The digits we search come from one of the biggest calculations ever done: 100 trillion decimals of π, computed on Google Cloud in 2022. But people have been chasing π's decimals for well over two thousand years, and for most of that time, the record was set with nothing but a pen, a lot of patience and some very clever ideas.
Trapping a circle (about 250 BC)
The first person we know who worked π out properly, rather than guessing, was Archimedes of Syracuse. His idea was beautiful. You can't measure a curve with a straight ruler, but you can measure a polygon, a shape with straight sides. So he drew one polygon just inside a circle and another just outside it. The circle's length had to be somewhere in between.
He started with hexagons and kept doubling the number of sides until he had two 96-sided polygons squeezing the circle. That told him π was between 223/71 and 22/7: about 3.14. Two correct decimals, and a method that people would use for nearly two thousand years.
Records that lasted centuries
In China, Liu Hui used the same squeezing trick around the year 263 and reached 3.1416. Then, around 480, the mathematician Zu Chongzhi pinned π between 3.1415926 and 3.1415927, and found the fraction 355/113, which is right to six decimals. His record stood for about 900 years, which may be the longest-lasting record in the history of maths.
Around 1400, in Kerala in southern India, Madhava of Sangamagrama found something new: a way to write π as an infinite sum, a list of fractions that you add up forever, getting closer each time. He reached ten decimals, and Europe wouldn't discover the same idea for another two centuries or more.
Polygons weren't finished yet, though. In 1424, in Samarkand, Jamshīd al-Kāshī used a polygon with 805,306,368 sides and got sixteen decimals. And in 1596 the Dutch-German mathematician Ludolph van Ceulen spent much of his life on polygons with billions of sides, reaching twenty and then more decimals. In Germany, π was called the "Ludolphine number" for centuries afterwards.
The age of clever formulas
In 1706 John Machin found a smarter formula, using a bit of mathematics called the arctangent, and calculated 100 decimals. Versions of his formula set nearly every record for the next 250 years.
The most famous calculation of that era is also a cautionary tale. The English amateur William Shanks spent years working out 707 decimals by hand and published them in 1873. They were admired for more than seventy years, until 1944, when D. F. Ferguson checked them and found that Shanks had made a mistake at decimal 528. Everything after it was wrong. Ferguson went on to calculate 808 correct decimals with a desk calculator, the last record set without an electronic computer.
Computers join the race
In 1949 ENIAC, one of the first electronic computers, worked out 2,037 decimals in about 70 hours. After that, the records came quickly:
- 1961: Daniel Shanks (no relation to William) and John Wrench passed one hundred thousand decimals on an IBM 7090.
- 1973: Jean Guilloud and Martine Bouyer reached the first million.
- 1989: the brothers David and Gregory Chudnovsky passed one billion, using a formula of their own. A version of their formula is still used for records today.
- 2002: Yasumasa Kanada's team in Tokyo passed a trillion.
- 2009: Fabrice Bellard computed nearly 2.7 trillion decimals on a single desktop PC.
100 trillion
In 2019 Emma Haruka Iwao, working at Google Cloud, computed 31.4 trillion digits and announced it on Pi Day. In 2022 she went further: 100 trillion decimals, using the program y-cruncher by Alexander Yee. The calculation ran for 157 days, 23 hours and a bit, and used 515 terabytes of storage. Those are the digits this site was built from: we searched the first 100 billion of them, one thousandth of the whole thing.
The race didn't stop there. Teams have since computed 202 trillion, 300 trillion and, in 2025, 314 trillion digits, which is a very satisfying number for a π record.
Why keep going?
Not for building anything. NASA's Jet Propulsion Laboratory uses just 15 decimals of π to steer spacecraft, and 37 or so would be enough to work out the size of the visible universe to within the width of an atom. Records are really a test: of computers, of storage, of new algorithms, and of the people patient enough to run them. Every record is also checked, usually with a second, completely different formula, so the digits can be trusted. Shanks would have approved.
Explore more
- See every record on a chalk timeline on the history page.
- Read how we search the digits once we had them.
- Find your number in the first 100 billion.