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Greek letters used in mathematics, science, and engineering
Symbols for constants, special functions

Greek letters play a vital role in mathematics, science, and engineering as symbols for constants, special functions, and variables. Capital and lowercase forms represent distinct entities, though letters resembling Latin letters like A, B, E, and others are rarely used. Some font variants distinguish particular letters such as ε/ϵ and π/ϖ, while the archaic digamma occasionally appears. Additionally, the Bayer designation employs Greek letters like α for naming stars by brightness order within constellations. In mathematical finance, the Greeks represent variables indicating investment risk.

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Typography

Some common conventions:

The Greek letter forms used in mathematics 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 in HTML and TeX (α–μ)
NameTeXHTML
Alpha A α {\displaystyle \mathrm {A} \,\alpha } Α α
Beta B β {\displaystyle \mathrm {B} \,\beta } Β β
Gamma Γ γ {\displaystyle \Gamma \,\gamma } Γ γ
Delta Δ δ {\displaystyle \Delta \,\delta } Δ δ
Epsilon E ϵ ε {\displaystyle \mathrm {E} \,\epsilon \,\varepsilon } Ε ϵ ε
Digamma Ϝ ϝ {\displaystyle \mathrm {\Digamma} \,\digamma } Ϝ ϝ
Zeta Z ζ {\displaystyle \mathrm {Z} \,\zeta } Ζ ζ
Eta H η {\displaystyle \mathrm {H} \,\eta } Η η
Theta Θ θ ϑ {\displaystyle \Theta \,\theta \,\vartheta } Θ θ ϑ
Iota I ι {\displaystyle \mathrm {I} \,\iota } Ι ι
Kappa K κ ϰ {\displaystyle \mathrm {K} \,\kappa \,\varkappa } Κ κ ϰ
Lambda Λ λ {\displaystyle \Lambda \,\lambda } Λ λ
Mu M μ {\displaystyle \mathrm {M} \,\mu } Μ μ
Greek letters in HTML and TeX (ν–ω)
NameTeXHTML
Nu N ν {\displaystyle \mathrm {N} \,\nu } Ν ν
Xi Ξ ξ {\displaystyle \Xi \,\xi } Ξ ξ
Omicron O o {\displaystyle \mathrm {O} \,o} Ο ο
Pi Π π ϖ {\displaystyle \Pi \,\pi \,\varpi } Π π ϖ
Rho P ρ ϱ {\displaystyle \mathrm {P} \,\rho \,\varrho } Ρ ρ ϱ
Sigma Σ σ ς {\displaystyle \Sigma \,\sigma \,\varsigma } Σ σ ς
Tau T τ {\displaystyle \mathrm {T} \,\tau } Τ τ
Upsilon Υ υ {\displaystyle \Upsilon \,\upsilon } Υ υ
Phi Φ ϕ φ {\displaystyle \Phi \,\phi \,\varphi } Φ ϕ φ
Chi X χ {\displaystyle \mathrm {X} \,\chi } Χ χ
Psi Ψ ψ {\displaystyle \Psi \,\psi } Ψ ψ
Omega Ω ω {\displaystyle \Omega \,\omega } Ω ω
Greek letters with typographical variations
NameGreek LetterBoldItalicBold ItalicSans-Serif BoldSans-Serif Bold ItalicAPLDouble struck boldUnicode variants or similar
AlphaΑ α𝚨 𝛂𝛢 𝛼𝜜 𝜶𝝖 𝝰𝞐 𝞪⍺ ⍶
BetaΒ β ϐ ᵝ ᵦ𝚩 𝛃𝛣 𝛽𝜝 𝜷𝝗 𝝱𝞑 𝞫
GammaΓ γ ᴦ ᵞ ᵧ𝚪 𝛄𝛤 𝛾𝜞 𝜸𝝘 𝝲𝞒 𝞬ℾ ℽ
DeltaΔ δ ᵟ𝚫 𝛅𝛥 𝛿𝜟 𝜹𝝙 𝝳𝞓 𝞭U+2206 ∆ INCREMENT, U+2207 ∇ NABLA
EpsilonΕ ε ϵ ϶𝚬 𝛆 𝛜𝛦 𝜀 𝜖𝜠 𝜺 𝝐𝝚 𝝴 𝞊𝞔 𝞮 𝟄U+2208 ∈ ELEMENT OF–U+220D ∍ SMALL CONTAINS AS MEMBER
ZetaΖ ζ𝚭 𝛇𝛧 𝜁𝜡 𝜻𝝛 𝝵𝞕 𝞯
EtaΗ η Ͱ ͱ𝚮 𝛈𝛨 𝜂𝜢 𝜼𝝜 𝝶𝞖 𝞰
ThetaΘ θ ϑ ϴ ᶿ𝚯 𝛉 𝚹 𝛝𝛩 𝜃 𝛳 𝜗𝜣 𝜽 𝜭 𝝑𝝝 𝝷 𝚹 𝞋𝞗 𝞱 𝜭 𝟅
IotaΙ ι ᶥ ℩𝚰 𝛊𝛪 𝜄𝜤 𝜾𝝞 𝝸𝞘 𝞲⍳ ⍸
KappaΚ κ ϰ𝚱 𝛋 𝛞𝛫 𝜅 𝜘𝜥 𝜿 𝝒𝝟 𝝹 𝞌𝞙 𝞳 𝟆
LambdaΛ λ ᴧ𝚲 𝛌𝛬 𝜆𝜦 𝝀𝝠 𝝺𝞚 𝞴
MuΜ μ𝚳 𝛍𝛭 𝜇𝜧 𝝁𝝡 𝝻𝞛 𝞵
NuΝ ν𝚴 𝛎𝛮 𝜈𝜨 𝝂𝝢 𝝼𝞜 𝞶
XiΞ ξ𝚵 𝛏𝛯 𝜉𝜩 𝝃𝝣 𝝽𝞝 𝞷
OmicronΟ ο𝚶 𝛐𝛰 𝜊𝜪 𝝄𝝤 𝝾𝞞 𝞸
PiΠ π ϖ ᴨ𝚷 𝛑 𝛡𝛱 𝜋 𝜛𝜫 𝝅 𝝕𝝥 𝝿 𝞏𝞟 𝞹 𝟉ℿ ℼU+220F ∏ N-ARY PRODUCT, U+2210 ∐ N-ARY COPRODUCT
RhoΡ ρ Ῥ ῥ ῤ ϱ ϼ ᴩ ᵨ ☧𝚸 𝛒 𝛠𝛲 𝜌 𝜚𝜬 𝝆 𝝔𝝦 𝞀 𝞎𝞠 𝞺 𝟈
SigmaΣ σ ς Ϲ ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ𝚺 𝛔 𝛓𝛴 𝜎 𝜍𝜮 𝝈 𝝇𝝨 𝞂 𝞁𝞢 𝞼 𝞻U+2211 ∑ N-ARY SUMMATION
TauΤ τ𝚻 𝛕𝛵 𝜏𝜯 𝝉𝝩 𝞃𝞣 𝞽
UpsilonΥ υ ϒ𝚼 𝛖𝛶 𝜐𝜰 𝝊𝝪 𝞄𝞤 𝞾
PhiΦ φ ϕ𝚽 𝛗 𝛟𝛷 𝜑 𝜙𝜱 𝝋 𝝓𝝫 𝞅 𝞍𝞥 𝞿 𝟇
ChiΧ χᵡᵪ☧𝚾 𝛘𝛸 𝜒𝜲 𝝌𝝬 𝞆𝞦 𝟀
PsiΨ ψ ᴪ𝚿 𝛙𝛹 𝜓𝜳 𝝍𝝭 𝞇𝞧 𝟁
OmegaΩ ω ꭥ𝛀 𝛚𝛺 𝜔𝜴 𝝎𝝮 𝞈𝞨 𝟂⍵ ⍹U+2126 Ω OHM SIGN, U+2127 ℧ INVERTED OHM SIGN

Concepts represented by a Greek letter

Αα (alpha)

See also: Alpha (disambiguation)

Ββ (beta)

See also: Beta (disambiguation)

Γγ (gamma)

See also: Gamma (disambiguation)

Δδ (delta)

See also: Delta (disambiguation)

Εε (epsilon)

See also: Epsilon (disambiguation)

Ϝϝ (digamma)

See also: Digamma

  • Ϝ is sometimes used to represent the digamma function, though the Latin letter F (which is nearly identical) is usually substituted.
  • A hypothetical particle Ϝ speculated to be implicated in the 750 GeV diphoton excess, now known to be simply a statistical anomaly

Ζζ (zeta)

See also: Zeta (disambiguation)

Ηη (eta)

See also: Eta (disambiguation)

Θθ (theta)

See also: Theta (disambiguation)

Ιι (iota)

See also: Iota (disambiguation)

Κκ (kappa)

See also: Kappa (disambiguation)

Λλ (lambda)

See also: Lambda (disambiguation)

Μμ (mu)

See also: Mu (disambiguation)

Νν (nu)

See also: Nu (disambiguation)

Ξξ (xi)

See also: Xi (disambiguation)

Οο (omicron)

See also: Omicron (disambiguation)

Ππ (pi)

See also: Pi (disambiguation)

Ρρ (rho)

See also: Rho (disambiguation)

Σσς (sigma)

See also: Sigma (disambiguation)

Ττ (tau)

See also: Tau (disambiguation)

ϒυ (upsilon)

See also: Upsilon (disambiguation)

  • Υ {\displaystyle \Upsilon } (U+03D2) represents:

Φφ (phi)

See also: Phi (disambiguation)

Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter.

Χχ (chi)

See also: Chi (disambiguation)

Ψψ (psi)

See also: Psi (disambiguation)

Ωω (omega)

See also: Omega (disambiguation)

See also

References

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  4. Rabinowitz, Harold; Vogel, Suzanne, eds. (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam ; Burlington, MA: Elsevier/Academic Press. p. 793. ISBN 978-0-12-373980-3. OCLC 156811865. 978-0-12-373980-3

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  6. Burns, M. Shane (2022). A practical guide to observational astronomy (First ed.). Boca Raton: CRC Press. p. 5. ISBN 978-0-367-76863-8. The two angles that specify the location of a point on the celestial sphere are called the right ascension α and the declination δ 978-0-367-76863-8

  7. Rabinowitz, Harold; Vogel, Suzanne (2009). The manual of scientific style: a guide for authors, editors, and researchers (1st ed.). Amsterdam Burlington, MA: Elsevier/Academic Press. p. 363. ISBN 978-0-12-373980-3. The primary designation system for bright stars, called Bayer designations… The Greek letters are assigned in order (α,β, γ,δ etc.) according to brightness. 978-0-12-373980-3

  8. Bhandari, Pritha (2021-01-18). "Type I & Type II Errors | Differences, Examples, Visualizations". Scribbr. Retrieved 2025-01-22. The probability of making a Type I error is the significance level, or alpha (α), while the probability of making a Type II error is beta (β). https://www.scribbr.com/statistics/type-i-and-type-ii-errors/

  9. Languis, M. L.; Buffer, James J.; Martin, Daniel; Naour, Paul J. (2011). Cognitive Science (RLE Edu E): Contributions to Educational Practice. Routledge Library Editions: Education. Hoboken: Taylor and Francis. p. 183. ISBN 978-0-415-68351-7. Vieth (1982) established that cognition could be quantified by summing the value of alpha plus beta brain waves. 978-0-415-68351-7

  10. Bowen, Alan C.; Rochberg, Francesca, eds. (2020). Hellenistic astronomy: the science in its contexts. Brill's companions in classical studies. Leiden ; Boston: Brill. pp. 16–17. ISBN 978-90-04-24336-1. Celestial longitude (λ) is measured eastward from the vernal equinox along the zodiacal circle, and celestial latitude (β) is the angular distance of the arc dropped perpendicularly from the body to the zodiacal circle. 978-90-04-24336-1

  11. Freidberg, Jeffrey P. (2014). Ideal MHD (1st ed.). West Nyack: Cambridge University Press. p. 68. ISBN 978-1-107-00625-6. The quantity β is a global plasma parameter whose value is critical for a fusion reactor... Qualitatively, β measures the ratio plasma pressure to magnetic pressure: 978-1-107-00625-6

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  64. Weisstein, Eric W. "Golden Ratio". mathworld.wolfram.com. Retrieved 2025-02-06. https://mathworld.wolfram.com/GoldenRatio.html

  65. Weisstein, Eric W. "Totient Function". mathworld.wolfram.com. Retrieved 2025-02-06. https://mathworld.wolfram.com/TotientFunction.html

  66. Weisstein, Eric W. "Chromatic Number". mathworld.wolfram.com. Retrieved 2025-02-09. The chromatic number of a graph G is most commonly denoted χ (G) (e.g., Skiena 1990, West 2000, Godsil and Royle 2001, Pemmaraju and Skiena 2003),... https://mathworld.wolfram.com/ChromaticNumber.html

  67. Weisstein, Eric W. "Euler Characteristic". mathworld.wolfram.com. Retrieved 2025-02-09. https://mathworld.wolfram.com/EulerCharacteristic.html

  68. Mugiraneza, Sam; Hallas, Alannah M. (2022-04-19). "Tutorial: a beginner's guide to interpreting magnetic susceptibility data with the Curie-Weiss law". Communications Physics. 5 (1): 95. arXiv:2205.07107. Bibcode:2022CmPhy...5...95M. doi:10.1038/s42005-022-00853-y. ISSN 2399-3650. However, for newly synthesized materials, there is one indispensable characterization technique that is as old as the field of magnetism itself: magnetic susceptibility, χ,... https://www.nature.com/articles/s42005-022-00853-y

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  70. Weisstein, Eric W. "Reciprocal Fibonacci Constant". mathworld.wolfram.com. Retrieved 2025-02-08. https://mathworld.wolfram.com/ReciprocalFibonacciConstant.html

  71. Weisstein, Eric W. "Chebyshev Functions". mathworld.wolfram.com. Retrieved 2025-02-08. https://mathworld.wolfram.com/ChebyshevFunctions.html

  72. Weisstein, Eric W. "Polygamma Function". mathworld.wolfram.com. Retrieved 2025-02-08. A special function mostly commonly denoted ψ_n(z), ψ^((n))(z), or F_n(z-1)... https://mathworld.wolfram.com/PolygammaFunction.html

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  74. Srivastava, Manishi; Varma, Vishwanath; Abhilash, Lakshman; Sharma, Vijay Kumar; Sheeba, Vasu (June 2019). "Circadian Clock Properties and Their Relationships as a Function of Free-Running Period in Drosophila melanogaster". Journal of Biological Rhythms. 34 (3): 231–248. doi:10.1177/0748730419837767. ISSN 1552-4531. PMID 30939971. ... 2) accuracy (i.e., day-to-day stability of the phase relationship (ψ), where ψ is the duration between a phase of the rhythm and a phase of the external cycle) is greater for clocks with τ close to 24 h; ... https://pubmed.ncbi.nlm.nih.gov/30939971/

  75. Rein, Alan (2020-07-28). "The heart of the HIV RNA packaging signal?". Proceedings of the National Academy of Sciences of the United States of America. 117 (33): 19621–19623. Bibcode:2020PNAS..11719621R. doi:10.1073/pnas.2013378117. PMC 7443930. PMID 32723818. vRNA is selectively packaged because it contains a "packaging signal" or "ψ" [also designated the "core encapsidation signal" (2)]. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7443930

  76. WELBAUM, GREGORY E.; BRADFORD, KENT J. (1991-03-01). "Water Relations of Seed Development and Germination in Muskmelon (Cucumis melo L.): VI. INFLUENCE OF PRIMING ON GERMINATION RESPONSES TO TEMPERATURE AND WATER POTENTIAL DURING SEED DEVELOPMENT". Journal of Experimental Botany. 42 (3): 393–399. doi:10.1093/jxb/42.3.393. ISSN 0022-0957. Germination sensitivities to temperature and water potential (ψ) were quantified as indicators of the influence of seed maturity and priming on seed vigour. https://academic.oup.com/jxb/article-abstract/42/3/393/495356?redirectedFrom=fulltext

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  79. Weisstein, Eric W. "Omega Constant". mathworld.wolfram.com. Retrieved 2025-02-06. https://mathworld.wolfram.com/OmegaConstant.html

  80. Weisstein, Eric W. "Solid Angle". mathworld.wolfram.com. Retrieved 2025-02-07. The solid angle Ω subtended by a surface S is defined as the surface area Ω of a unit sphere covered by the surface's projection onto the sphere. https://mathworld.wolfram.com/SolidAngle.html

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  82. "Density Parameter | COSMOS". astronomy.swin.edu.au. Retrieved 2025-02-07. https://astronomy.swin.edu.au/cosmos/D/Density+Parameter

  83. Weisstein, Eric W. "Ordinal Number". mathworld.wolfram.com. Retrieved 2025-02-06. The first transfinite ordinal, denoted ω ... https://mathworld.wolfram.com/OrdinalNumber.html

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  85. Weisstein, Eric W. "Distinct Prime Factors". mathworld.wolfram.com. Retrieved 2025-02-06. https://mathworld.wolfram.com/DistinctPrimeFactors.html

  86. Weisstein, Eric W. "Clique". mathworld.wolfram.com. Retrieved 2025-02-07. A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique number ω(G)). https://mathworld.wolfram.com/Clique.html