First N Digits Of Pi

What this calculator does

This shows the first however many digits of π (pi) you ask for, up to 100,000. Enter a number of digits and it lists them.

Choose how many digits you want, and the tool produces them.

Using the calculator

1. Enter how many digits you want, up to 100,000.
2. Press Calculate.

The result is π written out to that many digits.

What π is

π (pi) is the most famous constant in mathematics, the ratio of any circle's circumference to its diameter. It begins 3.14159265, and no matter how big or small the circle, that ratio is always exactly the same. It shows up wherever a circle or a wave appears, which is almost everywhere. It is the number doing the work inside the circle calculator and its relatives.

Digits that never end

π is an irrational number, which means it cannot be written exactly as a fraction, and its decimal digits run on forever without ever settling into a repeating pattern. That is what makes a tool like this useful: you can ask for as many digits as you need, and there is always another one waiting. π has been computed to trillions of digits.

How the tool finds them

Rather than storing a fixed value, this tool calculates the digits on demand, using an algorithm that spits them out one after another. That is how it can reach as far as 100,000 digits, far more than any everyday use would ever call for. In practice a handful of digits is plenty for almost any real calculation.

A worked example | the first 10 digits

Ask for the first 10 digits of π.

1. The tool returns 3.141592653.

For most practical work, even 3.14159 is more than accurate enough. The extra digits are mainly for curiosity and testing.

Questions people ask

What is π?

The ratio of a circle's circumference to its diameter, beginning 3.14159 and the same for every circle.

What are the first 10 digits of π?

3.141592653.

Do the digits of π ever end?

No. π is irrational, so its digits go on forever without repeating.

How many digits can it show?

Up to 100,000, calculated on demand.

References

A note on the idea behind it. π is the ratio of a circle's circumference to its diameter, approximately 3.14159, and it is irrational, so its decimal expansion never ends or repeats. The mathematical constant is documented in the NIST Digital Library of Mathematical Functions. For further reading, see Pi.

1. π, the ratio of a circle's circumference to its diameter, an irrational number. NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/.