A man knew the circumference of Earth 2000 years ago

No need to mention he knew the Earth was round!

4 min readJun 30, 2017

Image Credit: Eratosthenes Experiment, 23 September 2015 by Inspiring Science Education

On contrary to the common belief, it was known that Earth was round long before Portuguese explorer Ferdinand Magellan (1480–1521) had completed the first circumnavigation of the world [2] or Christopher Columbus (1451–1506) sailed to India [3].

Known as the father of geography, born at Cyrene (in modern-day Libya), Eratosthenes was the head librarian of Alexandria’s Great Library in Egypt. He was a scientific writer, an astronomer, and a poet [4] who was able to estimate the circumference of Earth (with a very small margin of error) using the difference in the elevation of the noontime sun at two different locations [5]. However, we indirectly learn his discoveries and experiments since the Libary of Alexandria was burned down and no copies of his work could survive. Therefore his work was lost for centuries which might have been even changed the course of history!

It was in Alexandria that Around 240 B.C.E. Eratosthenes heard about a town of Syene (known today as Aswan)[6], south of Alexandria, the sun passed directly overhead on the summer solstice* that sun casted no shadow on a local well but shined directly down inside.

Exact locations of Alexandria (Eratosthenes) and Syene (the well). Image Credit: Google Maps

So the angle of the sun rays must have been 0° in Syene during summer solstice*. Then he reasoned, assuming that the sun is far enough that its rays are parallel when they hit to Earth, he used a vertical rod (Gnomon**) [6] to measure the angle of the sun rays in Alexandria. Then he determined, the sun was 7.2° south of Zenith***, which is exactly 1/50th of a circle (a complete tour is 360°).

Image Credit: “*Eratosthenes — Measuring the Circumference of the Earth in 240 BC”*

Then he did the math. The distance between the 2 cities must be 1/50th of the Earth’s circumference since Earth is a sphere. He knew the distance between the cities from the travelers as 5000 stadia. The unit of length he used, stadia (sing. stadion), was the length of an athletic stadium. However not all the stadiums were built at the same size back in that time. In Greece, a stadion would roughly be 185 meters (607 feet), while in Egypt about 157.5 meters (517 feet) [7]. Assuming that he used the Egyptian one, 5000 stadia would be around 800 kilometers (≈500 miles), so he multiplied 5000 stadia with 50, he concluded the circumference of Earth must be 250000 stadia (≈ 39,375 kilometers or 24,860 miles), which means only a %2 of error since the actual circumference of Earth is 40,041. If he used the Greek stadion, he would get 46,620 kilometers, which is just 16% bigger than the actual value. Still pretty accurate!

Regardless of the actual values he found, Eratosthenes is credited as the first geographer as the concepts he invented are still widely used today (Like Earth is round!). Plus anyone today can measure the size of Earth with two locations at the same longitude and simultaneous measurements of shadow lengths [8].

To see how crucial his experiment was and to see his work being lost for centuries might have changed the course of history, consider this example. We know that Colombus estimated the circumference of Earth way smaller than how it actually was [4]. If the findings of Eratosthenes had not been lost for centuries, so if Columbus knew about Eratosthenes who had calculated the circumference of Earth, he would have never sailed to West, since at that time no ship could store enough water and provisions to stay that long in the sea [9]!

*Summer Solstice: The longest day of the year, when the sun rises highest in the sky.

** Gnomon: Part of a sundial that casts a shadow.

***Zenith: Point on the celestial sphere directly above an observer on the Earth.