Skip to main content

What Is Pi?

An illustration of the symbol for Pi.
Pi is an irrational number that's crucial to many mathematical formulas. (Image credit: MidSummerDay /

Understanding pi is as easy as counting to one, two, 3.1415926535…

OK, we'll be here for a while if we keep that up. Here's what's important: Pi (π) is the 16th letter of the Greek alphabet, and is used to represent the most widely known mathematical constant.

By definition, pi is the ratio of the circumference of a circle to its diameter. In other words, pi equals the circumference divided by the diameter (π = c/d). Conversely, the circumference of a circle is equal to pi times the diameter (c = πd). No matter how large or small a circle is, pi will always work out to be the same number. That number equals approximately 3.14, but it's a little more complicated than that. [10 Surprising Facts About Pi]

Value of pi

Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That's because pi is what mathematicians call an "infinite decimal" — after the decimal point, the digits go on forever and ever.

When starting off in math, students are introduced to pi as a value of 3.14 or 3.14159. Though it is an irrational number, some use rational expressions to estimate pi, like 22/7 of 333/106. (These rational expressions are only accurate to a couple of decimal places.) 

While there is no exact value of pi, many mathematicians and math fans are interested in calculating pi to as many digits as possible. The Guinness World Record for reciting the most digits of pi belongs to Rajveer Meenaof India, who recited pi to 70,000 decimal places (while blindfolded) in 2015. Meanwhile, some computer programmers have calculated the value of pi to more than 22 trillion digits. Calculations like these are often unveiled on Pi Day, a pseudo-holiday that occurs every year on March 14 (3/14).

Digits of pi

The first 100 digits of pi are:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067

The website has pi listed to the first million digits.

The life of pi

Pi has been known for nearly 4,000 years and was discovered by ancient Babylonians. A tablet from somewhere between 1900-1680 B.C. found pi to be 3.125. The ancient Egyptians were making similar discoveries, as evidenced by the Rhind Papyrus of 1650 B.C. In this document, the Egyptians calculated the area of a circle by a formula giving pi an approximate value of 3.1605. There is even a biblical verse where it appears pi was approximated:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. — I Kings 7:23 (King James Version)

The first calculation of pi was carried out by Archimedes of Syracuse (287-212 B.C.). One of the greatest mathematicians of the world, Archimedes used the Pythagorean Theorem to find the areas of two polygons. Archimedes approximated the area of a circle based on the area of a regular polygon inscribed within the circle and the area of a regular polygon within which the circle was circumscribed. The polygons, as Archimedes mapped them, gave the upper and lower bounds for the area of a circle, and he approximated that pi is between 3 1/7 and 3 10/71.

Pi began being symbolized by the pi symbol (π) in the 1706 by the British mathematician William Jones. Jones used 3.14159 as the calculation for pi.

Pi r squared

In basic mathematics, pi is used to find the area and circumference of a circle. Pi is used to find area by multiplying the radius squared times pi. So, in trying to find the area of a circle with a radius of 3 centimeters, π32 = 28.27 cm. Because circles are naturally occurring in nature, and are often used in other mathematical equations, pi is all around us and is constantly being used.

Pi has even trickled into the literary world. Pilish is a dialect of English in which the numbers of letters in successive words follow the digits of pi. Here's an example from "Not A Wake," by Mike Keith, the first book ever written completely in Pilish.

Now I fall, a tired suburbian in liquid under the trees, Drifting alongside forests simmering red in the twilight over Europe.

Now has 3 letters, I has 1 letter, fall has 4 letters, a has 1 letter, and so on, and so forth.

This article was updated on Oct. 19, 2018 by Live Science Senior Writer, Brandon Spektor.