c. 250 BCE

Eratosthenes Measures the Earth

Plato (427–347 BCE), Aristotle (384–322 BCE), Eratosthenes (c. 276–195 BCE)

The Greeks had generally accepted the fact that the Earth is round at least as far back as the time of Pythagoras, but estimates of the actual size of the Earth varied widely. Plato had guessed the Earth’s circumference to be around 44,000 miles (70,000 kilometers), corresponding to a diameter of about 14,000 miles (22,000 kilometers), and Archimedes had estimated a circumference of about 34,000 miles (55,000 kilometers) and diameter of 109,000 miles (17,500 kilometers). To make a more accurate determination, Eratosthenes, a mathematician, astronomer, and the third chief librarian of Alexandria, devised a simple experiment that was akin to treating the Earth as a giant sundial.

Eratosthenes had learned that at noon on the summer solstice in the southern Egyptian city of Syene, the Sun was almost exactly overhead (at the zenith), so posts in the ground did not cast any shadows. He also knew that in his own city of Alexandria in the north of Egypt, posts in the ground did cast (small) shadows at noon on the summer solstice. He made some measurements and determined that the Sun was a little over 7 degrees south of the zenith in Alexandria. This corresponds to about 1⁄50th of the circumference of a circle, so he surmised that the circumference of the Earth was about 50 times the distance between Alexandria and Syene. With a distance of about 5,000 stadia (the stadium was an ancient Egyptian and Greek unit of measure) between Alexandria and Syene, he estimated the circumference of the Earth at about 250,000 stadia, or 25,000 miles (40,000 kilometers). Assuming that 1 stadium was about 175 yards (160 meters) to Eratosthenes, this yields a circumference of about 25,000 miles (40,000 kilometers), which, given the various uncertainties and assumptions involved in the measurements, is essentially the correct answer.

Eratosthenes is widely regarded as the father of geography—indeed, he coined the word. It seems appropriate, then, that he was the first to accurately determine the size of the Earth. His method is also a fabulous example of the power of a simple, well-timed experiment. Archimedes had once quipped about levers, “Give me a place to stand, and I will move the Earth.” Eratosthenes could easily have retorted, “Give me a few sticks and some shadows, and I will measure the Earth.”

SEE ALSO Earth Is Round! (c. 500 BCE), Greek Geocentrism (c. 400 BCE), Sun-Centered Cosmos (c. 280 BCE).

Cartoon illustrating Eratosthenes’s simple method for measuring the circumference of the Earth. A vertical post in Syene (lower inset) casts no shadow at noon on the summer solstice. The same post in Alexandria (upper inset), however, casts a shadow that indicates it is 1⁄50th of a circle away from Syene.