Circumference and Area of Circles: What Pi (π) Really Means

Students frequently ask: "What is Pi, and why is it always 3.14?" Pi (written as the Greek letter π) is not just a random number to plug into formulas. It is a fundamental truth about every circle in the universe.

The String and Soup Can Experiment

1. Take any round object: a soup can, a coin, or a bicycle wheel.
2. Wrap a piece of string once around the outside edge. Cut the string to match the circle's distance around (the circumference).
3. Now measure the distance straight across the center of the circle (the diameter).
4. Lay the circumference string next to the diameter. Guess how many diameters long the string is?

It is always a little more than 3 times as long! Exactly 3.14159... times as long. That ratio is Pi!

The Two Essential Circle Formulas

• Circumference (Distance around): C = 2 × π × r (or π × d)
• Area (Space inside): A = π × r²