What is pi?
Quick answer
Pi (written π) is the mathematical constant equal to the ratio of a circle’s circumference to its diameter. It’s the same for every circle, about 3.14159. Pi is an irrational number, meaning its decimal digits go on forever without repeating. It’s used in calculations involving circles, spheres, waves and much more.
Key facts
- Value
- About 3.14159265358979…
- Type
- Irrational and transcendental
- Symbol
- π, the Greek letter pi
- Pi Day
- March 14 (3/14)
Pi in formulas
| Measure | Formula |
|---|---|
| Circumference of a circle | C = πd = 2πr |
| Area of a circle | A = πr² |
| Volume of a sphere | V = (4/3)πr³ |
| Surface area of a sphere | A = 4πr² |
Example: A pizza with a 30 cm diameter has a circumference of about 3.14 × 30 ≈ 94 cm.
A history of pi
| Who | Approximation |
|---|---|
| Ancient Babylonians (about 1900 BC) | 3.125 |
| Ancient Egyptians (Rhind Papyrus) | About 3.16; see what papyrus is |
| Archimedes (about 250 BC) | Between 3 10/71 and 3 1/7, using polygons |
| Zu Chongzhi, China (5th century) | 355/113 ≈ 3.1415929 |
Welsh mathematician William Jones first used the symbol π in 1706, and Leonhard Euler made it popular.
How many digits?
Computers have calculated pi to hundreds of trillions of digits. Yet for most science, a few dozen are plenty: NASA uses about 15 decimal places for interplanetary navigation.
Pi Day
March 14 is celebrated as Pi Day, often with pies. It’s also Albert Einstein’s birthday, and the day Stephen Hawking died in 2018; see who wrote A Brief History of Time. In 2019, UNESCO declared March 14 the International Day of Mathematics.
Fun facts
- People memorize pi’s digits for fun; record holders have recited tens of thousands of digits.
- Some writers compose “pilish” texts, in which word lengths follow pi’s digits.
- In 1897, a bill in the Indiana legislature nearly declared an incorrect value of pi into law.
For other famous numbers, see the only even prime number and the Fibonacci sequence. Circles also appear in the Pythagorean theorem’s many proofs.
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