# PEP 628 – Add `math.tau`

PEP
628
Title
Add `math.tau`
Author
Nick Coghlan <ncoghlan at gmail.com>
Status
Final
Type
Standards Track
Created
28-Jun-2011
Python-Version
3.6
Post-History
28-Jun-2011
Resolution
https://bugs.python.org/issue12345

Contents

## Abstract

In honour of Tau Day 2011, this PEP proposes the addition of the circle constant `math.tau` to the Python standard library.

The concept of `tau` (`τ`) is based on the observation that the ratio of a circle’s circumference to its radius is far more fundamental and interesting than the ratio between its circumference and diameter. It is simply a matter of assigning a name to the value `2 * pi` (`2π`).

## PEP Acceptance

This PEP is now accepted and math.tau will be a part of Python 3.6. Happy birthday Nick!

The idea in this PEP has been implemented in the auspiciously named issue 12345.

## The Rationale for Tau

`pi` is defined as the ratio of a circle’s circumference to its diameter. However, a circle is defined by its centre point and its radius. This is shown clearly when we note that the parameter of integration to go from a circle’s circumference to its area is the radius, not the diameter. If we use the diameter instead we have to divide by four to get rid of the extraneous multiplier.

When working with radians, it is trivial to convert any given fraction of a circle to a value in radians in terms of `tau`. A quarter circle is `tau/4`, a half circle is `tau/2`, seven 25ths is `7*tau/25`, etc. In contrast with the equivalent expressions in terms of `pi` (`pi/2`, `pi`, `14*pi/25`), the unnecessary and needlessly confusing multiplication by two is gone.

## Other Resources

I’ve barely skimmed the surface of the many examples put forward to point out just how much easier and more sensible many aspects of mathematics become when conceived in terms of `tau` rather than `pi`. If you don’t find my specific examples sufficiently persuasive, here are some more resources that may be of interest:

• Michael Hartl is the primary instigator of Tau Day in his Tau Manifesto
• Bob Palais, the author of the original mathematics journal article highlighting the problems with `pi` has a page of resources on the topic
• For those that prefer videos to written text, Pi is wrong! and Pi is (still) wrong are available on YouTube