How a smart Greek guy calculated the size of the earth over 2,250 years ago

How do you calculate the circumference of the Earth without modern technology? The year was 250B.C., the location, Alexandria, Egypt. Eratosthenes of Cyrene was a Greek astronomer and the chief librarian of the Library of Alexandria. Among his , Eratosthenes was able to estimate the circumference of the Earth with astonishing accuracy. His measurements were less than 1% off from the currently accepted value.

Measuring the circumference of the earth

In 250 B.C., distances were measured in "stadia" where one stade is roughly the length of a typical sports arena of the period. Eratosthenes calculated the circumference of the Earth to be 250,000 stadia. Assuming one stade is equivalent to 160m puts the circumference at about 40,000 km. This is only 75km off from the actual circumference of 40,075km.

Eratosthenes used the geometric concept of similar triangles to make his calculations. This required a few assumptions:

  • First, Eratosthenes observed that at noon during the summer solstice, the sun was directly overhead in the nearby town of Syene (modern-day Aswan)
  • Then, using data from other surveyors, Eratosthenes found that the distance from his home in Alexandria to Syene was about 5000 stadia. 

To set up his experiment, Eratosthenes stuck a pole in the ground in Alexandria and waited for the summer solstice to come around. At noon he measured the shadow of the pole, forming a right triangle with the angle of the sun and simple geometry showed an angle of seven degrees.

Seven degrees is approximately 1/50 of a circle, so the calculation was simple: 50 times the distance between Alexandria and Syene. The result is 250,000 stadia.

1/50 or a circle = 5,000 stadia
        1 circle = 50 x 5,000 stadia
                 = 250,000 stadia