Greek letters used in mathematics, science, and engineering

 

Greek alphabet Α α Alpha Β β Beta Γ γ Gamma Δ δ Delta Ε ε Epsilon Ζ ζ Zeta Η η Eta Θ θ Theta Ι ι Iota Κ κ Kappa Λ λ Lambda Μ μ Mu Ν ν Nu Ξ ξ Xi Ο ο Omicron Π π Pi Ρ ρ Rho Σ σ Sigma Τ τ Tau Υ υ Upsilon Φ φ Phi Χ χ Chi Ψ ψ Psi Ω ω Omega obsolete letters Ϝ ϝ Digamma San Ϙ ϙ Qoppa Ϡ ϡ Sampi

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 o. Small ι (iota) and υ (upsilon) are also rarely used, since they closely resemble the Latin letters i 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. [ˈθeɪtʌ] for θ cf. ancient [tʰɛ̂ːta] and modern [ˈθita].

Typography

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.

Greek Letters
Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML	Name	TeX	HTML
Alpha	Αα	Αα	Digamma		Ϝ	Kappa	Κκ	Κκ	Omicron		Οο	Upsilon	Υυ	Υυ
Beta	Ββ	Ββ	Zeta	Ζζ	Ζζ	Lambda	Λλ	Λλ	Pi	Ππ	Ππ	Phi	Φφ	Φφ
Gamma	Γγ	Γγ	Eta	Ηη	Ηη	Mu	Μμ	Μμ	Rho	Ρρ	Ρρ	Chi	Χχ	Χχ
Delta	Δδ	Δδ	Theta	Θθ	Θθ	Nu	Νν	Νν	Sigma	Σσ	Σσ	Psi	Ψψ	Ψψ
Epsilon	Εε	Εε	Iota	Ιι	Ιι	Xi	Ξξ	Ξξ	Tau	Ττ	Ττ	Omega	Ωω	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 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

Ββ (Beta)

• B 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
  • 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
  • the beta brain wave in brain or cognitive sciences

Γγ (Gamma)

• Γ represents:
  • the gamma function, a generalization of the factorial
  • the upper incomplete gamma function
  • 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
  • a gamma ray
  • 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
• δ represents:
  • a variation in the calculus of variations
  • the Kronecker delta function
  • the Dirac delta function
  • sensitivity to price in mathematical finance
  • a partial charge. δ- represents a negitive partial charge, and δ+ represents a positive partial charge Chemistry (See also: Solvation)

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 Levi-Civita symbol.
  • in electromagnetics, dielectric permittivity.
  • emissivity
  • strain
• set membership symbol ∈ is based on ε

Ϝ (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

Θθ (Theta)

• Θ represents:
  • an asymptotically tight bound related to Big O notation.
  • sensitivity to the passage of time in mathematical finance
• 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

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
  • curvature
  • dielectric constant (usually ε)
  • thermal conductivity (usually a lowercase Latin k)
  • a spring constant (usually a lowercase Latin k)

Λλ (Lambda)

• Λ represents
  • the set of logical axioms in the axiomatic method of logical deduction in first-order logic
  • the cosmological constant
  • a type of baryon
• 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
  • longitude in geodesy
  • linear density

Μμ (Mu)

• μ 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

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 coefficient

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)
• 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 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 ⍴)

Σσ (Sigma)

• Σ represents:
  • the summation operator.
• σ represents:
  • the divisor function in number theory
  • 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
  • areal density
  • nuclear cross section
  • uncertainty

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.
  • tau in astronomy is a measure of opacity, or how much sunlight cannot penetrate the atmosphere.
  • tau in biochemistry is 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.

Υυ (Upsilon)

• Y represents:
  • an elementary particle

Φφ (Phi)

• Φ represents:
  • a wave function
  • magnetic flux
• φ 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
  • latitude in geodesy
  • a wave function
  • electric potential

Χχ (Chi)

• χ represents:
  • the chi distribution in statistics (X² 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)

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
• ω represents:
  • the first infinite ordinal
  • 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
  • vertical velocity in pressure-based coordinate systems (commonly used in atmospheric dynamics)
  • a meson
• 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)

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