Around 240 BCE, a librarian in Alexandria calculated Earth's circumference to within 2% accuracy using only shadows, geometry, and a well in Syene.
The Sun in a Well
Around 240 BCE, Eratosthenes, the chief librarian at the great Library of Alexandria, encountered a curious report from the city of Syene, near modern-day Aswan. Travelers told of a deep well where, at noon on the summer solstice, the sun’s rays shone straight down to illuminate the bottom. No vertical object cast a shadow. This observation meant the sun was directly at the zenith, an angle of 0 degrees overhead. Syene's location is very close to the Tropic of Cancer, the line of latitude where the sun is directly overhead at noon on the solstice.
Eratosthenes, a polymath known for his work in geography and mathematics, understood the geometric implications. He thought that if the Earth was curved, the sun's rays would strike different parts of the planet at different angles at the same moment. He posited that the sun is so distant that its rays arrive at Earth essentially parallel to one another. This simple insight formed the basis of his experiment to measure the entire planet. He needed only one more measurement: the sun's angle at his own location.
Geometry on a Global Scale
On the next summer solstice, at the same time that the sun was illuminating the well in Syene, Eratosthenes measured the shadow cast by a vertical staff, or gnomon, in Alexandria. He found that the angle of the sun's rays was about 7.2 degrees from the vertical. This angle is 1/50th of a full 360-degree circle. Using basic geometry, Eratosthenes concluded that the physical distance between Alexandria and Syene must also represent 1/50th of the Earth's total circumference.
The distance between the two cities was known to be approximately 5,000 stadia. This figure was likely determined by bematists, professional surveyors trained to walk in equal steps to measure distances for maps and official records. Eratosthenes multiplied this distance by 50, resulting in a calculation of 250,000 stadia for the Earth's circumference.
The accuracy of his final number depends on the length of the stadion, a unit whose exact measure varied. If one uses a stadion of about 157.5 meters, his calculation comes to 39,375 kilometers—an error of less than 2% compared to the modern accepted polar circumference of 40,008 km. Even if a more common 185-meter stadion is used, his result of 46,250 km is still an achievement. His method made several small, incorrect assumptions that luckily cancelled each other out: Syene is not precisely on the Tropic of Cancer, and Alexandria is not directly north of it.
💡Fun Facts
Eratosthenes's nickname among some critics was "Beta" because they claimed he was the second-best in many fields, but never the first.
The distance of 5,000 stadia was not measured for the experiment but was likely a known figure from official land surveys conducted annually due to the Nile's shifting floodplains.
He also created a star catalog containing 675 stars and was the first person to calculate the tilt of the Earth's axis accurately.
The exact well in Syene is now lost, but the general location on Elephantine Island in Aswan is considered the probable site of the observation.
Elephantine Island is a public space, accessible throughout the day. The Aswan Museum on the island has specific hours, typically 9:00 AM to 5:00 PM.
Admission
Access to the island is free, though the local ferry has a small fee. The Aswan Museum requires an admission ticket.
Accessibility
The terrain on Elephantine Island includes sandy paths and uneven ground, especially around archaeological ruins. Paved walkways exist in the Nubian villages.
Eratosthenes Shadow Measurement Site - SyeneAswan Governorate, Egypt