How Eratosthenes Measured Earth Using Shadows and Math

Have you ever wondered how anyone figured out the size of our planet long before satellites and modern tools existed? Many parents feel unsure about explaining big concepts like Earth’s circumference, planetary size, or geometry to children. But the remarkable story of Eratosthenes—an ancient Greek mathematician—shows how simple observations and basic math can reveal astonishing truths about the world.

This story is not only fascinating but also a perfect way to spark curiosity in children about science, math, and how we understand our planet.

Eratosthenes’ Ingenious Observation

Around 240 BCE, many people still believed the Earth might be flat. Eratosthenes, however, was a scholar at the great Library of Alexandria and had access to reports from across Egypt. He learned something curious: in the southern city of Syene (modern Aswan), the sun cast no shadows at noon on the summer solstice. It shone straight down into deep wells—meaning the sun was directly overhead.

But in Alexandria, where he lived, a tall stick did cast a shadow at the same moment.

This difference sparked a revolutionary idea. If the sun were overhead in Syene but not in Alexandria, the Earth must be curved, not flat. If the Earth were flat, shadows would behave the same way in both cities.

An illustration showing Eratosthenes observing shadows at Alexandria and Syene, with parallel sun rays hitting a curved Earth.

How He Calculated Earth’s Circumference

Eratosthenes made two key assumptions:

1. The Earth is a sphere
2. The sun’s rays reaching Earth are essentially parallel because the sun is so far away

On the summer solstice, he measured the angle of the shadow cast by an obelisk in Alexandria. The angle was about 7.2 degrees.

This angle also represented the angle between Alexandria and Syene if you drew lines from each city to the Earth’s center—a brilliant use of geometry.

Next, he needed the distance between the two cities. Records suggested it was approximately 5,000 stadia, based on professional pacers or travel accounts.

He then used simple proportional reasoning:

• 7.2 degrees is 1/50th of a full circle (360°).
• If 5,000 stadia represent 1/50th of Earth’s full circle, then the entire circumference must be:
  5,000 × 50 = 250,000 stadia

A diagram illustrating Eratosthenes’ method using angles, sunlight, and the distance between the two cities.

A Legacy of Measurement

Eratosthenes’ estimate—250,000 stadia—comes remarkably close to modern measurements. Depending on the exact length of a stadion, his estimate was within 2% to 16% of the true value.

Modern science tells us Earth’s circumference is about 40,075 km (24,901 miles).

For his time, this was an extraordinary achievement. Using nothing but shadows, distances, and reasoning, Eratosthenes demonstrated:

• Observation
• Logical thinking
• Simple geometry
• Scientific curiosity

Why This Story Matters for Kids

Eratosthenes’ experiment shows children how simple ideas—angles, shadows, distances—can lead to big discoveries. It reinforces that:

• Science is about asking smart questions
• Math helps us understand the real world
• Curiosity can lead to major breakthroughs
• You don’t need advanced tools to do meaningful science

These ideas can inspire children to explore STEM, try their own experiments, and see math as powerful and exciting.

Conclusion

Eratosthenes’ story isn’t just ancient history—it’s a timeless lesson in how thinking, observing, and using simple math can uncover the secrets of our world. Sharing this story with your child can spark curiosity, foster scientific thinking, and show that even complex topics like Earth’s shape or size can be understood with basic tools and a curious mind.

It also highlights how mathematics supports early cartography, navigation, and astronomy—real-world applications that continue to shape our understanding of the Earth today.

About Think Academy

Think Academy, part of TAL Education Group, helps K–12 students succeed in school today by building strong math foundations and critical thinking skills. At the same time, we focus on the bigger picture—developing learning ability, curiosity, and healthy study habits that inspire a lifelong love of learning. With expert teachers, proven methods, and innovative AI tools, we support every child’s journey from classroom confidence to long-term growth.

Want more insights into math learning and parenting? Subscribe to our newsletter for weekly tips and the latest resources.