Greek letters used in mathematics, science, and engineering
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 A, B, E, Z, H, I, K, M, N, O, P, T, Y, X. 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 minuscules while 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 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.
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 Boltzmann's 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
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 pharmacology
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 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 Limit of a function § (ε, δ)-definition of limit
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 the non-negative numbers.
set membership symbol ∈ is based on ε
Ϝϝ (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)
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 Minkowski metric tensor in relativity
η-conversion in lambda calculus
the learning rate in machine learning and statistics
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
ϑ ("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 )
the heat capacity ratio in thermodynamics (usually )
the receptor which dynorphins have the highest affinity for in pharmacology
Einstein gravitational constant
Λλ (lambda)
represents:
the Lebesgue constant, a bound for the interpolation error
the von Mangoldt function in number theory
the set of logical axioms in the axiomatic method of logical deduction in first-order logic
the cosmological constant
the lambda baryon
a diagonal matrix of eigenvalues in linear algebra
a lattice
molar conductivity in electrochemistry
Iwasawa algebra
represents:
one wavelength of electromagnetic radiation
the decay constant in radioactivity
function expressions in the lambda calculus
a general eigenvalue in linear algebra
the expected number of occurrences in a Poisson distribution in probability
the arrival rate in queueing theory
the failure rate in reliability engineering
the Lagrange multiplier in mathematical optimization, known as the shadow price in economics
the Lebesgue measure denotes the volume or measure of a Lebesgue measurable set
longitude in geodesy
linear density
ecliptic longitude in astronomy
the Liouville function in number theory
the Carmichael function in number theory
the empty string in formal grammar
a formal system (lambda calculus) in mathematical logic
thermal conductivity
the Lorentz transformation
Μμ (mu)
represents:
the Möbius function in number theory
the population mean or expected value in probability and statistics
a measure in measure theory
micro-, an SI prefix denoting 10−6 (one millionth)
Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning)
the coefficient of friction in physics
the service rate in queueing theory
the dynamic viscosity in physics
magnetic permeability in electromagnetics
a muon
reduced mass
the ion mobility in plasma physics
the Standard gravitational parameter in celestial mechanics
population mean in statistics
chemical potential in thermodynamics
Absorption coefficient
Amplification factor
Magnetic moment of a dipole
Νν (nu)
represents:
frequency in physics in hertz (Hz)
Poisson's ratio in material science
a neutrino
kinematic viscosity of liquids
stoichiometric coefficient in chemistry
true anomaly in celestial mechanics
degrees of freedom in statistics
the matching number of a graph
the p-adic valuation of a number
Ξξ (xi)
represents:
the original Riemann Xi function, i.e. Riemann's lower case ξ, as denoted by Edmund Landau and currently
the xi baryon
represents:
the original Riemann Xi function
the modified definition of Riemann xi function, as denoted by Edmund Landau
the extent of reaction
Οο (omicron)
Ππ (pi)
represents:
the product operator in mathematics
a plane
the unary projection operation in relational algebra
osmotic pressure
represents:
Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter
the prime-counting function
the state distribution of a Markov chain
in reinforcement learning, a policy function defining how a software agent behaves for each possible state of its environment
a type of covalent bond in chemistry (pi bond)
a pion (pi meson) in particle physics
in statistics, the population proportion
nucleotide diversity in molecular genetics
in electronics, a special type of small signal model is referred to as a hybrid-pi model
in discrete mathematics, a permutation
Projection
ϖ (a graphic variant, see pomega) represents:
angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by but this may be confused with vorticity in a fluid dynamics context)
longitude of pericenter, in astronomy
comoving distance, in cosmology
Ρρ (rho)
represents:
one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P).
represents:
one of the Gegenbauer functions in analytic number theory.
the Dickman-de Bruijn function
the radius in a polar, cylindrical, or spherical coordinate system
the correlation coefficient in statistics
the radius of convergence in real analysis
the sensitivity to interest rate in mathematical finance
density (mass or charge per unit volume; may be replaced by the capital form of the Latin letter D)
resistivity
the shape and reshape operators in APL (in the form ⍴)
the rename operator in relational algebra
the plastic ratio
Rho meson
Σσς (sigma)
represents:
the summation operator
the covariance matrix
the set of terminal symbols in a formal grammar
Mathematical surface
Sigma baryon
represents:
Stefan–Boltzmann constant in blackbody radiation
the divisor function in number theory
the real part of the complex variable in analytic number theory
the sign of a permutation in the theory of finite groups
the population standard deviation, a measure of spread in probability and statistics
a type of covalent bond in chemistry (sigma bond)
the selection operator in relational algebra
stress in mechanics
electrical conductivity
area density
Cross section
nuclear cross section
surface charge density for microparticles
standard deviation of a random variable in statistics
Spectrum of a matrix
Spin
Ττ (tau)
represents:
torque, the net rotational force in mechanics
the elementary tau lepton in particle physics
a mean lifetime, of an exponential decay or spontaneous emission process
the time constant of any device, such as an RC circuit
proper time in relativity
one turn: the constant ratio of a circle's circumference to its radius, with value (6.283...).
Kendall tau rank correlation coefficient, a measure of rank correlation in statistics
Ramanujan's tau function in number theory
shear stress in continuum mechanics
a type variable in type theories, such as the simply typed lambda calculus
path tortuosity in reservoir engineering
in topology, a given topology
the tau in biochemistry, a protein associated to microtubules
the number of divisors of highly composite numbers (sequence A000005 in the OEIS)
precision (), the reciprocal of variance, in statistics
ϒυ (upsilon)
(U+03D2) represents:
the upsilon meson
Φφ (phi)
represents:
the work function in physics; the energy required by a photon to remove an electron from the surface of a metal
magnetic flux or electric flux
the cumulative distribution function of the normal distribution in statistics
phenyl functional group in organic chemistry (pseudoelement symbol)
the reciprocal of the golden ratio (represented by , below), also represented as
the value of the integration of information in a system (based on integrated information theory)
Geopotential
Alternative symbol for a wave function in quantum mechanics
Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter.
or represents:
the golden ratio 1.618... in mathematics, art, and architecture
Euler's totient function in number theory
the argument of a complex number in mathematics
the value of a plane angle in physics and mathematics
the angle to the z axis in spherical coordinates (mathematics)
epoch or phase difference between two waves or vectors
the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (physics)
latitude in geodesy
radiant flux
neutron flux
Potential energy
electric potential
a scalar field in quantum field theory
the probability density function of the normal distribution in statistics
the Veblen functions
Χχ (chi)
represents:
the chi distribution in statistics ( is the more frequently encountered chi-squared distribution)
the chromatic number of a graph in graph theory
the Euler characteristic in algebraic topology
electronegativity in the periodic table
the Fourier transform of a linear response function
a character in mathematics; especially a Dirichlet character in number theory
sometimes the mole fraction
a characteristic or indicator function in mathematics
the magnetic susceptibility of a material in physics
the fission neutron energy spectrum in neutron transport
Ψψ (psi)
represents:
water potential
a quaternary combinator in combinatory logic
a symbol for psychology
represents:
the wave function in the Schrödinger equation of quantum mechanics
the J/psi mesons in particle physics
the stream function in fluid dynamics
the reciprocal Fibonacci constant
the second Chebyshev function in number theory
the polygamma function in mathematics
the supergolden ratio
Ωω (omega)
represents:
Absolute infinite
the SI unit measure of electrical resistance, the ohm
the right ascension of the ascending node (RAAN) or Longitude of the ascending node in astronomy and orbital mechanics
the omega constant 0.5671432904097838729999686622...
an asymptotic lower bound notation related to big O notation
in probability theory and statistical mechanics, the support
a solid angle
the omega baryon
the arithmetic function counting a number's prime factors counted with multiplicity
the density parameter in cosmology
the first uncountable ordinal (also written as ω1)
Chaitin's constant for a given computer program
the vacuum state in quantum field theory
represents:
angular velocity / radian frequency (rad/sec)
the argument of periapsis in astronomy and orbital mechanics
a complex cube root of unity — the other is — (used to describe various ways of calculating the discrete Fourier transform)
the differentiability class (i.e.) for functions that are infinitely differentiable because they are complex analytic
the first infinite ordinal
the omega meson
the set of natural numbers in set theory (although or N is more common in other areas of mathematics)
an asymptotic dominant notation related to big O notation
in probability theory, a possible outcome of an experiment
the arithmetic function counting a number's distinct prime factors
the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π
the unsaturated fats nomenclature in biochemistry (e.g. ω−3 fatty acids)
the first uncountable ordinal (also written as Ω)
the clique number (number of vertices in a maximum clique) of a graph in graph theory
See also
Blackboard bold letters used in mathematics
English pronunciation of Greek letters
List of mathematical uses of Latin letters
List of letters used in mathematics and science
Glossary of mathematical symbols
Mathematical Alphanumeric Symbols (a Unicode block)