How Eratosthenes calculated the Earth's circumference?

Eratosthenes figured out how big Earth is by using shadows and a little bit of clever thinking.

Long ago, there was a smart person named Eratosthenes. He noticed that on a certain day in the city of Syene, the sun shone directly down a deep well, no shadow at all! But in another city called Alexandria, a few hundred kilometers away, the same day had a small shadow. That meant the sun wasn’t straight overhead there.

Eratosthenes thought this was because Earth is round, like a big ball. He measured the angle of the shadow in Alexandria, it was about 7.2 degrees. He knew that a full circle is 360 degrees, so he figured out how many of those 7.2-degree angles fit into 360.

Then, he asked someone how far it was from Syene to Alexandria, and they told him! It was about 5,000 stades, which is like a really long race.

He did the math: if 7.2 degrees equals 5,000 stades, then 360 degrees must be 5,000 times 50, that’s 250,000 stades! And he had just measured Earth's circumference!

It was pretty close to the real size of Earth, not bad for someone who only used shadows and a bit of math!