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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.

By
Jason Marshall, PhD
4-minute read
Episode #245

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Have you ever thought about how it’s kind of weird that a circle has 360 degrees? At first thought, it seems like a rather random number to have chosen—why not 100, or 500, or 720 degrees? Was it really a random choice? Or was there actually some good reason that 360 was chosen to be the number of divisions in a circle?

As we’ll find out today, there was indeed a good reason. What was it? We’re not entirely sure. But we do have some pretty good ideas. And those ideas are exactly what we’re going to be talking about.

The When and Where of 360 Degrees

As you probably know, these days we humans like to divide a circle up into 360 pie-shaped wedges. Each of these wedges contains an angle at its vertex, and we say that the size of this angle is 1 degree. As you also probably know, degrees aren’t the only way we can measure angles. Angles are also measured in radians and sometimes (very rarely), they are even measured in obscure military units called gradians (which is why a lot of calculators have “deg rad grad” buttons on them).

While we don’t know exactly why the 360 degree convention was chosen (more on that in a minute), we do know approximately when and where it all started. At least we know that it came to be a long, long time ago—as in 4 or 5 thousand years ago with the Babylonians, the Greeks, and perhaps other even more ancient groups.

As to the question of why 360 degrees was chosen, here’s what we think happened …

Reason #1: The Length of the Year

Even if you have absolutely no idea right at this instant why there are 360 degrees in a circle, I bet that if you stop and think for a few minutes you can figure out one possibility. If after those few minutes you’re still not sure, think about where else you’ve seen a number that’s close to 360 in your life. And if you’re still stuck after that, think about the Sun … the Earth … orbits … and calendars.

Got it?

You might conclude that the Sun moves about 1/360 of the way along this circle every day.

The Earth takes one year to orbit the Sun. And a year is just a little more than 365 days. That means that the Earth rotates on its axis a little more than 365 times every year. And it means that every day the Sun appears to move about 1/365 of the way along a huge circle projected onto the sky that extends all the way around the Earth (called the ecliptic). If you lived a few millennia ago and didn’t have modern instruments to accurately record the positions of objects in the sky, you might conclude that the Sun moves about 1/360 of the way along this circle every day, which is exactly what ancient astronomers did. And they then made a leap and decided to divide this circle on the sky—and all circles—into 360 even parts so that the Sun would move through 1 part per day. Each of these parts was dubbed 1 degree, thus giving us the idea that a circle contains 360 degrees.

Makes sense, right? And given that the ancient Babylonian and Persian calendars were both based upon 360-day years, it seems likely that this simple astronomical observation is the reason a circle contains 360 degrees.

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.