Pi (letter)

Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
History
Archaic local variants  ·  ·  ·  ·  ·
Ligatures (ϛ, ȣ, ϗ) · Diacritics
Numerals: (6) · (90) · (900)
In other languages
Bactrian  · Coptic  · Albanian
Scientific symbols
Book  · Category · Commons

Pi ( /ˈpaɪ/; Greek: [ˈpi], uppercase Π, lowercase π) is the sixteenth letter of the Greek alphabet, representing [p]. In the system of Greek numerals it has a value of 80. Letters that arose from pi include Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).

The upper-case letter Π is used as a symbol for:

• The product operator in mathematics, indicated with capital pi notation ∏ (in analogy to the use of the capital Sigma Σ as summation symbol).
• In textual criticism, Codex Petropolitanus, a 9th century, uncial codex of the Gospels, now located in St. Petersburg, Russia.
• In legal shorthand, it represents a plaintiff.

The lower-case letter π is used as a symbol for:

• The mathematical transcendental (and thus irrational) constant π ≈ 3.14159…, the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter "π" is the first letter of the Greek words "περιφέρεια" 'periphery' and "περίμετρος" 'perimeter', i.e. the circumference.
• The prime-counting function in mathematics.
• Homotopy groups in algebraic topology.
• Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.
• The osmotic pressure in chemistry. π=MRT
• The elementary particle called the pi meson or pion.
• Economic profit in microeconomics.
• Inflation rate in macroeconomics.
• A type of chemical bond in which the P-orbitals overlap, called a pi bond.
• The natural projection on the tangent bundle on a manifold.
• The unary operation of projection in relational algebra.

Variant pi

Variant pi or "pomega" ($\varpi\,\!$ or ϖ) is a glyph variant of lower case pi sometimes used in technical contexts as though it were a lower-case omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It is used as a symbol for:

• Angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by $\omega$ but this may be confused with vorticity in a fluid dynamics context).
• Longitude of pericenter, in celestial mechanics.
• Comoving distance in cosmology.

The various forms of pi are present in Unicode as:

• U+03A0 Π greek capital letter pi (HTML: Π Π)
• U+03C0 π greek small letter pi (HTML: π π)
• U+03D6 ϖ greek pi symbol (HTML: ϖ ϖ)
• U+220F ∏ n-ary product (HTML: ∏ ∏).

See also

• П, п - Pe (Cyrillic)
• Р, р - Er (Cyrillic)
• P, p - Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)