General

How many digits of Pi have been calculated?

Pi is one of the first (and most memorable) irrational numbers you learn about in school. Like the Energizer Bunny, it keeps going and going and going—Pi cannot be expressed as a whole number. Many have tried, but no one has ever calculated Pi to its end or to a point where Pi repeats itself. It's truly one of the most mysterious and elusive numbers in math. So, how many digits of Pi have been calculated?

What is Pi?

Person writing pi on a chalkboard
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Before you can jump into calculation, it’s important to understand what Pi stands for. Pi is helpful for calculating the dimensions of circles and other circular-shaped objects. Pi equals the circumference divided by the diameter of a circle. For those who are okay with rounding, Pi is often referred to as about 3.14. It doesn’t matter how big or small the circle is, Pi is always the same.

History of Pi

The Babylonians were the first people to attempt to calculate the enigmatic number. Around 1900 BCE, they found that Pi was equal to 3.125, which is pretty close considering that mathematics was a relatively new concept back then. For the Babylonians, Pi was important for architecture and measurements.

The first person to take an interest in Pi and attempt an accurate calculation was the Ancient Greek mathematician Archimedes of Syracuse in the 3rd century CE. To find the exact area of a circle, he used the Pythagorean Theorem to calculate the area of multiple polygons inside of a circle and add them together to get the closest possible approximation. In his treatise "Measurement of a Circle," Archimedes stated that "The ratio of the circumference of any circle to its diameter is less than 3 1/7 but greater than 3 10/71." They’re both ugly fractions, but they were a closer approximation than had ever been calculated before.

Greek symbol

Although people had been attempting to calculate Pi for thousands of years, it wasn’t until 1737 that Pi became associated with the Greek symbol “π.” Since the number proved impossible (so far) to calculate, a Welsh mathematician named William Jones decided to give it a symbol instead. That way, it can be described accurately in formulas without a lengthy decimal or impossible ratio.

Calculation by probability

Person writing what pi is equal to on a chalkboard
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In 1777, another brilliant mathematician, France's Georges-Louis Leclerc, Comte de Buffon, discovered that he could calculate many digits of Pi with some accuracy based on probability. His experiment involved dropping needles on lined sheets of paper. He would then determine the probability of a needle crossing one of the lines on the page. It might sound random, but the result of the experiment showed that the probability is directly related to the value of Pi. (Try this simple online simulation to see Buffon’s Needle experiment in action.)

Modern calculation

Of course, with technology, scientists can now calculate Pi more accurately than the mathematicians of ages past. In 2019, a Google developer named Emma Haruka Iwao used Google cloud technology to smash the previous Pi calculation record by 9 trillion digits. The official digit count on Iwao’s calculation is 31.4 trillion digits or, more precisely, 31,415,926,535,897 digits. To put the number in perspective, if the computer calculated one digit per second, it would take 995,687 years to reach the final number. Even out that many digits, there’s still no end in sight.

Memorizing Pi

For some people, simply calculating Pi isn’t enough; they want to memorize it. The challenge to memorize the most digits of Pi has been a popular contest for years. People from all over the world compete to see who has the best memory.

The current Guinness World Record holder for most digits of Pi memorized is Rajveer Meena from India. In 2015, the 21-year-old managed to successfully recite 70,000 digits of Pi from memory while blindfolded. The entire recitation took nearly 10 hours to complete.