Published and verified: 13 July 2026
The surviving account
Eratosthenes’ own account does not survive. Later authors, especially Cleomedes, describe a comparison between Alexandria and Syene in which the angular difference is treated as one fiftieth of a circle.
The baseline does the heavy work
The received distance is 5,000 stadia. Multiply that baseline by fifty and the circumference becomes 250,000 stadia; another transmitted total is 252,000. The method joins astronomy, geometry, and an inherited geographic distance.
Which stadion?
A stadion is not one universal modern length. Attic, Olympic, itinerary, and other standards produce different kilometre totals. The converter can reproduce several candidates, but it does not add a fictional Eratosthenes stadion where the historical magnitude remains disputed.
The larger lesson
Ancient long-distance calculation often depended on route knowledge, survey records, paced distances, administrative geography, and mathematical abstraction. The intellectual achievement remains striking even when modern conversion cannot be reduced to one exact kilometre figure.
Sources for this essay
- Mathematical Association of America, Eratosthenes and the Mystery of the Stades
- Oxford Academic, Eratosthenes and the Measurement of the Earth’s Circumference
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