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

#### 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.