# What is a slide rule, and why was it’s invention such a big deal?

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What is a slide rule, and why was it’s invention such a big deal?

In: 1999

Electronic calculators, let alone a full “scientific calculator” like the ones you get for college courses, weren’t always a thing of course. The invention of the slide rule was big deal because it allowed you to calculate complex equations and large numbers much faster by hand. And by hand was still the only way to do it.

It’s an extremely simple mechanical calculator, based on the fact that log(A) + log(B) = log(A*B), so that a simple addition/ subtraction operation can be used to multiply numbers quickly. A skilled slide rule user could do calculations quickly and accurately enough to support things like manned space flight.

It basically automates the use of log tables to do multiplication and division. I used one in the early 70s to do physics and engineering calculations before I could afford a calculator – which were expensive!

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Multiplying numbers is harder than adding them. You need to do a bunch of smaller multiplications then add them up, and there’s plenty of scope for error.

Maths has a trick (invented by a Scot called John Napier) that lets you turn multiplication into addition. There’s this thing called the logarithm, and if you take the log of two numbers and add them together, it gives you the same answer as multiplying the two numbers and then taking the log of that. In other words log(A)+log(B)=log(A×B). This means you could convert the numbers to logs, add them together (easy) and then convert the answer back.

But, logs are tricky. We can’t easily do them in our heads. So we had to use charts known as log tables. You’d look up log(A) and log(B), add them together, then find the answer in the table to convert back. If this seems like a lot of effort with a lot of scope for error, that’s because it is!

Slide rules simplify this process. Instead of having the numbers spaces out linearly so the distance from 1 to 2 is the same as the distance from 2 to 3, slide rules use a logarithmic scale. This means the distance from 1 to 10 is the same as the distance from 10 to 100. Effectively, the distance along the ruler becomes the log of the number. And slide rules have two of these scales on them which can slide past each other.

So, when you want to multiply A and B, all you do is slide the ruler so the 1 on one ruler is beside the A on the second. That means every number y on the first is now lined up with y×A on the second, because the distances are added together (and the distances are the logs of the numbers). Then you just look along to find B on the first ruler, and the number across from it on the second ruler is just A×B.

This takes complicated, intricate multiplications and turns them into sliding a thing and reading a number!

Edit: thanks, kind stranger 🙂

Edit2: and all you other strangers too. Who’d have thunk so many folk cared about the length of tools used for multiplying. Oh, wait…