Google Developers Have Set Another Record For Calculating Numbers Of Pi: 100 Trillion!

Illustration showing pi and pie
Calculating 100 trillion digits of pi is a feat worth celebrating with a pie. (Google Graphic / The Keyword)

Three years after Seattle software developer Emma Haruka Iwao and her teammates at Google set the world record for accurately calculating pi, they did it again. Thanks to Iwao and Google Cloud, we now know what pi equals to an incredible precision of 100 trillion digits.

Why pi?

Mathematicians have worked on the ratio of a circle’s circumference to its diameter for millennia, going back at least as far as the Babylonians (who figured it at 3.125). It’s important for scientists and engineers to know the value of the irrational number with a high degree of precision, but beyond a certain point it’s really about showing how well an algorithm or computer network can manage more practical problems.


That’s what motivated the Iwao team to do the math with an accuracy of 31.4 trillion digits (pi times 10 trillion) in 2019. As a developer advocate for Google Cloud, what better way to demonstrate the power of your cloud computing service than by leading the pi pack?

Since 2019, the state of the art in computer science and engineering has been advancing at an accelerated pace. Google Cloud record was broken less than a year later, and in 2021, that the record was broken in turn (with an accuracy of 62.8 trillion digits, or pi times 20 trillion).

historyOfPi 7June2022
This chart shows how the accuracy of pi calculations has improved over the millennia. The vertical axis reflects the number of digits on a logarithmic scale. Also note that there are gaps in the years shown on the horizontal axis. Click on the image to enlarge. (Google chart)

The state of the art has also advanced at Google Cloud.

“Combining all the new features introduced over the past three years, I thought we would be able to break a record again, and not just by a few numbers, but by a good margin,” Iwao told GeekWire. “We thought, OK, 100 trillion sounds reasonable, and a significant step up from the previous album. »

Thanks to upgrades to Google Cloud’s compute engine and increased throughput, Iwao and the Google team were able to get 100 trillion digits in 157 days of compute time, or just over a month of more than the 121 days it took to calculate 31.4 trillion digits in 2019.

About 82,000 terabytes of data were processed, using a pi computing program known as y-cruncher. That’s more than four times the amount of data processed in 2019. For what it’s worth, Google says 82,000 terabytes of data would equal 2,598 years of HD movies.

For the number geeks, here are the last 100 digits of the result, ending in zero as the 100 trillionth digit:

4658718895 1242883556 4671544483 9873493812 1206904813 

2656719174 5255431487 2142102057 7077336434 3095295560

You can check the numbers yourself via Pi.Delivery, a website created by the Google Cloud Platform Developer Advocacy team. And you can read a pair of blog posts by Iwao and the Google Cloud team to learn more about how the numbers were made.

Iwao suspects it won’t be long before another record is set.

Emma Haruka Iwao is a senior developer advocate for Google Cloud Platform. (Picture via Google)

“Computers keep getting better,” she said. “The same goes for Google Cloud infrastructure. We have limits. Y-cruncher has certain limits, and we are well below those limits. … There are a lot of people who want to target more pi numbers, including me. »

It’s not just about the raw numbers: “I’m really looking forward to further advancements and changes in computer science and engineering, as well as algorithms and math,” Iwao said.

These advancements can be applied to down-to-earth computing tasks as well as pi-in-the-sky problems.

“You may not be calculating trillion-digit pi, but you have other problems and applications that you want to run in the cloud or on computers,” Iwao said. “It could be scientific research, it could be multimedia, transcoding, 3D rendering, games, anything. Communicating new technologies, new hardware and architectures to developers and practitioners is one of my areas of interest. »

And who knows? Maybe someone can find real-world applications for 100 trillion digits of pi. “I actually look forward to hearing from people who look at the website and come up with new ideas,” Iwao said. “We publish all the figures (…) and see if there is something they can do with these figures.

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