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 rarely used: capital Α, Β, Ε, Ζ, Η, Ι, Κ, Μ, Ν, Ο, Ρ, Τ, Υ, and Χ. Small ι, ο and υ 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 ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.
The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters.
In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.
Typography
Some common conventions: Intensive quantities in physics are usually denoted with minusculeswhile extensive are denoted with capital letters. Most symbols are written in italics. Vectors can be denoted in boldface. Sets of numbers are typically bold or blackboard bold.
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 lowercase Greek letters 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. Unlike Unicode and HTML, TeX does not have special symbols for Greek capital letters that look identical to their Latin counterparts. Instead the Latin capital letters A, E, Z, H, I, K, M, N, O, P, T, X are used for capital Alpha, Epsilon, Zeta, Eta, Iota, Kappa, Mu, Nu, Omicron, Rho, Tau, and Chi respectively.
+ Greek letters in HTML and TeX (α–μ) Name TeX HTML Alpha Α α Beta Β β Gamma Γ γ Delta Δ δ Epsilon Ε ϵ ε Digamma Ϝ ϝ Zeta Ζ ζ Eta Η η Theta Iota Ι ι Kappa Lambda Λ λ Mu Μ μ + Greek letters in HTML and TeX (ν–ω) Name TeX HTML Nu Ν ν Xi Ξ ξ Omicron Ο ο Pi Π π ϖ Rho Ρ ρ Sigma Σ σ ς Tau Τ τ Upsilon Υ υ Phi Chi Χ χ Psi Ψ ψ Omega Ω ω
+ Greek letters with typographical variations Name Greek Letter Bold Italic Bold Italic Sans-Serif Bold Sans-Serif Bold Italic APL Double struck bold Unicode variants or similar Alpha Α α 𝚨 𝛂 𝛢 𝛼 𝜜 𝜶 𝝖 𝝰 𝞐 𝞪 ⍺ ⍶ Beta Β β 𝚩 𝛃 𝛣 𝛽 𝜝 𝜷 𝝗 𝝱 𝞑 𝞫 Gamma 𝚪 𝛄 𝛤 𝛾 𝜞 𝜸 𝝘 𝝲 𝞒 𝞬 Delta Δ δ 𝚫 𝛅 𝛥 𝛿 𝜟 𝜹 𝝙 𝝳 𝞓 𝞭 , Epsilon Ε ε ϵ ϶ 𝚬 𝛆 𝛜 𝛦 𝜀 𝜖 𝜠 𝜺 𝝐 𝝚 𝝴 𝞊 𝞔 𝞮 𝟄 ⍷ – Zeta Ζ ζ 𝚭 𝛇 𝛧 𝜁 𝜡 𝜻 𝝛 𝝵 𝞕 𝞯 Eta Η η Ͱ ͱ 𝚮 𝛈 𝛨 𝜂 𝜢 𝜼 𝝜 𝝶 𝞖 𝞰 Theta Iota 𝚰 𝛊 𝛪 𝜄 𝜤 𝜾 𝝞 𝝸 𝞘 𝞲 ⍳ ⍸ Kappa Lambda Λ λ ᴧ 𝚲 𝛌 𝛬 𝜆 𝜦 𝝀 𝝠 𝝺 𝞚 𝞴 Mu Μ μ 𝚳 𝛍 𝛭 𝜇 𝜧 𝝁 𝝡 𝝻 𝞛 𝞵 Nu Ν ν 𝚴 𝛎 𝛮 𝜈 𝜨 𝝂 𝝢 𝝼 𝞜 𝞶 Xi Ξ ξ 𝚵 𝛏 𝛯 𝜉 𝜩 𝝃 𝝣 𝝽 𝞝 𝞷 Omicron Ο ο 𝚶 𝛐 𝛰 𝜊 𝜪 𝝄 𝝤 𝝾 𝞞 𝞸 Pi Π π ϖ ᴨ 𝚷 𝛑 𝛡 𝛱 𝜋 𝜛 𝜫 𝝅 𝝕 𝝥 𝝿 𝞏 𝞟 𝞹 𝟉 , Rho 𝚸 𝛒 𝛠 𝛲 𝜌 𝜚 𝜬 𝝆 𝝔 𝝦 𝞀 𝞎 𝞠 𝞺 𝟈 ⍴ Sigma Σ σ ς Ϲ ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ 𝚺 𝛔 𝛓 𝛴 𝜎 𝜍 𝜮 𝝈 𝝇 𝝨 𝞂 𝞁 𝞢 𝞼 𝞻 Tau Τ τ 𝚻 𝛕 𝛵 𝜏 𝜯 𝝉 𝝩 𝞃 𝞣 𝞽 Upsilon Υ υ ϒ 𝚼 𝛖 𝛶 𝜐 𝜰 𝝊 𝝪 𝞄 𝞤 𝞾 Phi 𝚽 𝛗 𝛟 𝛷 𝜑 𝜙 𝜱 𝝋 𝝓 𝝫 𝞅 𝞍 𝞥 𝞿 𝟇 Chi 𝚾 𝛘 𝛸 𝜒 𝜲 𝝌 𝝬 𝞆 𝞦 𝟀 Psi Ψ ψ ᴪ 𝚿 𝛙 𝛹 𝜓 𝜳 𝝍 𝝭 𝞇 𝞧 𝟁 Omega Ω ω ꭥ 𝛀 𝛚 𝛺 𝜔 𝜴 𝝎 𝝮 𝞈 𝞨 𝟂 ⍵ ⍹ ,
Concepts represented by a Greek letter
Αα (alpha)
represents: the first angle in a triangle, opposite the side a the statistical significance of a result the false positive rate in statistics ("Type I" error) the fine-structure constant in physics the angle of attack of an aircraft an alpha particle (He2+) angular acceleration in physics the linear thermal expansion coefficient the thermal diffusivity In organic chemistry the α-carbon is the backbone carbon next to the carbonyl carbon, most often for amino acids right ascension in astronomy the brightest star in a constellation Iron ferrite and numerous phases within materials science the return in excess of the compensation for the risk borne in investment the α-conversion in lambda calculus the independence number of a graph a placeholder for ordinal numbers in mathematical logic a type of receptor for the neurotransmitter noradrenaline in neuroscience
Ββ (beta)
represents the beta function represents: the thermodynamic beta, equal to (kBT)−1, where kB is the Boltzmann constant and T is the absolute temperature. the second angle in a triangle, opposite the side b the standardized regression coefficient for predictor or independent variables in linear regression (unstandardized regression coefficients are represented with the lower-case Latin b, but are often called "betas" as well) the ratio of collector current to base current in a bipolar junction transistor (BJT) in electronics (current gain) the false negative rate in statistics ("Type II" error) the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance the sideslip angle of an airplane a beta particle (e− or e+) the beta brain wave in brain or cognitive sciences ecliptic latitude in astronomy the ratio of plasma pressure to magnetic pressure in plasma physics β-reduction in lambda calculus the ratio of the velocity of an object to the speed of light as used in the Lorentz factor a type of receptor for the noradrenaline neurotransmitter in neuroscience
Γγ (gamma)
represents: the circulation in fluid dynamics the reflection coefficient of a transmission or telecommunication line. the confinement factor of an optical mode in a waveguide the gamma function, a generalization of the factorial the upper incomplete gamma function the modular group, the group of fractional linear transformations the gamma distribution, a continuous probability distribution defined using the gamma function second-order sensitivity to price in mathematical finance the Christoffel symbols that describe components of a metric connection the stack alphabet in the formal definition of a pushdown automaton, or the tape-alphabet in the formal definition of a Turing machine the Feferman–Schütte ordinal Γ0 atmospheric lapse rates in meteorology represents: the specific weight of substances the lower incomplete gamma function the third angle in a triangle, opposite the side c the Euler–Mascheroni constant in mathematics gamma rays and the photon the heat capacity ratio in thermodynamics the Lorentz factor in special relativity the flight path angle of an airplane
Δδ (delta)
represents: a finite difference a difference operator a symmetric difference the Laplace operator giving heat in a chemical reaction the angle that subtends the arc of a circular curve in surveying the maximum degree of any vertex in a given graph sensitivity to price in mathematical finance the discriminant of a polynomial (in a quadratic polynomial determines the nature of the roots) represents: percent error a variation in the calculus of variations the Kronecker delta function the Feigenbaum constants the force of interest in mathematical finance the Dirac delta function the receptor which enkephalins have the highest affinity for in pharmacologyKatzung & Trevor's Pharmacology Examination & Board Review (9th Edition.). Anthony J. Trevor, Bertram G. Katzung, Susan B. Masters . B. Opioid Peptides + 268 pp. the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis the minimum degree of any vertex in a given graph a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge in chemistry(See also: Solvation) the chemical shift of an atomic nucleus in NMR spectroscopy. For protons, this is relative to tetramethylsilane = 0 stable isotope compositions declination in astronomy noncentrality measure in statistics The transition function in the formal definition of a finite automaton, pushdown automaton, or Turing machine Infinitesimal - see Not to be confused with ∂ which is based on the Latin letter d but often called a "script delta"
Εε (epsilon)
represents: a small positive quantity; see limit a random error in regression analysis the absolute value of an error in set theory, the limit ordinal of the sequence in computer science, the empty string the Levi-Civita symbol in electromagnetics, dielectric permittivity emissivity strain in continuum mechanics permittivity the Earth's axial tilt in astronomy elasticity in economics electromotive force in chemistry, the molar extinction coefficient of a chromophore in mathematics, a surreal number that is bigger than zero, but smaller than all positive real numbers. set membership symbol ∈ is based on ε
(digamma)
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)
represents: the Riemann zeta function and other zeta functions in mathematics the damping ratio the value for the Zeta potential, i.e., the electrical potential at the slipping plane, used often in colloidal chemistry
Ηη (eta)
represents: the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics Information theoretic (Shannon) entropy represents: the intrinsic wave impedance of a medium (e.g. the impedance of free space) the partial regression coefficient in statistics, also interpreted as an effect size measure for analyses of variance the eta meson viscosity the Dedekind eta function energy conversion efficiency efficiency (physics) the pseudorapidity of a particle in physics the Minkowski metric tensor in relativity η-conversion in lambda calculus the learning rate in machine learning and statistics the hapticity of a coordination complex ligand
Θθ (theta)
(uppercase) represents: an asymptotically tight bound related to big O notation. sensitivity to the passage of time in mathematical finance in set theory, a certain ordinal number Heaviside step function (lowercase) represents: a plane angle in geometry the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) the angle to the z axis in spherical coordinates (physics) the potential temperature in thermodynamics theta functions the angle of a scattered photon during a Compton scattering interaction the angular displacement of a particle rotating about an axis the Watterson estimator in population genetics the thermal resistance between two bodies ("script theta"), the cursive form of theta, often used in handwriting, represents the first Chebyshev function in number theory Theta role in linguistics
Ιι (iota)
represents: an inclusion map in set theory the index generator function in APL (in the form ⍳) the interior product
Κκ (kappa)
represents: the Kappa number, indicating lignin content in pulp represents: the Von Kármán constant, describing the velocity profile of turbulent flow the kappa curve, a two-dimensional algebraic curve the condition number of a matrix in numerical analysis the connectivity of a graph in graph theory curvature dielectric constant thermal conductivity (usually a lowercase Latin ) electrical conductivity of a solution thermal diffusivity a spring constant (usually a lowercase Latin )