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Measuring the circumference of the world

Illustration for article titled Measuring the circumference of the world

Do you know how to measure the diameter of the earth? No? Then you're less advanced than they were in 230 BC. You're basically a Neanderthal with access to a microwave. Find out how to fix that in this post.


Part of getting a good education these days is finding out that people in ancient Greece were smarter than you are, or ever will be. For example, when Eratosthenes, the Greek guy who invented the word and science of geography, looked into a well at noon, he calculated a way to measure the diameter of the earth. When you look into a well at noon, all you're probably calculating is a way to unobtrusively stagger back home without your glasses, since people might get mad at you if you confess that you accidentally dropped them in there. (I'd like to take this opportunity to extend my apologies, once again, to the town of Sandover, Kansas. I hope your lemonade no longer tastes like eyeball guck.) Here's a way to begin to catch up, intellectually, with a guy who has been dead for two thousand years.

Eratosthenes looked into a well at noon in one place on a particular day of the year, and noticed that the sun hit full on the bottom of the well. On that same day of the year, in another year and another place a few hundred miles to the north, the sun cast a shadow over part of the bottom of the well.


Using the difference in the length of the shadows, he could calculate the difference in the angle at which the sunlight hit the northern most point, and the sunlight that hit the southernmost point. That angle is a tiny little slice of 360 degrees. The distance between the two of the points is a tiny little slice of the earth's surface.

Those little slices are proportionate to the whole, so by figuring out what percentage of 360 degrees that small angle is, it's possible to calculate what percentage of the earth's circumference the distance between the northernmost and southernmost point is.

Illustration for article titled Measuring the circumference of the world

Now, there's a slim chance that you do not live in a town with an open well. Many towns have been eliminating their wells, what with all the trouble Timmy caused in Lassie. This gives us all a chance for more math!


Get a couple of equal length poles, and a friend who is either already a few hundred miles directly to the north or south of you, or willing to drive there. Once both of you are in position at the same time on the same day, hold the poles perpendicular to the earth and measure the shadows they cast.

The pole, shadow and ground will form a right triangle. This lets you calculate the angle of the shadow using everyone's favorite part of the SOH CAH TOA acronym – the tangent. The length of the shadow is the O – opposite side – and the length of the pole is the A – adjacent side. These let you find the angle. Subtract the southernmost angle from the northernmost angle, and you have the slice of 360 degrees that you need. Now use this equation:

(Difference in angle)/360 = (Distance between the two points)/(Circumference of the earth)



Circumference of the earth = (360 x Distance between points)/(Difference in angle)


Spoiler? The circumference of the earth between poles is 40,008 kilometers.

Via Wikipedia, and the University of Utah, and


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Ghost in the Machine

Wow. I've never heard of the SOH CAH TOA acronym. We had to do brute force memorization of stuff like that. This was also before calculators so you had to look up the sine, cosine, and tangent of angles in a big table in the back of the textbook.

Now get off my lawn.