τ (Tau) N decimals Generator

Tau is two pi, roughly 6.283185. The proposal to use this constant instead of pi comes from a simple observation: a full turn of the circle is tau radians, not two pi. A quarter turn is tau over 4, half a turn is tau over 2 — angles become direct fractions of a turn, without the factor of 2 turning up in nearly every trigonometric formula.

Choose how many places you want and the page delivers up to a thousand digits. They were computed with arbitrary-precision arithmetic using Machin's formula, which expresses pi through two fast-converging arctangents, and checked against published values before going in — a constant hardcoded in source is exactly the kind of thing nobody reviews and that stays wrong in silence.

The case for tau is pedagogical rather than mathematical: both constants describe the same thing, and no formula becomes right or wrong because of the choice. What changes is how many factors of 2 end up scattered through the text. Where pi stays more natural is the area of a circle, which is pi times r squared — with tau it becomes tau over 2 times r squared, which is slightly worse to write.