Why are there 360 degrees in a circle?

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The below video covers the written tutorial below - why are there 360 degrees in a circle?

Theory 1

Why are there 360 degrees in a circle, and not a different number - a hundred for example. Well there are different theories. One theory is that the number 360 is divisible by many numbers. Compared to 100 for example, which is only divisible by 9 numbers, 360 is divisible by 24:

This makes the number 360 easier to work with in different situations. For example, one can divide an analogue clock face into 12 hours easily, by assigning 30 degrees to each 'hour'. And every minute, the minute hand moves half a degree.

If we assigned 100 degrees to a circle instead of 360 degrees, the maths would be messy - 8.3 degrees per hour and 4.167 degrees per minute.

Theory 2

But why 360? Why not 720 or 1080 degrees? They would be divisible by even more numbers.

The next theory is that there are roughly 365 days in the solar calendar, and 355 days in the lunar calendar. The number 360 is right in the middle, and it is much easier to work with compared to 355 and 365 (for the reason above).

Theory 3

The last theory is that a circle can hold six equilateral triangles, with sides that are the length of the radius of a circle. Roll your mouse over the image below to see.

So why 360 and not 6 degrees in a circle? The numerical system in current use is the decimal system. It has a base number of 10 - everything from currency (100 cents in a dollar) to measurements (e.g. 100 cm in a meter), to the major milestones in birthdays (the big '50' bash) use multiples of ten.

It's thought that this system came about in part because we have ten fingers and toes, making it easy to use our appendages to count.

This wasn't always the case (that is, we didn't always use the decimal system). In the past, some people used a sexagesimal system, which had a base number of 60. So the thought is that each of the angles in the six equilateral triangles that make up a circle were assigned the base number of 60 degrees, and 6 x 60 = 360 degrees.


So there you have it - three theories as to why circles have been assigned 360 degrees over any other number. At the end of the day, it doesn't really matter why we use 360 - what's important is that you know how to measure angles and use them when needed. But the trivia is cool, isn't it?