Math Project: Measure the Earth

Tomorrow, September 23, is the equinox — when night and day are equally balanced (or would be, if the sun appeared as a point, rather than a disc). If we lived on the equator, the sun would appear directly overhead at noon and would cast no shadow. Therefore, it’s a great day to perform Eratosthenes’ experiment of measuring the earth:

The Noon Day Project

The goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth.

I think this would be great fun for a math club or homeschool group, though it’s rather late notice to plan a meeting this week. But that’s okay — there’s another equinox 6 months from now.

Meanwhile, DO try this at home:

To find the latitude of your position:

To convert your latitude to a distance measurement:

  • GPS Latitude and Longitude Distance Calculator
    Enter your latitude, but enter 0 (zero) for longitude. Then enter 0 for both latitude and longitude for the equator. Click to calculate your distance to the equator in meters, km, feet, or miles.

And if it rains tomorrow, don’t worry! According to the Noon Day Project, the margin of error is very small as long as we do our measurements within a week of the equinox.

What Should the Answer Be?

According to, the circumference of the earth is about 40,000 km or 24,900 miles.

[Hat tip: CLIME Connections.]

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5 thoughts on “Math Project: Measure the Earth

    1. Not too late! Equinox is tomorrow, and you have up to a week of grace period before the error margin even begins to come close to the errors inherent in the measurement anyway. (Wobbly stick, fuzzy shadow, etc.) So you could really do this anytime through the end of the month or maybe a little beyond.

      For the official project, measurements are supposed to be made by the 28th, but for a personal project you could allow more time if needed…

  1. Oh, Denise! I’m so glad I commented! We’ll try this Friday, when their dad’s home to play with the math experiment with us. (We’ve been having great times with codes & ciphers over dinner lately.)

  2. A few of my Math Club kids got together to do this experiment on Thursday and Friday. We calculated the circumference of the earth with a less than 2% error. Woohoo!

  3. This sounds so fun to my math mind. Not sure if my kids would actually care or not though. I’m going to save this for trying next spring.

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