How Eratosthenes Measured the Earth

Have you ever looked up at the sky and wondered just how enormous our planet really is? Measuring something as vast as the Earth seems impossible—especially without satellites, GPS, or modern tools. Yet over 2,000 years ago, one brilliant thinker managed to do it with nothing more than shadows, curiosity, and clever reasoning. His achievement isn’t just a scientific milestone—it’s a powerful reminder of how observation and imagination can unlock the world’s biggest mysteries.

An Ancient Puzzle: How Big Is Our World?

Imagine living in a time without satellites, GPS, or precise maps. People understood the Earth was large, but no one knew its true size. In ancient Alexandria, a scholar named Eratosthenes—a mathematician, geographer, and librarian—began asking deep questions about the world around him.
Historical details about his life are documented in Britannica’s biography of Eratosthenes.

He learned that in the city of Syene (modern-day Aswan), something remarkable happened every year during the summer solstice: at noon, the sun shone straight down a well, casting no shadow. This simple observation sparked a revolutionary idea.

The Shadow that Revealed Earth’s Curve

On the same day in Alexandria, a vertical stick did cast a shadow at noon. Eratosthenes realized this difference was only possible if:

• The Earth is curved, and
• The sun’s rays are nearly parallel when reaching Earth (a concept supported by NASA Earth Observatory)

He measured the shadow’s angle at about 7.2 degrees, roughly 1/50th of a full circle. He then used trained “pacers” to estimate the distance between Syene and Alexandria: 5,000 stadia.

Turning Observation into a Global Calculation

Using geometry, Eratosthenes realized:

• 7.2° = 1/50th of a full circle
• Therefore, the distance between the cities represented 1/50th of Earth’s circumference

He multiplied:

5,000 stadia × 50 = 250,000 stadia

Depending on which stadion length historians use (about 157–185 meters), Eratosthenes’ result ranges from:

39,375 km to 46,250 km

Modern measurement: 40,075 km

His result was amazingly accurate. His method is detailed in historical analyses like Smithsonian Magazine’s explanation of Eratosthenes’ technique.

Why This Story Inspires Young Learners

Eratosthenes didn’t need advanced technology—just shadows, distance, and logical thinking. His discovery teaches children that:

• Math begins with curiosity
• Big problems can be solved with simple observations
• Geometry helps us understand the world
• Creative thinking leads to real scientific breakthroughs

This story helps children see math as a powerful tool for making sense of everyday experiences.

Conclusion

The story of Eratosthenes shows that mathematical discovery often begins with simple questions. By using shadows and distances, he produced one of history’s most accurate scientific calculations. His work inspires children to explore, ask questions, and apply logical thinking to the world around them—proving that even the biggest mysteries can be solved with curiosity and clever reasoning.

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.

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