turn C until the voltage across C is equal to the output from B and C, at which point the current meter will read null or zero.

With this equipment, we can do the following:

Multiplication is a straightforward operation as long as both numbers being multiplied are between 0.0 and 1.0. For all other values, one must simply convert the numbers to fit within that domain, using powers of ten. E.g., 832 becomes 0.832 x 10³. Then, in the end, add the exponents. Slide rule users will find this intuitive.

Division is similar, but uses the potentiometers in reverse: after converting numbers as necessary, you set the number you want to divide on C, then the number you want to divide by on B, and then null A to get the result on A. However, you run into some trouble if your first number is greater than the second number, as it will not be possible to null A. The recommended approach is to divide the first number by ten again, so that it is less than the second number. This is problematic, though, as then your first number will be less than 0.1 and therefore you will have lower precision. The manual also mentions that the computer is less accurate generally when dealing with lower voltage levels.

With square roots, you convert the number using powers of ten, set it on C, and then turn A and B together until you get a null. This is a straightforward procedure, unless you have an odd number of significant digits in the number you want to get the root of. In that case, you will need to multiply the number again by 0.316 to deal with that extra power of ten. I.e., √(10^-1) = 0.316.

Powers are based on the logarithm rule stating that when

then

So the linear scale is multiplied against the log scale to raise a number to a power. This is somewhat complicated as there are several steps, which involve converting the numbers to the correct domain — between 0.0 and 1.0; then getting the result log(y); reversing the conversion; pulling out the y value; then using the non-fractional part of the log(y) value to scale the y value up by the appropriate power of ten. The math involved here is interesting, but I think the steps are significantly more complicated than using the Log-Log scales on a slide rule.

Trigonometry is just multiplication and division, but using trig scales that have the degree values marked out to the appropriate linear value.

After studying this, I cannot see how using this kind of calculator would ever be more practical than using a slide rule. The precision on my slide rule is a lot better than the precision on the Edmund Analog Computer, as well. However, I imagine the precision gap between slide rules, and this sort of computer, could be narrowed somewhat by the use of op amp isolation between the potentiometers, and also fancier precision potentiometers.

I did a multiplication on my THAT, using two of the built-in pots, and the LCD voltage output display for port U. Accuracy was around 1%. However, THAT potentiometers are not very fancy, and they are difficult to set to a value more precise than 0.01 Machine Unit.

This work © 2026 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.

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