Why Does a Circle Have 360 Degrees?

Where do the 360 degrees of a circle come from? When did this way of divvying up a circle become common practice? Who made this choice? And why? Keep on reading to find out.

Jason Marshall, PhD
4-minute read
Episode #245

Reason #2: Babylonians and Base-60 Numbers

But that’s not the end of the story. Because there are other reasonable ideas out there as to the origin of the 360 degree convention. As we saw earlier, the Babylonians used a 360 day calendar. And, as it turns out, the Babylonians also used a base-60 number system (called the sexagesimal system). Just as we use 10 different symbols to represent numbers in our base 10 decimal system, the ancient Babylonians used 60 symbols to represent numbers.

Why does this matter? Well, 60 x 6 = 360. This means that 360 is a nice even multiple of the number base in the Babylonian system (which would have had the same aesthetic value to their brains that a nice even multiple of 10 has to ours). But there’s more to it than that. The Babylonians knew about equilateral triangles. And they knew that if you arranged 6 of these equilateral triangles in a certain way with the edge of one aligned on top of the edge of the next, the last one would end up meeting back up with the first. In other words, the total angle formed by 6 of these equilateral triangles would be the same as the angle around a circle. Given the Babylonian usage of 60 as their number base, they decided that each of the angles of an equilateral triangle would be 60 degrees. And thus, when you multiply these 60 degrees by the 6 equilateral triangles that combine to create a sort of circle, you get 6 x 60 = 360 degrees. And thus, 360 degrees in a circle.

So, there’s that.

Reason #3: The Many Factors of 360

But that’s still not the end of the story … because there’s another reason to love the number 360. Namely, it’s evenly divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, and 180. That's a lot of factors!

And that makes 360 a really convenient number because it means we can divide a circle into 2, 3, 4, 5, 6, 8, 9, 10, 12, and so on even parts. It makes solving problems by hand—which, mind you, was the only way to solve problems thousands of years ago—much easier.

While this alone doesn’t seem like enough reason to have swayed people to define a circle as having 360 degrees, it certainly wouldn’t have hurt. And it’s entirely possible that it was a combination of all three reasons (and possibly others as well) that ultimately lead us to the definition of a degree that we still use today.

Wrap Up

OK, that’s all the ancient math we have time for today.

For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Earth and Sun image from Shutterstock.


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.