Greek letters used in mathematics, science, and engineering

• ${\displaystyle \alpha }$ 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

• Β represents the beta function
• ${\displaystyle \beta }$ represents:
  • the thermodynamic beta, equal to (k_BT)⁻¹, where k_B 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

• 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 stack alphabet in the formal definition of a pushdown automaton , or the tape-alphabet in the formal definition of a Turing machine
• ${\displaystyle \gamma }$ 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

• 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 maximum degree of any vertex in a given graph
  • sensitivity to price in mathematical finance
  • the discriminant in the quadratic formula which determines the nature of the roots
• ${\displaystyle \delta }$ 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
  • noncentrality measure in statistics[2]
  • The transition function in the formal definition of a finite automaton, pushdown automaton, or Turing machine
• Not to be confused with ∂ which is based on the Latin letter d but often called a "script delta."

• ${\displaystyle \epsilon }$ 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 ${\displaystyle \omega ,\omega ^{\omega },\omega ^{\omega ^{\omega }},\dots }$
  • 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

• 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

• ${\displaystyle \zeta }$ represents:
  • the Riemann zeta function and other zeta functions in mathematics
  • the damping ratio

• Η represents:
  • the Eta function of Ludwig Boltzmann's H-theorem ("Eta" theorem), in statistical mechanics
  • Information theoretic (Shannon) entropy
• ${\displaystyle \eta }$ represents:
  • the intrinsic wave impedance of a medium (e.g. the impedance of free space)
  • the partial regression coefficient in statistics
  • the eta meson
  • viscosity
  • energy conversion efficiency
  • efficiency (physics)
  • the Minkowski metric tensor in relativity
  • η-conversion in lambda calculus
  • A right angle, i.e., π/2, as a follow-up to the tau/pi argument[4]

• Θ (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
• ${\displaystyle \theta }$ (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.
• ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
  • the first Chebyshev function in number theory

• ${\displaystyle \iota }$ represents:
  • an inclusion map in set theory
  • the index generator function in APL (in the form ⍳)

• Κ represents:
  • the Kappa number, indicating lignin content in pulp
• ${\displaystyle \kappa }$ 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 ${\displaystyle (\varepsilon /\varepsilon _{0})}$
  • thermal conductivity (usually a lowercase Latin k)
  • electrical conductivity of a solution
  • 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]

• 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 first-order logic
  • the cosmological constant
  • the lambda baryon
  • a diagonal matrix of eigenvalues in linear algebra
  • a lattice
  • molar conductivity in electrochemistry
• ${\displaystyle \lambda }$ 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 in mathematical logic
  • thermal conductivity

• ${\displaystyle \mu }$ 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)
  • 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
  • a micron or micrometer (10⁻⁶ meter) (common usage in biology, though officially revoked in 1967)
  • population mean in statistics
  • chemical potential in thermodynamics

• ${\displaystyle \nu }$ 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
  • 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 xi baryon
• ${\displaystyle \xi }$ represents:
  • the original Riemann Xi function
  • the modified definition of Riemann xi function, as denoted by Edmund Landau and currently

• Ο represents:
  • big O notation (historically (1894) an uppercase Latin O)
• ${\displaystyle \mathrm {o} }$ represents:
  • small o notation (historically (1909) a lowercase Latin o)

• Π represents:
  • the product operator in mathematics
  • a plane
  • the unary projection operation in relational algebra
  • osmotic pressure
• ${\displaystyle \pi }$ represents:
  • Archimedes' constant, 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 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 ${\displaystyle \omega }$ but this may be confused with vorticity in a fluid dynamics context)
  • longitude of pericenter, in astronomy[5]
  • comoving distance, in cosmology[6]

• Ρ represents:
  • one of the Gegenbauer functions in analytic number theory (may be replaced by the capital form of the Latin letter P).
• ${\displaystyle \rho }$ 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 rename operator in relational algebra

• Σ represents:
  • the summation operator
  • the covariance matrix
  • the set of terminal symbols in a formal grammar
• ${\displaystyle \sigma }$ 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
  • standard deviation of a random variable in statistics

• ${\displaystyle \tau }$ 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
  • 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 (τ²), the reciprocal of variance, in statistics

• ϒ (U+03D2) represents:
  • the upsilon meson

• 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 or electric 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, ${\displaystyle \varnothing }$, resembles Φ but is not Φ.

• ${\displaystyle \phi }$ 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
  • electric potential
  • the probability density function of the normal distribution in statistics

• ${\displaystyle \chi }$ represents:
  • the chi distribution in statistics (${\displaystyle \chi ^{2}}$ 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 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

• Ψ represents:
  • water potential
  • a quaternary combinator in combinatory logic
  • a symbol for psychology
• ${\displaystyle \psi }$ represents:
  • the wave function in the Schrödinger equation of quantum mechanics
  • 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[8]

• Ω represents:
  • 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
• ${\displaystyle \omega }$ 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. ${\displaystyle C^{\omega }}$) 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 ${\displaystyle \mathbb {N} }$ 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)