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Syene, near modern Aswân, Egypt, is close to the tropic of Cancer (23.5° N). At that line of latitude, at noon on the summer solstice (June 20 or 21), the Sun is directly overhead. Stand there and you’ll have no shadow. Alexandria is farther north, so there the noon Sun is not quite overhead on the solstice. You, or a stick, will cast a shadow that’s
at about a 7° angle.
Both cities lie near the same meridian, or longitude line, which is a north-south great circle (a circumference, really) around the Earth. Like all circles, the meridian has 360°. Since 7° is about Z\b/ of 360°, the distance between the two cities (5,000 stadia) must be Z\b/ of the distance around the meridian. By multiplying 5,000 by 50, Eratosthenes estimated Earth’s circumference at 250,000 stadia. Then, since he was aiming for an easy-to-use number, he added 2,000 stadia and got 252,000. (It’s evenly divisible by 60 and 360.)
So, you might be wondering by now, just how long was a stadium (singular for stadia)? The experts aren’t quite sure, but they say it’s between 150 and 158 meters (164 and 173 yards). At 157 meters (172 yards), a popular choice, Eratosthenes figured Earth’s circumference at about 39,250 kilometers (24,390 miles). That’s amazingly close to today’s measures of the north-south circumference, which is about 40,000 kilometers (24,855 miles).
—J.H.
