Calculating the Value of Pi using Toothpicks ... an experiment for Junior High math students.

... an experiment for Jr. High math classes

Pi is an irrational number. Its value is approximately 3.14159... ; the number of decimal places is infinite, and there is no repeating pattern.
If you'd like to see the first four thousand decimal places, you can visit our 'Pi' page.
Or perhaps you're curious as to what Pi actually is ... in that case, you can have a look at where Pi comes from.

One way to calculate for yourself the value of pi is to drop a lot of toothpicks onto a large piece of paper that has lines drawn on it!

Here's how it works. You'll need several boxes of toothpicks. Get a large piece of chart paper, and draw parallel lines on it, from one side to the other. The lines should be separated by a distance just slightly larger than the length of a toothpick.

(If you would like to send us your results, you'll have to
use standard toothpicks and a set line width; see below)

From a height of about one metre, drop a measured number of toothpicks onto the chart paper, so that they all fall randomly somewhere on the paper. Count how many toothpicks are touching a line (or would be, if they weren't resting on another toothpick).

Repeat this process as many times as you can. Lots of people can do it at once. All that's important is that, each time you drop some toothpicks, you write down how many you dropped, and how many of those ended up touching a line.

When you're done, find a total for each quantity.

You now have all the numbers you need to calculate Pi:

c ... toothpick length (in mm)
a ... line separation (in mm)
N ... total number of toothpicks dropped
M ... total number of intersections
(c must be less than a)

Here's the formula you need to calculate Pi:

(If you're interested in finding out where this formula
comes from, visit our main 'Calculating Pi' page)
You know the values for c (the length of a toothpick) and a (the distance between the lines). These must be measured in the same units.
You also have M (the total number of toothpicks that were touching a line), and N (the total number of toothpicks dropped).
Fill them in the formula, and work out your own value of Pi!
How many decimal places did you get to agree with the real value 3.14159...?

Send us your results! We'd like to collect as many results of this experiment as we can, and display them here, with running totals, and the value of Pi they generate. If your class would like to participate, you MUST use standard flat toothpicks:

Length 56 mm
The distance between the lines drawn on the paper must be 60 mm (6.0 cm)

(If you're just doing the experiment on your own you can use any type of toothpick, and any line spacing, as long as the units of measure are the same, and the line spacing is greater than the toothpick length. But if you want to add your results to others', to help us get a more accurate value for Pi, we all must be using the same values for c and a.)

Use the form below to send us the results of your class experiment.
All entries will be posted, with credit given to the contributors.

Buffon Applet | Deriving the Formula | Results