How did Eratosthenes calculate Earth’s circumference in Alexandria?

Eratosthenes calculated the Earth’s circumference by applying a geometric method based on the assumption that the Sun’s rays strike the Earth in parallel lines.12

During the summer solstice at noon, he observed that the Sun shone vertically into a well in Syene, meaning the rays were at the zenith. At the same time in Alexandria, he measured the angle of the Sun’s rays from the vertical to be approximately 7.2°, or one-fiftieth of a circle.312

By knowing the distance between Alexandria and Syene—estimated at 5,000 stadia—he used the proportion of the arc length to the total circumference to determine the Earth's size. Specifically, he multiplied the distance by 50 to arrive at a total circumference of 250,000 stadia. This pioneering work established him as a founder of geodesy, providing a remarkably accurate estimate given the tools available at the time.12