How Did Eratosthenes Measure The Circumference Of The Earth

How Did Eratosthenes Measure The Circumference Of The Earth

How Did Eratosthenes Measure The Circumference Of The Earth – Eratosthenes, a Greek mathematician, astronomer, and geographer, is renowned for his remarkable achievement in accurately calculating the circumference of the Earth over two thousand years ago. His method, which involved simple geometric principles and observations of the sun’s angles, remains a testament to ancient scientific ingenuity. In this article, we delve into how Eratosthenes measured the Earth’s circumference and the significance of his accomplishment in the history of science.


Eratosthenes lived in the 3rd century BCE in Alexandria, Egypt, a center of learning and scholarship at the time. He was appointed as the chief librarian of the Library of Alexandria, where he had access to a vast collection of knowledge from various cultures. One of his notable contributions was the measurement of the Earth’s circumference.

The Method

Eratosthenes’ method relied on a few key observations and calculations:

  1. Sun’s Zenith Angle: Eratosthenes observed that on the summer solstice in Syene (modern-day Aswan, Egypt), the sun was directly overhead, casting no shadow. He measured the angle of the sun’s rays using a vertical stick, known as a gnomon, and found it to be 7.2 degrees from the vertical.
  2. Distance Between Syene and Alexandria: Eratosthenes knew the distance between Alexandria and Syene, approximately 800 kilometers (500 miles), as it was recorded in Egyptian surveying records.
  3. Assumption of Earth’s Sphericity: Eratosthenes assumed that the Earth was a sphere, which was a common belief among Greek scholars at the time.

The Calculation

Using the above observations and assumptions, Eratosthenes calculated the Earth’s circumference using basic trigonometry:

  1. Angle and Circumference Relationship: Eratosthenes realized that the 7.2-degree angle at Syene represented 1/50th of a full circle (360 degrees). Therefore, the distance between Syene and Alexandria represented 1/50th of the Earth’s circumference.
  2. Calculation: By multiplying the distance between Syene and Alexandria by 50, Eratosthenes estimated the Earth’s circumference to be approximately 40,000 kilometers (25,000 miles), remarkably close to the modern value of approximately 40,075 kilometers (24,901 miles).


Eratosthenes’ measurement of the Earth’s circumference was a groundbreaking achievement with profound implications:

  1. Confirmation of Earth’s Sphericity: Eratosthenes’ method provided empirical evidence for the sphericity of the Earth, a concept that had been theorized but not conclusively proven.
  2. Advancement of Geographical Knowledge: Eratosthenes’ calculation significantly advanced the understanding of the Earth’s size and shape, laying the foundation for future geographical exploration and mapping.
  3. Pioneering Scientific Method: Eratosthenes’ method exemplifies the use of empirical observation, mathematical reasoning, and deductive logic, establishing a precedent for the scientific method.
  4. Legacy in Science: Eratosthenes’ measurement of the Earth’s circumference remains a landmark achievement in the history of science, highlighting the capabilities of ancient scholars and their contributions to human knowledge.

Eratosthenes’ measurement of the Earth’s circumference stands as a testament to ancient scientific achievement and ingenuity. Through simple observations and calculations, Eratosthenes not only accurately estimated the Earth’s size but also demonstrated the power of scientific inquiry and reasoning. His method remains a cornerstone of scientific methodology and serves as an inspiration for generations of scientists and scholars.