Voltage Divider on Slide Rule
published 2026-02-23
by Christopher Howard
The voltage divider formula is represented on Wikipedia as
Vout = (Z₂ / (Z₁ + Z₂)) × Vin
This is really just a ratio equation:
Vout : Vin = Z₂ : (Z₁ + Z₂)
As such, this is well-suited for our slide rule, except we have to reckon with the addition in the denominator.
I had a case of this last week, where I was wanting a voltage divider for biasing, with 15 V input and 696 mV output. I wanted the resistor values to be as high as practical. So I aligned the top C scale value 6.96 with the bottom D scale value 1.5, setting the ratio. I could tell — using a little rounding — that the denominator should be somewhere between 15 and 30 times the numerator. I can start with the small resistor — the numerator — and get an idea of what the denominator resistance would need to be.
At the moment, my horizontal ruler shows C scale values between about 5 and 10 and D scale values between about 1 and 2, which — on the lower end of that — could be interpreted for our purposes as 500 kΩ and 10 MΩ. But 10 MΩ is not ideal, as the biggest resistors I have left are 5.6 MΩ.
So, I mark the D scale position of the C index, and slide the C scale over to allow access to the other C scale values. If I slide over to 2.7 on the C scale, i.e., a 270 kΩ resistor — which I have in abundance — that gives me 5.82 MΩ on the D scale. Conveniently, 5.82 MΩ - 270 kΩ = 5.55 MΩ, which is close enough to 5.6 MΩ for my tolerances. So, a 270 kΩ resistor and a 5.6 MΩ resistor will do the job.
Another combo I can see easily, if I slide the cursor over a bit more: is 390 kΩ for the C scale and 8.39 MΩ on the D scale. I just ran out of 8.2 MΩ resistors, but if I hadn't, then 8.2 MΩ + 390 kΩ = 8.59 MΩ which is not too far off from 8.39 MΩ, though my previous combination of resistors is more ideal in terms of output precision.
This is a selling point of the slide rule, namely, the ease with which we can explore various instantiated values of a ratio, using whatever specific numbers we are constrained to for practical reasons. E.g., the specific values of resistors we have on hand.
Copyright
This work © 2026 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.