Greek letters used in mathematics, science, and engineering

Greek alphabet Αα Alpha Νν Nu Ββ Beta Ξξ Xi Γγ Gamma Οο Omicron Δδ Delta Ππ Pi Εε Epsilon Ρρ Rho Ζζ Zeta Σσς Sigma Ηη Eta Ττ Tau Θθ Theta Υυ Upsilon Ιι Iota Φφ Phi Κκ Kappa Χχ Chi Λλ Lambda Ψψ Psi Μμ Mu Ωω Omega History Archaic local variants
· · · · ·Ligatures (ϛ, ȣ, ϗ) · Diacritics Numerals: (6) · (90) · (900) In other languages Bactrian · Coptic · Albanian Scientific symbols
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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 usually not used: capital A, B, E, H, I, K, M, N, O, P, T, X, Y, Z. Small ι (iota), ο (omicron) and υ (upsilon) 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 φ (phi) and π (pi).
In mathematical finance, the Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.
Englishspeaking 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, cf. ancient [tʰɛ̂ːta] and modern [ˈθita].
Typography
The Greek letter forms used in maths 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 Αα Digamma Ϝϝ Kappa Κκ Omicron Οο Upsilon Υυ Beta Ββ Zeta Ζζ Lambda Λλ Pi Ππϖ Phi Φϕφ Gamma Γγ Eta Ηη Mu Μμ Rho Ρρϱ Chi Χχ Delta Δδ Theta Θθϑ Nu Νν Sigma Σσς Psi Ψψ Epsilon Εϵε Iota Ιι Xi Ξξ Tau Ττ Omega Ωω Concepts represented by a Greek letter
Αα (alpha)
 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
 the reciprocal of the sacrifice ratio
 the fine structure constant in physics
 the angle of attack of an airplane
 an alpha particle (He^{2+})
 angular acceleration in physics
 the linear thermal expansion coefficient
 the thermal diffusivity
 the alpha carbon is the first carbon after the carbon that attaches to a functional group in organic chemistry
 the αcarbon is the backbone carbon next to the carbonyl carbon in amino acids
 right ascension in astrometry
Ββ (beta)
 Β represents the beta function
 β represents:
 the second angle in a triangle, opposite the side B
 one root of a quadratic equation, where α represents the other
 the ratio of collector current to base current in a bipolar junction transistor (BJT) in electronics (current gain)
 the false negative rate in statistics
 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^{})
 sound intensity
 velocity divided by the speed of light in special relativity
 the beta brain wave in brain or cognitive sciences
 ecliptic latitude in astrometry
Γγ (gamma)
 Γ represents:
 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
 γ represents:
 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 EulerMascheroni 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^{[1]}
 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
 δ represents:
 a variation in the calculus of variations
 the Kronecker delta function
 the force of interest in mathematical finance
 the Dirac delta function
 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)
 declination in astrometry
 the Turner Function in computational material science
 noncentrality measure in statistics^{[2]}
Εε (epsilon)
 ε represents:
 a small positive quantity; see limit
 a random error in regression analysis
 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 astrometry
 elasticity in economics
 expected value in probability theory and statistics
 electromotive force
 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.
Ζζ (zeta)
 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
Ηη (eta)
 η represents:
 the intrinsic impedance of medium (usually 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
 a type of meson
 viscosity
 efficiency
 the Minkowski metric tensor in relativity
 noise in communication system models
Θθ (theta)
 Θ represents:
 an asymptotically tight bound related to big O notation.
 sensitivity to the passage of time in mathematical finance
 Θ (set theory), a certain ordinal number
 θ represents:
 a plane angle in geometry
 the angle to the x axis in the xyplane in spherical or cylindrical coordinates
 potential temperature in thermodynamics
 the mean time between failure in reliability engineering
 soil water contents in soil science
 Debye temperature
 theta functions
 sometimes also ϑ ("script theta"), cursive form of theta, often used in handwriting
 the first Chebyshev function in number theory
Ιι (iota)
 ι represents:
 the index generator function in APL (in the form ⍳)
Κκ (kappa)
 κ represents:
 the Von Kármán constant
 the kappa 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)
Λλ (lambda)
 Λ represents:
 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
 a type of baryon
 a diagonal matrix of eigenvalues in linear algebra
 the permeance of a material in electromagnetism
 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 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 astrometry
 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
Μμ (mu)
 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
Νν (nu)
 ν represents:
 frequency in physics in hertz (Hz)
 Poisson's ratio in material science
 a neutrino
 kinematic viscosity of liquids
 stoichiometric coefficient in chemistry
 dimension of nullspace in maths
Ξξ (xi)
 Ξ represents:
 the grand canonical ensemble found in statistical mechanics
 a type of baryon
 ξ represents:
 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 as well)
Ππ (pi)
 Π represents:
 the product operator in mathematics
 a plane
 π 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
 a type of covalent bond in chemistry (pi bond)
 a pion (pi meson) in particle physics
 in electronics, a special type of small signal model is referred to as a hybridpi model
 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 celestial mechanics^{[3]}
 comoving distance, in cosmology^{[4]}
Ρρ (rho)
 ρ represents:
 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)
 resistivity
 the shape and reshape operators in APL (in the form ⍴)
 the utilization in queueing theory
 the rank of a matrix
Σσ (sigma)
 Σ represents:
 the summation operator
 the covariance matrix
 the set of terminal symbols in a formal grammar
 σ represents:
 Stefan's 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 or 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
Ττ (tau)
 τ (lowercase) represents:
 an interval of time
 a mean lifetime
 torque, the rotational force in mechanics
 the elementary tau lepton in particle physics
 the lifetime of a spontaneous emission process
 the time constant of any device, such as an RC circuit
 proper time in relativity
 a correlation coefficient — see Kendall's tau
 the golden ratio 1.618... (although φ (phi) is more common)
 Ramanujan's tau function in number theory
 in astronomy, a measure of opacity, or how much sunlight cannot penetrate the atmosphere
 the intertwining operator in representation theory
 the tau in biochemistry, a protein associated to microtubules
 shear stress in continuum mechanics
 the number of divisors of highly composite numbers (sequence A000005 in OEIS)
 the prefix of many stars, via the Bayer stellar designation system
 an internal system step in transition systems
 a type variable in type theories, such as the simply typed lambda calculus
 τ has been suggested as a circle constant to replace pi and has a value of 6.283..., or 2×π
Υυ (upsilon)
 Υ represents:
 an elementary particle
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
 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
 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
Χχ (chi)
 χ represents:
 the chi distribution in statistics (χ^{2} is the more frequently encountered chisquare distribution)
 the chromatic number of a graph in graph theory
 the Euler characteristic in algebraic topology
 a variable in algebraic equations
 electronegativity in the periodic table
 the Rabi frequency
 the spinor of a fundamental particle
 the Fourier transform of a linear response function (see susceptibility)
 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
Ψψ (psi)
 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 xaxis and the tangent to the curve in the intrinsic coordinates system
 the second Chebyshev function in number theory
Ωω (omega)
 Ω represents:
 the Omega constant
 an asymptotic lower bound related to big O notation
 in probability theory and statistical mechanics, the set of possible distinct system states
 the SI unit measure of electric resistance, the ohm
 the rotation rate of an object, particularly a planet, in dynamics
 a solid angle
 a baryon
 the arithmetic function counting a number's prime factors
 the right ascension of the ascending node in celestial mechanics
 the density parameter in cosmology
 ω represents:
 the first infinite ordinal
 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
 angular velocity / radian frequency
 a complex cube root of unity — the other is ω² — (used to describe various ways of calculating the discrete Fourier transform)
 vertical velocity in pressurebased coordinate systems (commonly used in atmospheric dynamics)
 a meson
 the arithmetic function counting a number's distinct prime factors
 a differential form (esp. on an analytic space)
 the argument of periapsis in celestial mechanics
 the symbol ϖ, a graphic variant of π, is sometimes construed as omega with a bar over it; see π
See also
 Greek alphabet
 English pronunciation of Greek letters
 A pronunciation guide with audio
 Latin letters used in mathematics
 Mathematical alphanumeric symbols
 Table of mathematical symbols
 Typographical conventions in mathematical formulae
 The Greeks (Greek letters used in mathematical finance)
References
 ^ http://www.maths.abdn.ac.uk/~igc/tch/eg1006/notes/node119.html
 ^ 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.
 ^ Pomega  from Eric Weisstein's World of Physics
 ^ Outline for Weeks 14&15, Astronomy 225 Spring 2008
Categories: Mathematical notation
 Greek letters
 α represents:
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