---
title: 'How Earth''s size was computed by Eratosthenes'
source: 'https://youtube.com/watch?v=9s0srZneJ38'
video_id: '9s0srZneJ38'
date: 2026-08-08
duration_sec: 127
---

# How Earth's size was computed by Eratosthenes

> Source: [How Earth's size was computed by Eratosthenes](https://youtube.com/watch?v=9s0srZneJ38)

## Summary

This video explains how the ancient Greek scholar Eratosthenes measured the circumference of the Earth using a well, a stick, and geometry. It walks through the key steps of his reasoning, from observing the sun's reflection in a well to calculating the angle and applying a ratio.

### Key Points

- **The Well in Syene** [00:01] — Eratosthenes learned about a well in Syene, Egypt, where on the summer solstice the sun's reflection could be seen at the bottom.
- **Observation in Alexandria** [00:27] — He waited for the summer solstice and checked his own well in Alexandria, but there was no reflection, indicating the sun was not directly overhead.
- **Parallel Rays** [00:42] — The sun's rays are effectively parallel because the sun is far away, which is key to the geometric reasoning.
- **The Tropic of Cancer** [01:08] — On the summer solstice, the Earth's axis is tilted toward the sun, creating a line of latitude where the sun is directly overhead—the Tropic of Cancer.
- **Measuring the Angle** [01:37] — Eratosthenes measured the angle between the sun's rays and the vertical in Alexandria as about 7 degrees, which corresponds to the arc between Alexandria and Syene.
- **Calculating the Earth's Size** [01:53] — By taking the ratio of the angle (7°) to 360°, he could deduce the Earth's circumference from the known distance between the two cities.

## Transcript

learned about you know the technique for measuring the radius of the Earth I think I saw so there's this old TV series called Cosmos and uh the way the story goes is that he had read somewhere of this well in this town called sinin
in Egypt uh where on one day of the year the summer soltice you could look down in the well and you could see the sun reflected in the water underneath and he said oh that's kind of cool uh um I don't live there but I have a well in my
the same thing so he wait until the summer solstice and he at noon he went down and looked at the well and there was no reflection of the Sun and he knew round let's think of the Sun as far enough away from Earth that all of its
rays of light are effectively parallel at any given moment if you draw a line from the center of the earth straight to the sun it passes through some point on the surface which must be experiencing this phenomenon where the sun is
directly overhead but if you were someone in aatosan time it would be very difficult to know exactly where this was happening at a given moment so what makes the summer solstice special is that on that day the axis of Earth's
rotation is tilted directly towards the Sun and as a result on this day as the Earth revolves around that axis over 24 hours there's a consistent line of latitude where all of the locations on this line predictably experience this
phenomenon this line has a special name it's called the Tropic of Cancer and the town cine that aatosan had read about sits on this line now aatosan himself was in Alexandria which is a bit north of that so the direction that he
perceives as straight up is going to sit at a certain angle away from the Rays of that Sun so by measuring that this angle was about 7° he could reason that the arc along the planet Earth between his Town Alexandria and Cen is about 7° so
if you take the ratio between this angle and the full 360° around a circle that should be the ratio of the distance between his town and Cen and the full know that distance you can deduce the size of the Earth