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.
Greek alphabet  



History  
Use in other languages  
Related topics  
 
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
The Greek letter forms used in mathematics are often different from those used in Greeklanguage 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  Α α  Digamma  Ϝ ϝ  Kappa  Κ κ ϰ  Omicron  Ο ο  Upsilon  Υ υ  
Beta  Β β  Zeta  Ζ ζ  Lambda  Λ λ  Pi  Π π ϖ  Phi  Φ ϕ φ  
Gamma  Γ γ  Eta  Η η  Mu  Μ μ  Rho  Ρ ρ ϱ  Chi  Χ χ  
Delta  Δ δ  Theta  Θ θ ϑ  Nu  Ν ν  Sigma  Σ σ ς  Psi  Ψ ψ  
Epsilon  Ε ϵ ε  Iota  Ι ι  Xi  Ξ ξ  Tau  Τ τ  Omega  Ω ω 
Concepts represented by a Greek letter
Αα (alpha)
 represents:
 the first angle in a triangle, opposite the side A
 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 fine structure constant in physics
 the angle of attack of an aircraft
 an alpha particle (He^{2+})
 angular acceleration in physics
 the linear thermal expansion coefficient
 the thermal diffusivity
 In organic chemistry the αcarbon 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 αconversion in lambda calculus
 the independence number of a graph
Ββ (beta)
 Β represents the beta function
 represents:
 the thermodynamic beta, equal to (k_{B}T)^{−1}, where k_{B} 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 lowercase 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 nondiversifiable risk, of an asset in mathematical finance
 the sideslip angle of an airplane
 the firstorder effects of variations in Coriolis force with latitude in planetary dynamics
 a beta particle (e^{−} or 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
 βreduction 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
Γγ (gamma)
 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
 secondorder 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
 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)
Δδ (delta)
 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 nonpooled statistical hypothesis test of two population means
 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[1]
 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[2]
 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[3]
 in set theory, the limit ordinal of the sequence
 in computer science, the empty string
 the LeviCivita 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
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 coefficient of viscous friction in polymer dynamics
 the damping ratio
 relative vertical vorticity in fluid dynamics
Ηη (eta)
 Η represents:
 the Eta function of Ludwig Boltzmann's Htheorem ("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
 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
 ηconversion in lambda calculus
 Costpush supply side shocks in the Phillips curve equation (economics)
 A right angle, i.e., π/2, as a followup to the tau/pi argument[4]
Θθ (theta)
 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
 (lowercase) represents:
 a plane angle in geometry
 the angle to the x axis in the xyplane 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
 the angular displacement of a particle rotating about an axis.
 ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
 the first Chebyshev function in number theory
Ιι (iota)
 represents:
 an inclusion map in set theory
 the index generator function in APL (in the form ⍳)
 the orbital inclination in celestial mechanics.
Κκ (kappa)
 Κ 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 twodimensional 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 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[1]
Λλ (lambda)
 Λ represents:
 the Lebesgue constant (interpolation), 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 firstorder logic
 the cosmological constant
 the lambda baryon
 a diagonal matrix of eigenvalues in linear algebra
 the permeance of a material in electromagnetism
 a lattice
 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 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
 a unit of measure of volume equal to one microlitre (1 μL) or one cubic millimetre (1 mm³)
 the empty string in formal grammar
 a formal system in mathematical logic
 the thermal conductivity.
Μμ (mu)
 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
 the refractive index of a medium with respect to another medium or vacuum.
 a micron or micrometer (10^{6} meter) (common usage in biology, though officially revoked in 1967)
Νν (nu)
 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
Ξξ (xi)
 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
 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
Οο (omicron)
 Ο represents:
 big O notation (may be represented by an uppercase Latin O)
 represents:
 small o notation (may be represented by a lowercase Latin o)
Ππ (pi)
 Π represents:
 the product operator in mathematics
 a plane
 the unary projection operation in relational algebra
 osmotic pressure
 represents:
 Archimedes' constant, the ratio of a circle's circumference to its diameter
 the primecounting 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 hybridpi 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 but this may be confused with vorticity in a fluid dynamics context)
 longitude of pericenter, in astronomy[5]
 comoving distance, in cosmology[6]
Ρρ (rho)
 Ρ 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 Dickmande 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
Σσς (sigma)
 Σ represents:
 the summation operator
 the covariance matrix
 the set of terminal symbols in a formal grammar
 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
 surface charge density for microparticles
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 2π (6.283...).[7]
 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
Υυ (upsilon)
 Υ represents:
 the upsilon meson
Φφ (phi)
 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)
 Geopotential
Note: A symbol for the empty set, , resembles Φ but is not 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 xyplane 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
Χχ (chi)
 represents:
 the chi distribution in statistics ( is the more frequently encountered chisquared 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
Ψψ (psi)
 Ψ represents:
 water potential
 a quaternary combinator in combinatory logic
 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 xaxis 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[8]
Ωω (omega)
 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 support
 a solid angle
 the omega baryon
 the arithmetic function counting a number's prime factors
 the density parameter in cosmology
 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. ) 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 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 pressurebased 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.
See also
 Blackboard bold letters used in mathematics
 English pronunciation of Greek letters
 Greeks (finance) (Greek letters used in mathematical finance, including several invented names similar to Greek letters)
 Latin letters used in mathematics
 List of letters used in mathematics and science
 List of mathematical symbols
 Mathematical Alphanumeric Symbols (a Unicode block)
 Typographical conventions in mathematical formulae
References
 Katzung & Trevor's Pharmacology Examination & Board Review (9th Edition.). Anthony J. Trevor, Bertram G. Katzung, Susan B. Masters ISBN 9780071701556. B. Opioid Peptides + 268 pp.
 Applied Linear Statistical Models (5th ed.). Michael H. Kutner, Christopher J. Nachtsheim, John Neter, & William Li. New York: McGrawHill, 2005. ISBN 007310874X. xxviii + 1396 pp.
 Golub, Gene; Charles F. Van Loan (1996). Matrix Computations – Third Edition. Baltimore: The Johns Hopkins University Press. p. 53. ISBN 080185413X.
 Pi, Tau and Eta. David Butler, Making Your Own Sense (blog). https://blogs.adelaide.edu.au/mathslearning/2011/06/08/pitauandeta/
 Pomega – from Eric Weisstein's World of Physics
 Outline for Weeks 14&15, Astronomy 225 Spring 2008 Archived 20100615 at the Wayback Machine
 "Tau Day – No, really, pi is wrong: The Tau Manifesto by Michael Hartl". 2010. Retrieved 20150320.
 "A supergolden rectangle"