Tau (uppercase Τ, lowercase τ) is a letter of the Greek alphabet. It occupies the 19th position in the standard order and corresponds to a voiceless dental/alveolar plosive — the sound usually written as "t" in English — in both Ancient and Modern Greek; historical and modern pronunciations differ somewhat. The name of the letter in Greek is ταυ and it is commonly transcribed into Latin characters as "tau".

Like most Greek letters, tau traces its ancestry to a Semitic prototype: the Phoenician letter taw. Through the Greek adoption of Phoenician characters in the first millennium BCE, the sign evolved into the forms used in classical writings. In the system of Greek numerals, tau has the numeric value 300 and appears in inscriptions and manuscripts where letters double as numbers.

Typographically, the uppercase form Τ is visually identical to the Latin T, while the lowercase τ has developed several shapes in handwriting and print. The common printed lowercase resembles a small t with a descender or a single-stroke hook, depending on typeface and era. The letter also influenced other alphabets: the Latin T and the Cyrillic Т descend from the same Greek prototype.

Common uses and symbolic roles

  • Mathematics: The symbol τ is used in a variety of notations. A contemporary proposal popular in some circles designates τ as the circle constant equal to 2π (about 6.283...), arguing it as a more natural constant for many formulas.
  • Physics and engineering: τ commonly denotes torque and shear stress, and it frequently represents the time constant in exponential decay processes and RC circuits.
  • Relativity and particle physics: τ can denote proper time in relativity and is the symbol for the tau lepton, a heavier cousin of the electron.
  • Biology: The name "tau" is also used for tau protein, a microtubule-associated protein that is studied in neurodegenerative disease research.

When discussing the letter itself, scholars distinguish its phonetic role, numeric use, and graphic evolution. For students of writing systems, tau is a clear example of how Greek adapted Semitic signs and how those forms, in turn, informed the shapes of letters in later alphabets. For practitioners in science and engineering, the same glyph functions as a convenient symbol with many context-dependent meanings.

For further general information on the Greek script and letter names see entries on the Greek alphabet and on the historical use of letters in Ancient and Modern Greek. The numerical role of tau is summarized in standard treatments of Greek numerals, and its descendants in other scripts are discussed in sources on alphabetic history such as entries about the Latin T.