Pi (π)

pi circle diameter


Draw a circle with a diameter (all the way across the circle) of 1

Then the circumference (all the way around the circle) is 3.14159265... a number known as Pi (its symbol is π)

circumference, diameter, radius

So Pi is:

The Circumference
divided by the Diameter
of a Circle.

Example: You walk around a circle which has a diameter of 100 m, how far have you walked?

pi circle 100m diameter

Distance walked   = Circumference
    = π × 100 m
    = 314.159... m
    = 314 m (to the nearest m)


pi circle diameter


To help you remember what π is ... just draw this diagram.

Finding Pi Yourself

Draw a circle, or use something circular like a plate.

Measure around the edge (the circumference):

plate circumference 82
I got 82 cm

Measure across the circle (the diameter):

plate diameter
I got 26 cm


82 cm / 26 cm = 3.1538...

That is pretty close to π. Maybe if I measured more accurately?


The radius is half of the diameter, so we can also say:

circle radius=1, half circumference=pi


For a circle with a radius of 1

The distance half way around the circle is Pi = 3.14159265...


In fact π is approximately equal to:


The digits go on and on with no pattern. π has been calculated to over two quadrillion decimal places and still there is no pattern to the digits


A quick and easy approximation for π is 22/7

22/7 = 3.1428571...

But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.


A better approximation (but still not exact) is:

355/113 = 3.1415929...
(think "113355", then divide the "355" by the "113")

Remembering The Digits

I usually just remember "3.14159", but you can also count the letters of:

"May I have a large container of butter today"
3 1 4 1 5 9 2 6 5

To 100 Decimal Places

Here is π with the first 100 decimal places:



Calculating Pi Yourself

There are many special methods used to calculate π and here is one you can try yourself: it is called the Nilakantha series (after an Indian mathematician who lived in the years 1444–1544).

It goes on for ever and has this pattern:

3 + 4 2×3×4 4 4×5×6 + 4 6×7×8 4 8×9×10 + ...

(Notice the + and pattern, and also the pattern of numbers below the lines.)

It gives these results:

Term Result (to 12 decimals)
1 3
2 3.166666666667
3 3.133333333333
4 3.145238095238
... ... etc! ...

Get a calculator (or use a spreadsheet) and see if you can get better results.


Pi Day

Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14


Activity: Find an Approximate Value For Pi