Greek letters used in mathematics, science, and engineering

Greek letters used in mathematics, science, and engineering
Greek alphabet alpha-omega.svg
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
Archaic local variants
Digamma · Heta · San · Koppa · Sampi  · Tsan
Ligatures (ϛ, ȣ, ϗ) · Diacritics
Numerals: Greek letter Stigma.svg (6) · Greek Koppa lamedh-shaped.svg (90) · Sampi.svg (900)
In other languages
Bactrian  · Coptic  · Albanian
Scientific symbols

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Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are usually not used: capital A, B, E, H, I, K, M, N, O, P, T, X, Y, Z. Small ι (iota), ο (omicron) and υ (upsilon) are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes font variants of Greek letters are used as distinct symbols in mathematics, in particular for φ (phi) and π (pi).

In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.

English-speaking mathematicians use neither the modern nor the historical Greek pronunciations of the names of the letters, but the traditional English pronunciation, e.g. /ˈθeɪtə/ for θ, cf. ancient [tʰɛ̂ːta] and modern [ˈθita].



The Greek letter forms used in maths are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography.

The OpenType font format has the feature tag 'mgrk' "Mathematical Greek" to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts.

The table below shows a comparison of Greek letters rendered in TeX and HTML. The font used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics.

Greek letters
Alpha \Alpha \alpha \, Αα Digamma \digamma \, Ϝϝ Kappa \Kappa \kappa \, Κκ Omicron \Omicron \omicron \, Οο Upsilon \Upsilon \upsilon \, Υυ
Beta \Beta \beta \, Ββ Zeta \Zeta \zeta \, Ζζ Lambda \Lambda \lambda \, Λλ Pi \Pi \pi \varpi \, Ππϖ Phi \Phi \phi \varphi \, Φϕφ
Gamma \Gamma \gamma \, Γγ Eta \Eta \eta \, Ηη Mu \Mu \mu \, Μμ Rho \Rho \rho \varrho \, Ρρϱ Chi \Chi \chi \, Χχ
Delta \Delta \delta \, Δδ Theta \Theta \theta \vartheta \, Θθϑ Nu \Nu \nu \, Νν Sigma \Sigma \sigma \varsigma \, Σσς Psi \Psi \psi \, Ψψ
Epsilon \Epsilon \epsilon \varepsilon \, Εϵε Iota \Iota \iota \, Ιι Xi \Xi \xi \, Ξξ Tau \Tau \tau \, Ττ Omega \Omega \omega \, Ωω

Concepts represented by a Greek letter

Αα (alpha)

Ββ (beta)

Γγ (gamma)

Δδ (delta)

Εε (epsilon)

Ϝϝ (digamma)

  • Ϝ is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted.

Ζζ (zeta)

Ηη (eta)

  • η represents:
    • the intrinsic impedance of medium (usually free space)
    • the partial regression coefficient in statistics
    • elasticities in economics
    • the absolute vertical vorticity (relative vertical vorticity + Coriolis effect) in fluid dynamics
    • an index of refraction
    • a type of meson
    • viscosity
    • efficiency
    • the Minkowski metric tensor in relativity
    • noise in communication system models

Θθ (theta)

Ιι (iota)

  • ι represents:
    • the index generator function in APL (in the form ⍳)

Κκ (kappa)

Λλ (lambda)

Μμ (mu)

Νν (nu)

  • ν represents:
    • frequency in physics in hertz (Hz)
    • Poisson's ratio in material science
    • a neutrino
    • kinematic viscosity of liquids
    • stoichiometric coefficient in chemistry
    • dimension of nullspace in maths

Ξξ (xi)

Οο (omicron)

  • Ο represents:

Ππ (pi)

Ρρ (rho)

Σσ (sigma)

Ττ (tau)

Υυ (upsilon)

  • Υ represents:
    • an elementary particle

Φφ (phi)

Χχ (chi)

Ψψ (psi)

Ωω (omega)

See also


  1. ^
  2. ^ Applied Linear Statistical Models (5th ed.). Michael H. Kutner, Christopher J. Nachtsheim, John Neter, & William Li. New York: McGraw-Hill, 2005. ISBN 0-07-310874-X. xxviii + 1396 pp.
  3. ^ Pomega - from Eric Weisstein's World of Physics
  4. ^ Outline for Weeks 14&15, Astronomy 225 Spring 2008

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