Tau, denoted $\tau$, is most commonly used as 2$\pi$ or 2 pi. Tau is the number of radians in a circle. For a convincing proof that $\tau$ is a better circle constant than $\pi$, see The Tau Manifesto by Michael Hartl. This following section will summarize one main point of the Tau Manifesto.

Why $\tau$ Is Better Than $\pi$

Have you ever been in geometry class and been asked to graph sine waves with their ridiculous extra factor of 2 in the x-axis? Have you ever thought radian angle measure was hopelessly tainted with the superfluous and yet unavoidable factor of 2 (There are 2$\pi$ radians in a full revolution)? $\tau$ resolves that. One $\tau$ is one revolution. Simple as that. While you have to remember that $\frac{\pi}{8}$ radians is NOT $\frac{1}{8}$ of a revolution, but is equal to $\frac{1}{16}$ of a revolution because of that idiosyncratic factor of 2, $\frac{\tau}{8}$ radians is just $\frac{1}{8}$ of a revolution. Likewise, $\frac{\tau}{3}$ radians is just $\frac{1}{3}$ of a revolution, $9001\tau$ radians is just 9001 revolutions, $123456789\tau$ radians is just 123456789 revolutions, and $x\tau$ radians is $x$ revolutions for any real $x$.

Some may argue that $\pi r^2$ is simpler than $\frac{1}{2}\tau r^2$, but as noted in the Tau Manifesto, many quadratic forms in physics contain a factor of $\frac{1}{2}$ which is unavoidable.

Other Uses of Tau

$\tau$ can have other meanings:

  • Tau is the 19th letter of the Greek alphabet.
  • Tau is also an uncommon name for Phi.

See Also