How Eratosthenes Measured Earth's Circumference
The Story
Around 240 BCE, Eratosthenes, a Greek mathematician and the chief librarian at the Library of Alexandria, made one of the most remarkable measurements in ancient science—he calculated the circumference of the Earth with surprising accuracy using just simple observations and geometry.
Key observation: Eratosthenes noticed that at noon on the summer solstice, the Sun cast no shadow in Syene (modern-day Aswan, Egypt), while in Alexandria, about 800 km to the north, it cast a measurable shadow.
The Experiment
Eratosthenes' experiment relied on two critical observations:
- At noon on the summer solstice in Syene, the Sun's rays shone directly down a deep well, casting no shadow—meaning the Sun was directly overhead.
- At the same time in Alexandria, a vertical stick cast a shadow, indicating the Sun was not directly overhead.
By measuring the angle of the shadow in Alexandria (about 7.2°), Eratosthenes determined this was the same angle subtended at the center of the Earth between Alexandria and Syene.
The insight: Since 7.2° is approximately 1/50 of a full circle (360°), the distance between Alexandria and Syene (about 800 kilometers or 5,000 stadia) must be 1/50 of Earth's total circumference!
Interactive Demonstration
The Sun's rays at different locations create different shadow angles, which reveal Earth's curvature.
The Calculation
Eratosthenes used the following logic:
If the shadow angle is 7.2° and this represents the angle between the two cities as seen from Earth's center...
And the distance between cities is 5000 stadia...
Then Earth's circumference = 5000 stadia × (360° ÷ 7.2°)
Earth's circumference = 250,000 stadia (about 40,000 km in modern units)
Earth Model
This model shows how the shadow measurements from different cities can reveal Earth's curvature and size.
Historical Significance
Eratosthenes' calculation gave a circumference of about 250,000 stadia, which is remarkably close to the modern value of about 40,000 km (depending on which ancient stadion length is used for conversion).
This experiment, conducted over 2,200 years ago with simple tools, demonstrates how careful observation and mathematical reasoning can reveal fundamental truths about our world.
Fun fact: Eratosthenes didn't need to travel between the two cities himself. He learned about the no-shadow phenomenon in Syene from records and measured the shadow in Alexandria where he lived.