Some of the most famous science experiments to do at home are also the oldest. More than 2,000 years ago, a librarian in Alexandria measured the size of the entire Earth with a stick, a shadow, and careful reasoning. You can repeat his experiment this week with a ruler, a sunny day, and a calculator.

It’s a perfect project for lifelong learners. There’s no kit, the math fits on an index card, and at the end you’ll have measured your own planet. That’s the 25Pages approach in action: master one idea deeply enough to explain it to anyone.

How Eratosthenes did it

Eratosthenes, born around 276 B.C., became chief librarian of the Library of Alexandria, according to APS News from the American Physical Society. He heard that in Syene (today’s Aswan, Egypt), at noon on the summer solstice, the Sun lit the entire bottom of a well. The Sun was directly overhead.

At noon on the same date in Alexandria, a vertical stick still cast a shadow. Eratosthenes measured the Sun’s angle from straight overhead as about 7.2 degrees, or 1/50 of a full circle. If the Earth is round and the Sun’s rays arrive parallel, that 7.2 degrees is also the slice of Earth’s circle between the two cities. The cities were about 5,000 stadia apart, so the whole circumference had to be about 50 times that: 250,000 stadia.

NASA’s Imagine the Universe notes that if a stadion was about 0.15 km, his answer works out to roughly 40,000 km. That’s remarkably close to the modern value of about 40,070 km. Historians still debate the exact length of the stadion he used, which is a good reminder to always ask what units a measurement is in.

Make a prediction first

Write down your best guess for Earth’s circumference in miles or kilometers, without looking it up. Then guess how close a stick-and-shadow measurement can get: within 50 percent? Within 10 percent? You’ll compare at the end.

What you need

• A straight stick, dowel, or pencil (a 1-meter stick makes the math easy)
• A level, sunny surface
• A way to check the stick is vertical: a small level, or a string with a weight
• A tape measure or ruler
• A calculator with an inverse tangent (tan⁻¹) button. Most phones have one in scientific mode.
• The NOAA Solar Calculator to find solar noon and the Sun’s declination for your location and date

Step-by-step

1. Find solar noon. Enter your location and date in the NOAA calculator. Solar noon is when the Sun crosses your local meridian, and it’s usually not 12:00 on the clock. At that moment, a vertical pole’s shadow points due north or due south, per NOAA’s glossary.
2. Note the solar declination for that date from the same calculator. This is the latitude where the Sun is directly overhead at noon today. It ranges from −23.44° to +23.44° through the year. It’s your modern “Syene.”
3. Set up the stick. Stand it perfectly vertical on level ground and measure its height above the ground.
4. Measure the shadow at solar noon, from the base of the stick to the tip of the shadow.
5. Find the angle. Angle from vertical = tan⁻¹(shadow length ÷ stick height). For a 1 m stick with a 0.70 m shadow, that’s tan⁻¹(0.70) ≈ 35°.
6. Find the arc. On a map, measure the north–south distance from your location to the latitude where the Sun is overhead (the declination from step 2).
7. Scale up to the whole Earth. Circumference = distance × (360 ÷ your angle).

Partner version: for a result closer to the original, team up with a friend or family member several hundred miles due north or south of you. Both of you measure at local solar noon on the same day. Use the difference between your two angles and the north–south distance between you. A global Eratosthenes Experiment project connects schools for exactly this kind of paired measurement.

Why your answer won’t be perfect (and why that’s the point)

• A stick that leans by a single degree shifts your angle by about a degree. On an arc of a few hundred miles, that’s a big error.
• The Sun is not a point, so the shadow tip is fuzzy. Measure to the center of the blur.
• Eratosthenes assumed Alexandria was due north of Syene. According to APS News, that wasn’t exactly true.

Repeat on three days, average your results, and estimate your error. That’s how real measurement science works.

Safety notes

• Never look at the Sun, directly or through any lens, binoculars, or camera. You only need to look at the shadow on the ground.
• Use sunscreen and a hat, since solar noon is when sunlight is strongest.
• Set up in a safe spot away from traffic, and don’t leave a sharp stake where someone could trip.

Check your prediction

Compare your result with your guess and with the modern value of about 40,070 km (24,900 miles). How close did you get? Can you explain to someone else why a shadow in one city tells you the size of the planet?

Keep learning, one idea at a time

If you love the stories behind great ideas, The Chronicle MMXXVI Editor’s Edition ($480) is the 25Pages annual hardback for lifelong learners. The Chronicle 2026 Vol. I Standard Edition is $347. For more hands-on projects, see the DIY Blue Book of Experiments MMXXVI ($480). Explore everything at 25Pages.com.