What Is Pi?

By: Marshall Brain, Dave Roos & Austin Henderson  | 
Pi is a fascinating number that is important to all sorts of mathematical calculations. The circumference of a circle divided by its diameter will always equal pi. alengo/Getty Images

Pi has mesmerized mathematicians for 4,000 years. It's the rarest mathematical constant, an unfailingly accurate ratio that's also never-ending. Researchers have calculated the digits of pi to more than 22 trillion decimal places without any repetition (that's called an "irrational number").

But what is pi? The answer is simpler than you think.


What Is Pi?

Pi is a circle's circumference divided by its diameter. (The diameter is twice the radius or double the length from any point on the circle to its center. The circumference is the distance around a circle.)

But what's remarkable is that no matter the size of the circle you are measuring, that ratio of circumference to diameter will always equal 3.1415926535897, usually shortened to 3.14.


Divide the circumference of a tennis ball by its diameter and you get 3.14. Divide the circumference of the planet Mars by its diameter and you get 3.14. Divide the circumference of the known universe by its diameter (assuming it's a perfect circle or sphere) — you get the point. As one mathematician put it, "Pi is part of the nature of the circle. If the ratio was different, it wouldn't be a circle."

This figure shows how the circumference of a circle with a diameter of 1.27 inches (32.35 millimeters) is equal to a linear distance of 4 inches (10.16 centimeters):

Calculating pi involves dividing the circumference of a circle by its diameter.

As you might imagine, 4.0 (the circumference) / 1.27 (the diameter) = 3.14.


A Storied Past: Tracing Pi's History

Both the Babylonians and the Ancient Egyptians tried to estimate pi. Back in 1900 B.C.E., the Babylonians dabbled in the circle's circumference and decided that pi equals approximately 3.125. Meanwhile, the Ancient Egyptians pitched in with their own rough numerical approximation: 3.1605.

Enter the Mathematicians

But it wasn’t until the Greek mathematician Archimedes and the Chinese mathematician Zu Chongzhi stepped onto the scene that pi's estimation truly got refined to the most accurate approximation before calculus and supercomputers gave us the definitive answer [source: Exploratorium].


  • Archimedes of ancient Greece: Particularly Archimedes, who lived between 287-212 B.C.E., brought polygonal methods to the forefront. He established upper and lower bounds for pi, getting impressively close to its true value.
  • Zu Chongzhi’s contribution: From 429-501 C.E., this Chinese mathematician didn't just calculate pi; he honed it to an impressive seven decimal places!

Symbolism and Pi's Universal Adoption

In 1706, the British mathematician William Jones made a choice that would become iconic. Jones assigned the Greek letter π to this wondrous number, perhaps because π is the first letter of the Greek words for periphery and perimeter.

Leonhard Euler, an 18th-century Swiss mathematician, took this symbolism to heart, popularizing its use. However, π wouldn't become a standard mathematical notation worldwide until 1934.

Pi in the Modern Era: From Tattoos to Holidays

The fact that you can find pi everywhere — not only in circles, but in arcs, pendulums and interplanetary navigation — and that it's infinitely long has inspired a cult following that includes plenty of geeky tattoos. In fact, it even has its own national holiday.


National Pi Day: A Mathematical Celebration

This model is ready to celebrate Pi Day as he walks the runway at the Niyazi Erdogan show during Mercedes Benz Fashion Week in Istanbul, Turkey, 2015.
Andreas Rentz/Getty Images For IMG

The Roots of the Holiday

The U.S. Congress might have officially recognized National Pi Day in 2009, but the roots of the holiday trace back to 1988.

Enter Larry "The Prince of π" Shaw, a beloved figure at the Exploratorium, San Francisco's renowned science museum [source: Exploratorium]. After the passing of the Exploratorium's founder, Frank Oppenheimer, Shaw crafted the idea of "π Day." The date, March 14 (or 3.14), fittingly echoes the initial digits of pi.


Even better, March 14 is also Albert Einstein's birthday, making π Day the ultimate geeky double-header.

The first π Day celebration was nothing more than Shaw and his wife handing out slices of fruit pie and tea at 1:59 PM (the three digits following 3.14), but the holiday quickly gained fame in the Bay Area.

Shaw eventually built the "Pi Shrine" at the Exploratorium, a circular classroom with a circular brass plaque at its center. Every Pi Day celebration at the Exploratorium ended with a colorful parade led by Shaw blasting his boombox (with a remix of "Pomp and Circumstance" set to the digits of pi) and circling the Pi Shrine exactly 3.14 times. The parade ended with the singing of "Happy Birthday" to Albert Einstein.

Celebrating π Day Worldwide

The Prince of π passed away in 2017, but the annual Exploratorium party continues, as do π Day celebrations the world over. How can you celebrate this quirky day?

  • Baking and eating: The wordplay between "pi" and "pie" isn't lost on enthusiasts. Pies and other circular treats become the delectable heroes of the day.
  • Crafting with pi: Unleash creativity with a construction paper pi chain, where every 10 digits adopt a different hue. Or, immerse in art by creating collages brimming with circular patterns.
  • Testing memory: Challenge friends in a pi memorization contest! Want to aim high? Consider the Pi World Ranking List. For context, Suresh Kumar Sharma from India set a record in 2015, recalling an astounding 70,030 digits of pi in just over 17 hours. Starting with the first 20 digits might be more achievable for most [source: National Pi Day]!

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.


Frequently Answered Questions

What are the first 200 digits of pi?
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644 2881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458 7006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270 3657759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362 440656643086021394946395224737190702179860943702770539217176
What is the first 100 digits of pi?
What number is pi exactly?

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More Great Links

  • Exploratorium. "A Brief History of Pi (π)" (March 8, 2019) https://www.exploratorium.edu/pi/history-of-pi
  • Exploratorium. "A Slice of Pi (π) Day History" (March 8, 2019) https://www.exploratorium.edu/pi/pi-day-history
  • NASA Jet Propulsion Laboratory. "How Many Decimals of Pi Do We Really Need?" March 16, 2016. (March 8, 2019) https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/
  • Pi World Ranking List. "Pi World Ranking List" (March 8, 2019) http://www.pi-world-ranking-list.com/index.php?page=lists&category=pi
  • Roberts, Gareth Ffowc. "Pi Day 2015: Meet the Man Who Invented Pi." The Guardian. March 14, 2015 (March 8, 2019) https://www.theguardian.com/science/alexs-adventures-in-numberland/2015/mar/14/pi-day-2015-william-jones-the-welshman-who-invented-pi