Eratosthenes took the angle between an obelisk and its shadow at both Syene and Alexandria, Egypt at the same time during the day. It turned out that the difference was 7.2 degrees. They also figured out that the distance between the cities was 5000 stades, or stadium lengths. This was approximately 800 km. This was very inaccurate, but they did it by getting the army to march the entire way. So 7.2/360 degrees = 800 km/the circumference of the Earth.

So, his result was about 40,000 km as the circumference of the earth. The real circumference of the earth is 40,075 km, which makes it pretty remarkable how close he got.

David Witten