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 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 phi and pi.

In mathematical finance, The Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.

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, cf. ancient [tʰɛ̂ːta] and modern [ˈθita].

Typography

The Greek letter forms used in math 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.

Greek Letters
Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML
Alpha	$\mathrm {A} \alpha \,$	Αα	Digamma	$\digamma \,$	Ϝϝ	Kappa	$\mathrm {K} \kappa \,$	Κκ	Omicron	$\mathrm {O} \mathrm {o} \,$	Οο	Upsilon	$\Upsilon \upsilon \,$	Υυ
Beta	$\mathrm {B} \beta \,$	Ββ	Zeta	$\mathrm {Z} \zeta \,$	Ζζ	Lambda	$\Lambda \lambda \,$	Λλ	Pi	$\Pi \pi \,$	Ππ	Phi	$\Phi \phi \,$	Φφ
Gamma	$\Gamma \gamma \,$	Γγ	Eta	$\mathrm {H} \eta \,$	Ηη	Mu	$\mathrm {M} \mu \,$	Μμ	Rho	$\mathrm {P} \rho \,$	Ρρ	Chi	$\mathrm {X} \chi \,$	Χχ
Delta	$\Delta \delta \,$	Δδ	Theta	$\Theta \theta \,$	Θθ	Nu	$\mathrm {N} \nu \,$	Νν	Sigma	$\Sigma \sigma \,$	Σσ	Psi	$\Psi \psi \,$	Ψψ
Epsilon	$\mathrm {E} \epsilon \,$	Εε	Iota	$\mathrm {I} \iota \,$	Ιι	Xi	$\Xi \xi \,$	Ξξ	Tau	$\mathrm {T} \tau \,$	Ττ	Omega	$\Omega \omega \,$	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 (He²⁺)
  • angular acceleration in physics
  • the linear thermal expansion coefficient
  • the alpha carbon is the first carbon after the carbon that attaches to a functional group in organic chemistry
  • the α-carbon 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 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 astrometry

Γγ (Gamma)

• Γ represents:
  • 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
  • the Christoffel symbols of the second kind
• γ represents:
  • the lower incomplete gamma function
  • the third angle in a triangle, opposite the side C
  • the Euler-Mascheroni constant in mathematics.
  • second-order sensitivity to price in mathematical finance
  • gamma rays and the photon
  • the heat capacity ratio in thermodynamics
  • the Lorentz factor in special relativity

Δδ (Delta)

• Δ represents:
  • a finite difference
  • a difference operator
  • the Laplace operator
  • the angle that subtends the arc of a circular curve in surveying
  • the Determinant of an inverse Matrix (mathematics)
  • 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
  • distance to Earth, measured in astronomical units
  • Heat in a chemical formula
• δ represents:
  • a variation in the calculus of variations
  • the Kronecker delta function
  • the Dirac delta function
  • the Skorohod Integral in Malliavin Calculus, a subfield of stochastic analysis
  • the minimum degree of any vertex in a given graph
  • sensitivity to price in mathematical finance
  • 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

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 $\omega ,\omega ^{\omega },\omega ^{\omega ^{\omega }},\dots$
  • in computer science, the empty string
  • the Levi-Civita symbol
  • in electromagnetics, dielectric permittivity
  • emissivity
  • strain
  • the Earth's axial tilt in astrometry
• 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 normally 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 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

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 xy-plane 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

Ιι (Iota)

• ι represents:
  • the index generator function in APL (in the form ⍳)

Κκ (Kappa)

• κ represents:
  • the kappa curve
  • the condition number of a matrix in numerical analysis
  • the connectivity of a graph in graph theory
  • curvature
  • dielectric constant (usually ε)
  • thermal conductivity (usually a lowercase Latin k)
  • 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 first-order 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:
  • a unit of measure of volume equal to one microlitre (1 μL) or one cubic millimetre (1 mm³)
  • function expressions in the lambda calculus
  • a general eigenvalue in linear algebra
  • one wavelength in electromagnetic radiation, especially radio.
  • the arrival rate in queueing theory
  • the average life time or rate parameter in an exponential distribution (commonly used across statistics, physics, and engineering)
  • the failure rate in reliability engineering
  • the expected number of occurrences in a Poisson distribution in probability
  • 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

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
  • a neutrino

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 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
  • a type of covalent bond in Chemistry (Pi bond)
  • a pion (pi meson)
  • in Electronics, a special type of Small signal model is referred to as a Hybrid-pi model
• ϖ (a graphic variant, see pomega) represents:
  • angular frequency of a wave, in fluid dynamics
  • longitude of pericenter in celestial mechanics
  • the comoving distance in cosmology

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 per unit volume)
  • resistivity
  • the shape and reshape operators in APL (in the form ⍴)
  • the utilization in queueing theory

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
  • electrical conductivity
  • area density
  • nuclear cross section
  • uncertainty
  • utilization in operations management

Ττ (Tau)

• τ (lower-case) represents:
  • an interval of time
  • a mean lifetime
  • torque, the rotational force in mechanics
  • the elementary tau lepton particle 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 the OEIS)
  • the prefix of many stars, via the Bayer stellar designation system

Υυ (Upsilon)

• Υ represents:
  • an elementary particle

Φφ (Phi)

• Φ represents:
  • a wave function
  • magnetic flux
  • the cumulative distribution function of the normal distribution in statistics
  • phenyl functional group
  • Empty set
• 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
  • electric potential
  • the probability density function of the normal distribution in statistics

Χχ (Chi)

• χ represents:
  • the chi distribution in statistics (χ$^{2}$ is the more frequently encountered chi-square 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 Fourier transform of a linear response function (see susceptibility)
  • the Sigma vectors in the Unscented Transform (UT), used in the Unscented Kalman Filter
  • sometimes the mole fraction

Ψψ (Psi)

• Ψ represents:
  • Water potential
• ψ represents:
  • the wave function in the Schrödinger equation of quantum mechanics
  • the stream function in fluid dynamics
  • yaw angle in vehicle dynamics

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 longitude of the ascending node in celestial mechanics
• ω represents:
  • the first infinite ordinal
  • the set of natural numbers in set theory (although $\mathbb {N}$ 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
  • angular velocity / radian frequency
  • a complex cube root of unity -- root of unity -- the other is ω². (Used to describe various ways of calculating the discrete Fourier transform).
  • vertical velocity in pressure-based coordinate systems (commonly used in atmospheric dynamics)
  • a meson
  • a differential form (esp. on an analytic space)
  • the argument of periapsis in celestial mechanics
• The symbol ϖ, a graphic variant of pi, is sometimes construed as omega with a bar over it; see Pi

See also

• Greek alphabet
• How to write Greek letters
• English pronunciation of Greek letters
• A pronunciation guide with audio
• Roman letters used in mathematics
• Mathematical alphanumeric symbols
• Table of mathematical symbols
• Typographical conventions in mathematical formulae
• The Greeks (Greek letters used in mathematical finance)