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How to Use a Slide Rule

Analog WeekJust because ‘there’s an app for that’ doesn’t mean you have to use it. This week we’re going analog, reminding ourselves that we can live—and live _well_ —without smartphones, and seeing what’s worth preserving from the time before we were all plugged in 24/7.  

I’ve always felt a little left out of the traditional nerd stereotypes. I don’t wear glasses, my lady clothes have no real pockets so I can’t use a pocket protector, and I was born well after the reign of the slide rule. But in the spirit of Analog Week, I’m trying to learn.

A slide rule is a multi-purpose calculator tool. It’s what people used to do math in the days before calculators and now ever-present phones and computers. It looks like a ruler, but has a slide-y part in the middle. You can use it to quickly multiply and divide large numbers, and if you are a slide rule whiz you can even do exponents, roots, and trigonometry.

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You don’t have to track down vintage slide rules to play along: there’s a virtual slide rule right here. Slide rules can get very fancy, but the basic type has a body, one slide (the thing running down the middle), and a cursor that gives you a line so you can accurately line up the body and the slide with each other.

See those letters next to each scale of numbers? To multiply or divide, we can use the C scale (on the bottom of the slide) together with the D scale (right next to it, on the bottom part of the body). Ready?

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How to multiply

Let’s say you want to multiply two numbers, perhaps 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 here, you can see the C and D scales both have the number 1, then the number 1 again, then numbers up through 9, and then, finally, 2. All of those numbers in between actually represent 1.1, 1.2, 1.3, and so on. So when we go ahead with our example, make sure that if you’re looking for number 3, that you find actual number 3 and not 1.3.

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Okay. Are you ready? Let’s try 32 × 45. Photos of each step are in the slideshow above.

  1. Put the cursor’s hairline over the first number you want to multiply (let’s go with 32) on the D scale. To get 32, you’ll have to look for the 3, and then go two hash marks beyond it. (In other words, now you’re working with 3.2 instead of 32. You’re smart, you’ll remember to fix the decimals in your final answer.)
  2. Move the slide so that the index—the very beginning or end of the C scale on the slide—lines up with the hairline on the cursor. If we use the index at the beginning of the scale, our slide will be slid so far over that we won’t be able to move the cursor to get the answer. So we’ll use the index at the end.
  3. Find your other number, 45 (actually 4.5), on the C scale (on the slide). Move the hairline to this number. The matching number on the D scale (on the body) is the answer. It’s 1.44, but we’re smart about decimals, remember? So our answer is actually: 32 × 45 = 1440.

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Division is similar. Say you’re trying to do 16 ÷ 3.

  1. Find 16 on the D (body) scale.
  2. Slide the rule so that 16 on the D scale lines up with 3 on the C scale.
  3. The C scale’s index will point to the answer on the D scale. In this case, 5.3 and a smidge. (A modern day calculator tells me the answer is 5.33333 repeating.)

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For more advanced calculations on the slide rule, and to read up on how a slide rule even works (hint: logarithms), we recommend this excellently nerdy page from the University of Utah.