Tau (mathematics)

The number τ (/ˈtaʊ, ˈtɔː, ˈtɒ/ ^ⓘ; spelled out as tau) is a mathematical constant that is the ratio of a circle's circumference to its radius. It is exactly equal to 2π and approximately equal to 6.28.

τ and π are both circle constants relating the circumference of a circle to its linear dimension: the radius in the case of τ; the diameter in the case of π.

While π is used almost exclusively in mainstream mathematical education and practice, it has been proposed, most notably by Michael Hartl in 2010, that τ should be used instead. Hartl and other proponents argue that τ is the more natural circle constant and its use leads to conceptually simpler and more intuitive mathematical notation.

Critics have responded that the benefits of using τ over π are trivial and that given the ubiquity and historical significance of π a change is unlikely to occur.

The proposal did not initially gain widespread acceptance in the mathematical community, but awareness of τ has become more widespread, including having been added to several major programming languages and calculators.