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.
The majority of 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 (US pronunciation), cf. ancient [tʰɛ̂ːta] and modern [ˈθita] (although the latter pronunciation is used in British English).
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.
α
represents:
the first angle in a triangle, opposite the side A
one root of a quadratic equation, where β represents the other
the ratio of collector current to emitter current in a bipolar junction transistor (BJT) in electronics
the statistical significance of a result
the false positive rate in statistics ("Type I" error)
the reciprocal of the sacrifice ratio
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
Β represents the beta function
β 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
one root of a quadratic equation, where α represents the other
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
the first-order effects of variations in Coriolis force with latitude in planetary dynamics
a beta particle (e−)
sound intensity
velocity divided by the speed of light in special relativity
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
In organic chemistry, β represents the second carbon from a functional group
Γ 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 of the second kind
the neighbourhood of a vertex in a graph
the stack alphabet in the formal definition of a pushdown automaton
γ represents:
the circulation strength in fluid dynamics
the partial safety factors applied to loads and materials in structural engineering
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 damping constant (kg/s)
Δ represents:
a finite difference
a difference operator
a symmetric difference
the Laplace operator
the angle that subtends the arc of a circular curve in surveying
the determinant of an inverse matrix
the maximum degree of any vertex in a given graph
the difference or change in a given variable, e.g. ∆v means a difference or change in velocity
sensitivity to price in mathematical finance
distance to Earth, measured in astronomical units
heat in a chemical formula
the discriminant in the quadratic formula which determines the nature of the roots
the degrees of freedom in a non-pooled statistical hypothesis test of two population means
δ represents:
percent error
a variation in the calculus of variations
the Kronecker delta function
the Feigenbaum constant
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
the Turner function in computational material science
depreciation in macroeconomics
noncentrality measure in statistics
ε 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
ω
,
ω
ω
,
ω
ω
ω
,
…
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
expected value in probability theory and statistics
electromotive force
in chemistry, the molar extinction coefficient of a chromophore.
set membership symbol ∈ is based on ε
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
ζ represents:
the Riemann zeta function and other zeta functions in mathematics
the coefficient of viscous friction in polymer dynamics
the damping ratio
relative vertical vorticity in fluid dynamics
Η represents:
the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics
Information theoretic (Shannon) entropy
η represents:
the intrinsic wave impedance of a medium (e.g. the impedance of 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
the eta meson
viscosity
energy conversion efficiency
efficiency (physics)
the Minkowski metric tensor in relativity
noise in communication system models
η-conversion in lambda calculus
Cost-push supply side shocks in the Phillips curve equation (economics)
A right angle, i.e., π/2, as a follow-up to the tau/pi argument
Θ (uppercase) represents:
an asymptotically tight bound related to big O notation.
Debye temperature in solid state physics
sensitivity to the passage of time in mathematical finance
in set theory, a certain ordinal number
in econometrics and statistics, a space of parameters from which estimates are drawn
θ (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)
Bragg's angle of diffraction
the potential temperature in thermodynamics
the mean time between failure in reliability engineering
soil water contents in soil science
in mathematical statistics, an unknown parameter
theta functions
the angle of a scattered photon during a Compton scattering interaction
ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
the first Chebyshev function in number theory
ι represents:
an inclusion map in set theory
the index generator function in APL (in the form ⍳)
the orbital inclination in celestial mechanics.
Κ represents:
the Kappa number, indicating lignin content in pulp
κ 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
(
ε
/
ε
0
)
thermal conductivity (usually a lowercase Latin k)
thermal diffusivity
a spring constant (usually a lowercase Latin k)
the heat capacity ratio in thermodynamics (usually γ)
the receptor which dynorphins have the highest affinity for in pharmacology
Λ represents:
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
the permeance of a material in electromagnetism
a lattice
λ 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 average lifetime or rate parameter in an exponential distribution (commonly used across statistics, physics, and engineering)
the failure rate in reliability engineering
the fundamental length of a fabrication process in VLSI design
the mean or average value (probability and statistics)
the latent heat of fusion
the lagrange multiplier in the mathematical optimization method, 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
a unit of measure of volume equal to one microlitre (1 μL) or one cubic millimetre (1 mm³)
the empty string in formal grammar
binding of a variable in a function in lambda calculus in computer science.
μ represents:
the Möbius function in number theory
the ring representation of a representation module
the population mean or expected value in probability and statistics
a measure in measure theory
micro-, an SI prefix denoting 10−6 (one millionth)
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
chemical potential in condensed matter physics
the ion mobility in plasma physics
the Standard gravitational parameter in celestial mechanics
ν represents:
frequency in physics in hertz (Hz)
degrees of freedom in statistics
Poisson's ratio in material science
a neutrino
kinematic viscosity of liquids
stoichiometric coefficient in chemistry
dimension of nullspace in mathematics
true anomaly in celestial mechanics
the matching number of a graph
Ξ represents:
the original Riemann Xi function, i.e. Riemann's lower case ξ, as denoted by Edmund Landau and currently
the grand canonical ensemble found in statistical mechanics
the xi baryon
ξ represents:
the original Riemann Xi function
the modified definition of Riemann xi function, as denoted by Edmund Landau and currently
a random variable
the extent of a chemical reaction
coherence length
the damping ratio
universal set
Ο represents:
big O notation (may be represented by an uppercase Latin O)
o represents:
small o notation (may be represented by a lowercase Latin o)
Π represents:
the product operator in mathematics
a plane
the unary projection operation in relational algebra
osmotic pressure
π represents:
Archimedes' constant, the ratio of a circle's circumference to its diameter
the prime-counting function
profit in microeconomics and game theory
inflation in macroeconomics, expressed as a constant with respect to time
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 relational algebra for databases, represents projection
ϖ (a graphic variant, see pomega) represents:
angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by
ω
but this may be confused with vorticity in a fluid dynamics context)
longitude of pericenter, in astronomy
comoving distance, in cosmology
Ρ represents:
one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P).
ρ 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 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 utilization in queueing theory
the rank of a matrix
the rename operator in relational algebra
Σ represents:
the summation operator
the covariance matrix
the set of terminal symbols in a formal grammar
σ represents:
Stefan–Boltzmann constant in blackbody radiation
the divisor function in number theory
the real part of the complex variable s = σ + i t 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
nuclear cross section
uncertainty
utilization in operations management
surface charge density for microparticles
τ (lower-case) 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 2π (6.283...).
Kendall tau rank correlation coefficient, a measure of rank correlation in statistics
Ramanujan's tau function in number theory
a measure of opacity, or how much sunlight cannot penetrate the atmosphere
the intertwining operator in representation theory
shear stress in continuum mechanics
an internal system step in transition systems
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 golden ratio 1.618... (although φ (phi) is more common)
the number of divisors of highly composite numbers (sequence A000005 in the OEIS)
in proton NMR spectroscopy, τ was formerly used for physical shift
Υ represents:
the upsilon meson
υ represents:
frequency in physics textbooks
Φ represents:
the work function in physics; the energy required by a photon to remove an electron from the surface of a metal
magnetic flux
the cumulative distribution function of the normal distribution in statistics
phenyl functional group
the reciprocal of the golden ratio (represented by φ, below), also represented as 1/φ
the value of the integration of information in a system (based on integrated information theory)
note: a symbol for the empty set,
∅
, resembles Φ but is not Φ
φ represents:
the golden ratio 1.618... in mathematics, art, and architecture
Euler's totient function in number theory
a holomorphic map on an analytic space
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)
the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (physics)
latitude in geodesy
a scalar field
radiant flux
electric potential
the probability density function of the normal distribution in statistics
a feature of a syntactic node giving that node characteristics such as gender, number and person in syntax
the diameter of a vessel (engineering)
capacity reduction factor of materials in structural engineering
χ represents:
the chi distribution in statistics (
χ
2
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 Rabi frequency
the spinor of a fundamental particle
the Fourier transform of a linear response function
a character in mathematics; especially a Dirichlet character in number theory
the Sigma vectors in the unscented transform used in the unscented Kalman filter
sometimes the mole fraction
a characteristic or indicator function in mathematics
the Magnetic susceptibility of a material in physics
Ψ represents:
water potential
a quaternary combinator in combinatory logic
ψ represents:
the wave function in the Schrödinger equation of quantum mechanics
the stream function in fluid dynamics
yaw angle in vehicle dynamics
the angle between the x-axis and the tangent to the curve in the intrinsic coordinates system
the reciprocal Fibonacci constant
the second Chebyshev function in number theory
the polygamma function in mathematics
load combination factor in structural engineering
the Supergolden Ratio
Ω represents:
the SI unit measure of electrical resistance, the ohm
angular velocity / radian frequency (rev/min)
the right ascension of the ascending node (RAAN) or Longitude of the ascending node in astronomy and orbital mechanics
the rotation rate of an object, particularly a planet, in dynamics
the omega constant 0.5671432904097838729999686622...
an asymptotic lower bound related to big O notation
in probability theory and statistical mechanics, the set of possible distinct system states
a solid angle
the omega baryon
the arithmetic function counting a number's prime factors
the density parameter in cosmology
ω 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 ω² — (used to describe various ways of calculating the discrete Fourier transform)
the differentiability class (i.e.
C
ω
) 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
N
or N is more common in other areas of mathematics)
an asymptotically dominant quantity related to big O notation
in probability theory, a possible outcome of an experiment
in economics, the total wealth of an agent in general equilibrium theory
vertical velocity in pressure-based coordinate systems (commonly used in atmospheric dynamics)
the arithmetic function counting a number's distinct prime factors
a differential form (esp. on an analytic space)
the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π
the last carbon atom of a chain of carbon atoms is sometimes called the ω (omega) position, reflecting that ω is the last letter of the Greek alphabet. This nomenclature can be useful in describing unsaturated fatty acids.
