Al-Biruni's measurement of Earth's radius

What was discovered

He measured the height of a mountain and the angle by which the horizon dipped below the horizontal as seen from its summit, and used trigonometry to obtain an Earth radius of about 6,340 km. A single observer sufficed, with no need to measure long distances.

The result depends on the value of the cubit and on atmospheric refraction, which al-Biruni did not correct for; its accuracy may be partly coincidental.

What it led to

• trigonometric geodesy
• reliable values for the size of the Earth in the Islamic world
• al-Mas'udi's Canon (1037)

Built on

• Measurement of Earth's circumference (Eratosthenes)c. 240 BCE
• Al-Ma'mun's meridian arc measurementc. 830
• Trigonometry as a disciplinec. 980

Links

Sources✓ verified 2026-09-25

• https://thatsmaths.com/2021/06/10/al-biruni-and-the-size-of-the-earth/