# Earth's circumference

Eratosthenes' method for determining the circumference of the Earth, with sunbeams shown as two rays hitting the ground at two locations in EgyptSyene (Aswan) and Alexandria.

Earth's circumference is the distance around the Earth, either around the equator (40,075.017 km [ 24,901.461 mi ])[1] or around the poles (40,007.863 km [ 24,859.734 mi ]).[2]

Measurement of Earth's circumference has been important to navigation since ancient times. It was first calculated by Eratosthenes, which he did by comparing altitudes of the mid-day sun at two places a known north–south distance apart.[3] In the Middle Ages, al-Biruni developed a way to perform the calculation from a single location and made a measurement at Nandana in present-day Pakistan.[4]

In modern times, Earth's circumference has been used to define fundamental units of measurement of length: the nautical mile in the seventeenth century and the metre in the eighteenth. Earth's polar circumference is very near to 21,600 nautical miles because the nautical mile was intended to express 1/60TH of a degree of latitude (i.e. 60 × 360), which is 21,600 partitions of the polar circumference. The polar circumference is even closer to 40,000 kilometres because the metre was originally defined to be one 10-millionth of the circumferential distance from pole to equator. The physical length of each unit of measure has remained close to what it was determined to be at the time, but the precision of measuring the circumference has improved since then.

Treated as a sphere, determining Earth's circumference would be its single most important measurement[5] (Earth actually deviates from a sphere by about 0.3% as characterized by flattening).

## History of calculation

Illustration showing a portion of the globe showing a part of the African continent. The sun beams shown as two rays hitting earth at Syene and Alexandria. Angle of sun beam and the gnomons (vertical sticks) is shown at Alexandria which allowed Eratosthenes' estimate of the circumference of Earth.

According to Cleomedes' On the Circular Motions of the Celestial Bodies, around 240 BC, Eratosthenes, the librarian of the Library of Alexandria, calculated the circumference of the Earth in Ptolemaic Egypt.[6] Using a scaphe, he knew that at local noon on the summer solstice in Syene (modern Aswan, Egypt), the Sun was directly overhead. (Syene is at latitude 24°05′ North, near to the Tropic of Cancer, which was 23°42′ North in 100 BC.[7]) He knew this because the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. He then measured the Sun's angle of elevation at noon in Alexandria by using a vertical rod, known as a gnomon, and measuring the length of its shadow on the ground.[8] Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays.[9] This angle was about 7°, or 1/50th the circumference of a circle; taking the Earth as perfectly spherical, he concluded that the Earth's circumference was 50 times the known distance from Alexandria to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia.[10] Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%.[10] In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference.[9]