How to measure the Earth’s circumference

In about 240 BCE, a Greek mathematician named Eratosthenes calculated the circumference of the Earth with remarkable accuracy. What makes it especially impressive is that it only required very simple tools: a stick, a lot of walking, and some math.

Eratosthenes’s method relied on two key observations. First, placing a stick in the ground at noon on the summer solstice creates different angles of shadows depending on where you are on Earth. On the Tropic of Cancer, the stick doesn’t cast a shadow. If you travel directly north a long distance and put the same stick in the ground at the same time, it does cast a shadow.

This phenomenon was known to be the result of a widely accepted fact, even in Ancient Greece: that the Earth is round. Ancient peoples understood this based on some common observations: ships disappeared over the horizon from the bottom to the top, the Earth’s shadow cast during a lunar eclipse is round, and the stars move through the night sky in a way that suggests the Earth is a rotating, round object.

Eratosthenes was the first person known to estimate the Earth’s circumference by measuring the angles of two shadows in two different places in Ancient Africa. The first was in Syene, which was close enough to the Tropic of Cancer that a shadow did not appear. The second was in the city of Alexandria, which was 5000 stadia (an ancient measurement of distance) north-northwest of Syene. This distance was known because of the hard work of bematists, professional surveyors who measured distances by counting paces over great distances.

Eratosthenes took the angle measured in Alexandria and the angle measured in Syene and imagined the two lines extended deep to the center of the Earth. He took the angle of where the two imaginary lines intersected, which he determined to be 1/50th of the total degrees in a circle. He then multiplied the distance between Alexandria and Syene by 50 and came up with 250,000 stadia.

While the exact length of stadia is contested, and changed depending on the era and place during Ancient Greece, historians today generally agree that a single stade was between 150-210m, which puts Eratosthenes’ estimate at between 37,500 km and 52,500 km. If you used the stade length of Alexandria at the time of Eratosthenes, then his estimate is about 39,690 km. The Earth’s actual circumference: 40,075km!

Today, researchers use satellites and radio telescopes to measure the Earth’s circumference to the millimeter. But, if you want to go for a very, very long walk, take a straight and trusty walking stick and you too can measure the Earth’s circumference with alarming accuracy!