How a Stick and a Shadow Measured the Entire Earth

In 240 BCE, the chief librarian of Alexandria had a problem: he'd heard a rumour about a well.

In Syene, a city about 800 kilometres south, locals said that on one specific day each year — the summer solstice — you could look straight down into a deep well at noon and see the sun's reflection perfectly centred in the water. No shadow on the walls. No tilt. The sun was directly, perfectly overhead.

Eratosthenes already knew that on that same day in Alexandria, a vertical stick cast a clear shadow. He measured the shadow angle: about 7.2 degrees.

Two cities. Two different shadow angles. On the same day, at the same time.

The only way this makes sense is if the Earth is curved — and Eratosthenes knew it. The question was: how curved?

A 7.2-degree shadow difference is exactly 1/50th of a full circle (360 degrees). That means Alexandria and Syene are separated by 1/50th of the Earth's circumference. So multiply their distance by 50, and you have the whole thing.

800 km × 50 = 40,000 km.

The actual circumference is 40,075 km. He was off by less than 2%.

What makes this remarkable isn't just the accuracy — it's the audacity. Eratosthenes reasoned from two shadow measurements to the size of an entire planet. He turned a local observation into a global fact. No satellites. No aircraft. No way to even see the curvature with his own eyes.

The method works for a surprisingly subtle reason: the sun is so enormously far away that its light rays arrive at Earth essentially parallel. Like light from a flashlight miles away — by the time it reaches you, it's basically a flat beam. Eratosthenes assumed this without fully knowing why it was true. He was right.