How to Use the Slide Rule
I’ve always felt a bit out of the ordinary nerd stereotypes. I don’t wear glasses, there are no real pockets in my women’s clothes, so I cannot use a pocket protector and I was born much later than the rule of the slide rule. But in the spirit of Analog Week, I’m trying to learn.
The slide rule is a versatile calculator. This is what people used to do math before calculators and now the ubiquitous phones and computers. It looks like a ruler, but there is a sliding part in the center. You can use it to quickly multiply and divide large numbers, and if you’re a slide rule expert, you can even do exponents, roots, and trigonometry.
You don’t have to look for old-fashioned slide rules to play along: there are virtual slide rules right here. Slide rules can be very fancy, but the base type has a body , one slide (the thing going down the middle), and a cursor that gives you a line so you can accurately align the body and slide with each other.
See these letters next to each scale of numbers? To multiply or divide, we can use the C scale (at the bottom of the slide) along with the D scale (next to it, at the bottom of the body). Ready?
How to reproduce
Let’s say you want to multiply two numbers, for example 32 * 45. Look at your slide rule. The C scale is on the slide and the D scale is on the body.
Now look at the numbers on each scale. There are … a lot of numbers. In the example given here, you can see that both the C and D scales have the number 1, then again the number 1 , then the numbers up to 9 and finally 2. All those numbers in between actually represent 1,1, 1,2, 1.3 and etc. So when we go on with our example, make sure that if you are looking for number 3, you will find a real number 3, not 1.3.
Okay. You are ready? Let’s try 32×45. Photos of each step are shown in the slideshow above.
- Place the hairline of your cursor on the first number you want to multiply (let’s make 32) on the D scale. To get 32, you will need to find 3 and then traverse the two bars behind it. (In other words, you are now working with 3.2 instead of 32. You are smart, you won’t forget to correct the decimals in your final answer.)
- Move the slide so that the pointer — the very beginning or end of the C scale on the slide — aligns with the hairline on the cursor. If we use the index at the beginning of the scale, our slide will be moved so far that we cannot move the cursor to get an answer. So, we’ll use the index at the end.
- Find your other number, 45 (actually 4.5), on the C scale (slide). Move your hairline by that number. The corresponding number on the D scale (on the body) is the answer. It’s 1.44, but we understand decimals, remember? So our answer is actually: 32 × 45 = 1440.
The division is similar. Let’s say you are trying to do 16 ÷ 3.
- Find 16 on the D scale (body).
- Move the ruler so that the 16 on the D scale matches the 3 on the C scale.
- The C scale index will indicate the answer on the D scale. In this case, 5.3 and a little. (A modern calculator tells me the answer is 5.33333 repetitions.)
For more complex slide rule calculations and how it works in general (hint: logarithms), we recommend this superb boring page from the University of Utah .