# Greek letters used in mathematics, science, and engineering

Greek alphabet History In other languages Scientific symbols 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  ·  ·  ·  ·  · Ligatures (ϛ, ȣ, ϗ) · Diacritics Numerals: (6) · (90) · (900) Bactrian  · Coptic  · Albanian Book  · Category · Commons

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].

## Typography

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
Name TeX HTML Name TeX HTML Name TeX HTML Name TeX HTML Name TeX HTML
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

### Ϝϝ (digamma)

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

### 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

### Ιι (iota)

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

### 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

### Οο (omicron)

• Ο represents:

### Υυ (upsilon)

• Υ represents:
• an elementary particle

## References

1. ^ http://www.maths.abdn.ac.uk/~igc/tch/eg1006/notes/node119.html
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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