#122 240 BCE · Eratosthenes, Library of Alexandria · Science / measurement
Eratosthenes measured the size of the entire planet without ever leaving Alexandria
the problem
A quantity seemed to require travel, instruments, or observation nobody in the ancient world had access to
background
By the 3rd century BCE, educated Greeks accepted the Earth was a sphere, but nobody had a way to say how big it was — the obvious method, circumnavigating or otherwise physically traversing the whole planet, was wildly beyond the technology and organization of the era. Eratosthenes, running the Library of Alexandria, had access to travelers' reports and geographic records but no instrument capable of surveying a curve that large directly.
He had one useful fact on hand: at noon on the summer solstice in Syene (modern Aswan), sunlight reportedly reached straight to the bottom of a deep vertical well, meaning the sun sat directly overhead there at that exact moment. Nobody before him had thought to pair that isolated travelers' curiosity with a second, ordinary measurement taken somewhere else at the same moment.
what everyone would do
Try to measure the Earth directly — survey or travel its full curve, the way you'd measure any large physical object by walking its length. That approach was hopelessly beyond the era's technology and organization; nobody could traverse the whole planet's circumference to lay a measuring line against it, so the direct method wasn't merely hard, it was simply unavailable.
what they saw
Eratosthenes saw that he didn't need to measure the Earth's curve directly at all — he needed two local, easy measurements taken far apart that would differ only because of that curve, and nothing else. A shadow angle in one city and no shadow at all in another, both taken at the identical moment on the same meridian, isolates the one variable he actually wanted: how much the Earth bends between the two points.
the move
On the same solstice noon, Eratosthenes measured the angle of the shadow cast by a vertical stick (a gnomon) in Alexandria and found it about 7.2 degrees off vertical — Syene's well proved the sun was at zero degrees there. Since Alexandria and Syene lay roughly on the same meridian, that 7.2-degree gap was exactly the curvature of the Earth between the two cities, one-fiftieth of a full circle; multiplying that fraction by the distance between them, paced out by professional bematists at about 5,000 stadia, gave the Earth's total circumference.
why it works
Because sunlight arrives at Earth from effectively the same direction across small distances, any difference between the sun's angle at two points on the same meridian at the same moment can only come from the curvature of the surface between them — nothing else varies. Measuring that angle with a simple stick in Alexandria and knowing it was zero in Syene converts an astronomical, planet-scale question into simple local geometry: the angle gives the fraction of a full circle the two cities span, and multiplying that fraction by the paced-out distance between them yields the whole circumference. Two measurements anyone could take with a stick, a well, and a walked distance stood in for a survey no one in the ancient world could ever have performed.
the payoff
Eratosthenes' result of roughly 250,000 stadia converts, depending on which ancient stadion length is used, to somewhere between about 39,000 and 46,000 km against a true equatorial circumference of 40,075 km — a result within a few percent of correct, obtained with a stick, a well, and a distance paced out on foot.
where it breaks
The method depends on both measurement points sitting on (or very close to) the same meridian and being taken at the exact same moment — any east-west offset or timing mismatch introduces an error the calculation has no way to detect or correct for. It also depends on the distance between the two points being measured accurately; Eratosthenes' result was only as good as the bematists' paced-out figure for the Alexandria-Syene distance, so any systematic error in that separate measurement propagates directly into the final answer, which is part of why different ancient stadion-length assumptions produce different modern conversions of his result.
what came after
The method is taught today as one of the founding demonstrations of geodesy and is still reproduced in classrooms as a hands-on shadow experiment; it stands as the standard historical example of deriving an apparently unmeasurable global quantity from two cheap, purely local, simultaneous observations.
references
- [1]EratosthenesWikipedia, 2026en.wikipedia.org
- [2]How Eratosthenes Measured The Earth's Circumference With A Stick In 240 BCEIFLScience, 2023iflscience.com
- [3]Eratosthenes Measures Earth's CircumferenceEBSCO Research Starters, 2024ebsco.com