Quantitative Skills > Teaching Resources > Activities > BotEC: Age of the Earth

Back-of-the-Envelope Calculations: Age of the Earth

Barbara Tewksbury

Hamilton College
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Summary

Question

The Earth is about 4.6 billion years old. Let's try to get a perspective on how long that really is. Suppose that you decided to count to 4.6 billion and that you counted 1 number every second. How long would it take you to count how old you are? How long would it take you to count the following numbers of years?

5,500 years (since construction of the pyramids at Giza)

700,000 years (since the earliest appearance of archaic Homo sapiens)

66,000,000 years (since the extinction of the dinosaurs)

545,000,000 years (since the first abundant evidence of animals with hard parts)

4,600,000,000 years (since the birth of the Earth)

Assessment

Answer

How long it would take you to count your age depends, obviously, on your age. It would take me about 45 seconds. Here's how long it takes to count the other times at one number per second:

5,500 years would take about an hour and a half
700,000 years would take about 8 days
66,000,000 years would take about 2 years
545,000,000 years would take about 17 years
4,600,000,000 years would take 146 years!!!

If you decide to sleep and eat, then double the times above!

References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.

Controlled Vocabulary Terms

Subject: Geoscience:Geology:Historical Geology
Resource Type: Activities:Classroom Activity:Short Activity
Special Interest: Quantitative
Quantitative Skills: Estimation
Ready for Use: Ready to Use
Topics: Time/Earth History

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