Slide Rules: Ratios, Square Scales, Power
published 2026-01-30
by Christopher Howard
During some electronics work, I was presented with a power (wattage) problem based on voltage and resistance. The formula for this is
P = E² / R
This got me wondering what would be the simplest way to do this using a slide rule. Ratio problems are simple, but we have the square function as well to deal with. My first though was to look for an A scale. My Pickett N-16-ES does not have one. The next slide rule I pulled out, the POST VERSALOG, does not have an A scale, but it does have R₁ and R₂ scales. The idea is similar to an A scale, except instead of having two normal log scales squeezed into one scale, you have half of one normal log scale taking up the full length of R₁, and the other half on R₂.
R₁ and R₂ are on the bottom ruler, so we can set a value on R₁ or R₂ with the cursor and the square will be on scale D on the same ruler. Since this is the bottom ruler, we rearrange P = E² / R into this form
1 / P = R / E²
Now, with the help of the cursor, align the bottom and middle rulers so that the resistance value on the middle ruler C scale lines up with the voltage on the R₁ or R₂ scale. Then the 1 (index) of the C scale on the middle ruler will line up with the power value on the D scale on the bottom ruler.
So, that is just two operations, basically — setting the cursor and sliding the middle ruler. As an interesting side note, we could see alternative combinations of voltage and resistance that would result in the same power output, though it maybe is a little difficult to see how that would be useful in practice. Alternatively, we could slide the middle ruler around to see how the power output would change if we tried some other resistor values.
A tricky part, though, is we still need to deal with the exponents, which is a little complicated because we have to double the exponent of the voltage. For that reason, we will likely need to do this on paper, to avoid making a mistake on the exponents. E.g., with a voltage of 120 V and a resistance of 16 Ω, you end up with a 10/10⁴ ratio, i.e., multiply by the result by 10³, and then you will need to divide off another power of ten because because 1.2² / 1.6 = 1.44 / 1.6 = 0.9. So, the result is 0.9 x 10³ or 9 x 10² = 900 Watts. So, you can see how it might be difficult not to mess up the exponent math without a visual reference on paper.
Copyright
This work © 2026 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.