Slide Rules and Ratios
published 2026-01-21
by Christopher Howard
An interesting way to work with slide rules is to think in terms of ratios, where the scale on one ruler is one side of the ratio or fraction, and the scale on the other rule is the other side of the ratio. You can, say, have the C scale on top be the numerator, and the D scale on the bottom be the denominator. This works nicely, of course, for conversion problems:
So, put 1.2 on the C scale over 1 on the D scale, then move the cursor over the 7 on the C scale, and the value of x will be on the D scale, which is 5.83, or 0.583 ft after scaling. You can put feet on top, and inches on the bottom, if you prefer — it doesn't matter.
A little snag you might run into, with a straight slide rule, is that the answer value you are looking for might possibly run off the end of the answer scale. In that case, you will need to mark where the answer scale index is (mentally, or with the cursor) and then move the index on the other side of the scale to that location. A circular slide rule avoids this step, since the scales all wrap back around on themselves.
Other sorts of problems can be recast as ratio problems. A multiplication problem, ab = c, can be thought of as a/1 = c/b. So, for 2.3 × 5.6 = x, we have 2.3/1 = x/5.6. So, put the 2.3 on the C scale over the (right) index on the D scale, then move the cursor to 5.6 on the D scale. That puts the cursor at about 1.29 on the C scale, or 12.9 after scaling.
So, we are establishing a ratio relationship between two scales, and then we can get any particular ratio we want anywhere along the scale. This is fundamentally the way the specialty scales work, like the impedance solver on the Pickett N-16-ES, though some more complications might be added in, such as having a third scale that you use to add (multiply) some value on to another scale.
If one of our scales is inverted, our a/1 = b/c problem becomes (1/a)/1 = (1/b)/c, which leads us down some interesting paths of thought. But I'm out of time for writing.
Copyright
This work © 2026 by Christopher Howard is licensed under Attribution-ShareAlike 4.0 International.