Latin letters used in mathematics

Many letters of the Latin alphabet, both capital and small, are used in mathematics, science and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, physical entities. Certain letters, when combined with special formatting, take on special meaning.

Below is an alphabetical list of the letters of the alphabet with some of their uses. The field in which the convention applies is mathematics unless otherwise noted.

Aa

• A represents:
  • the first corner of a triangle
  • the digit "10" in hexadecimal and other positional numeral systems with a radix of 11 or greater
  • the unit ampere for electrical current
  • the Area
  • the Mass number of an element
  • The Helmholtz free energy of a closed thermodynamic system of constant Pressure & Temperature
  • A Vector potential, in Electromagnetics it can refer to the magnetic vector potential
• 𝔸 ($\mathbb{A}$) represents the algebraic numbers or affine space in Algebraic Geometry
• a represents:
  • the first side of a triangle (opposite corner A)
  • the scale factor of the expanding universe in cosmology
  • the acceleration in mechanics equations
  • the x-intercept of a line using the line equation
  • the unit are for area (100 m²)
  • the unit prefix atto (10⁻¹⁸)
  • the first term in a sequence or series (e.g. S_n = n(a+l)/2)

Bb

• B represents:
  • the digit "11" in hexadecimal and other positional numeral systems with a radix of 12 or greater
  • the second corner of a triangle
  • a ball (also denoted by ℬ ($\mathcal{B}$) or 𝔹 ($\mathbb{B}$))
  • a basis of a vector space or of a filter (both also denoted by ℬ ($\mathcal{B}$))
  • in econometrics and time-series statistics it is often used for the (back)lag operator, the formal parameter of the lag polynomial
• B with various subscripts represents several variations of Brun's constant and Betti numbers
• b represents:
  • the second side of a triangle (opposite corner B)
  • The Impact parameter in Nuclear scattering
  • the y-intercept of a line using the line equation
  • (usually with an index, sometimes with an arrow over it) a basis vector

Cc

• C represents:
  • the third corner of a triangle
  • the digit "12" in hexadecimal and other positional numeral systems with a radix of 13 or greater
  • the unit coulomb of electrical charge
  • capacitance in electrical theory
  • with indices denotes the number of combinations, a binomial coefficient
  • together with a degree symbol (°) represents the Celsius measurement of temperature = °C
• ℂ ($\mathbb{C}$) represents the set of complex numbers
• A vertically elongated C with an integer subscript n sometimes denotes the n-th coefficient of a formal power series.
• c represents:
  • the unit prefix centi (10⁻²)
  • the Molar concentration in Chemes
• c represents:
  • the speed of light in vacuum
  • the third side of a triangle (opposite corner C)
• Small bold C denotes the cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers

Dd

• D represents the digit "13" in hexadecimal and other positional numeral systems with a radix of 14 or greater
• d represents
  • the differential operator
  • the unit day of time (86,400 s)
  • the difference in an arithmetic sequence (e.g. S_n = n(2a+(n-1)d)/2)
  • a metric operator/function

Ee

• E represents:
  • the digit "14" in hexadecimal and other positional numeral systems with a radix of 15 or greater
  • an exponent in decimal numbers 1.2E3 is 1.2×10³ or 1200
  • the set of edges in a graph or matroid
  • the unit prefix exa (10¹⁸)
  • Energy in physics
  • an event (as in P(E), which reads "the probability P of event E happening")
• e represents:
  • Euler's number, a transcendental number equal to 2.71828182845... which is used as the base for natural logarithms
  • a vector of unit length, especially in the direction of one of the coordinates axes
  • the elementary charge in physics
  • an electron, usually donated e^- to distinguish against a positron e⁺
  • the eccentricity of an ellipse

Ff

• F represents
  • the digit "15" in hexadecimal and other positional numeral systems with a radix of 16 or greater
  • the unit farad of electrical capacity
  • The Helmholtz free energy of a closed thermodynamic system of constant pressure & temperature
  • together with a degree symbol (°) represents the Fahrenheit measurement of temperature = °F
• F represents
  • force in mechanics equations
  • _pF_q is a hypergeometric series
  • the probability distribution function in statistics
• f represents:
  • the unit prefix femto (10⁻¹⁵)
• f represents:
  • the generic designation of a function

Gg

• G represents
  • an arbitrary graph, as in: G(V,E)
  • an arbitrary group
  • the unit prefix giga (10⁹)
  • Newton's gravitational constant
  • the Einstein tensor
  • the Gibbs free energy
• g represents:
  • the generic designation of a second function
  • the acceleration due to gravity on Earth

Hh

• H represents:
  • a Hilbert space
  • the unit henry of magnetic inductance
  • the homology and cohomology functors
  • the (Shannon) entropy of information
• H₀ represents Hubble's parameter as measures today (100 h km·s⁻¹·Mpc⁻¹ with h being the associated error)

• ℍ ($\mathbb{H}$) represents the quaternions (after William Rowan Hamilton)
• ℋ ($\mathcal{H}$) represents the Hamiltonian in Hamiltonian mechanics
• h represents:
  • the class number in algebraic number theory
  • a small increment in the argument of a function
  • the unit hour for time (3600 s)
  • the Planck constant (6.624 608 96(33) × 10⁻³⁴ J·s)
  • the unit prefix hecto (10²)

Ii

• I represents:
  • the closed unit interval, which contains all real numbers from 0 to 1, inclusive
  • the identity matrix
  • the Irradiance
  • Moment of inertia
  • Intensity
• i represents:
  • the imaginary unit, a complex number that is the square root of −1
  • a subscript to denote the ith term (that is, a general term or index) in a sequence or list
  • the index to the elements of a vector, written as a subscript after the vector name
  • the index to the rows of a matrix, written as the first subscript after the matrix name
  • an index of summation using the sigma notation
  • the unit vector in Cartesian coordinates going in the X-direction, usual bold i

Jj

• J represents:
  • the unit joule of energy
  • the current density in electromagnetism
  • the Radiosity in thermal mechanics
• j represents:
  • the index to the columns of a matrix, written as the second subscript after the matrix name
  • in electrical engineering, the square root of −1, instead of i
  • in electrical engineering, the principal cube root of 1: $-\frac{1}{2}+\frac{1}{2}i \sqrt 3$

Kk

• K represents:
  • the unit kelvin of temperature
  • the functors of K-theory
  • an unspecified (real) constant
  • a field in algebra
• k represents
  • the unit prefix kilo- (10³)
  • the Boltzmann constant, this is often represented as k_B to avoid confusion with
  • the Wavenumber of the wave equation
  • an integer, e.g. a dummy variable in summations, or an index of a matrix.
  • an unspecified (real) constant
  • the spring constant of Hooke's law
  • the spacetime Curvature from the Friedmann equations in cosmology

Ll

• L represents:
  • Length, used often in quantum mechanics as the size of an infinite square well
  • Angular momentum
  • the unit of volume the litre
  • the radiance
  • the space of all integrable real (or complex) functions
  • the space of linear maps, as in L(E,F) or L(E) = End(E)
  • the Likelihood function
  • a formal language
• l represents:
  • the length of a side of a rectangle or a rectangular prism (e.g. V = lwh; A = lw)
  • the last term of a sequence or series (e.g. S_n = n(a+l)/2)
• ℒ ($\mathcal{L}$) represents:
  • the Lagrangian (sometimes just L)
  • Exposure (in particle physics)

Mm

• M represents:
  • a manifold
  • a metric space
  • a matroid
  • the unit prefix mega- (10⁶)
  • the Madelung constant for crystal structures held by ionic bonding
• m represents:
  • the number of rows in a matrix
  • the slope in a linear regression or in any line
  • the mass in mechanics equations
  • the unit metre of length
  • the unit prefix milli (10⁻³)

Nn

• N represents
  • the unit newton of force
  • the Neutron number
  • the Particle number in thermodynamics
  • The number of particles of a thermodynamical system
• N_A represents the Avogadro constant which is the number of entities in one mole (used mainly in the counting of molecules and atoms) and is 6.022 141 79(30) × 10,²³ mol ⁻¹
• ℕ ($\mathbb{N}$) represents the natural numbers
• n represents
  • the number of columns in a matrix
  • the "number of" in algebraic equations.
  • A neutron, often shown as ¹₀n
  • the Number density of particles in a Volume
  • the unit prefix nano (10⁻⁹)
  • the nth term of a sequence or series (e.g. t_n = a+(n-1)d)

Oo

• O represents
  • the order of asymptotic behavior of a function (upper bound); see Big O notation
  • $(0,0,\ldots,0)$ — the origin of the coordinate system in Cartesian coordinates
• o represents
  • the order of asymptotic behavior of a function (strict upper bound); see Big O notation
  • the order of an element in a group

Pp

• P represents:
  • the pressure in physics equations
  • the unit prefix peta (10¹⁵)
  • Probability in Statistics and Statistical Mechanics
• ℙ ($\mathbb{P}$) represents
  • the prime numbers
  • projective space
  • a probability (as in P(E), which reads "the probability P of event E happening")
• p represents
  • the unit prefix pico (10⁻¹²)
  • a proton, often p⁺ or ¹₁p
  • the linear momentum in physics equations

Qq

• Q represents:
  • Heat energy
• ℚ ($\mathbb{Q}$) represents the rational numbers
• q represents:
  • the Deceleration parameter in Cosmology

Rr

• R represents:
  • the Ricci tensor
• ℝ ($\mathbb{R}$) represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as $\mathbb{R}^n$
• r represents:
  • the radius of a circle or sphere
  • the ratio of a geometric series (e.g. ar^n-1)
  • the separation of two objects, for example in Coulomb's law

Ss

• S represents
  • a sum
  • the unit siemens of electric conductance
  • the unit sphere (with superscript denoting dimension)
  • the scattering matrix
  • entropy
• s represents:
  • an arclength
  • the displacement in mechanics equations
  • the unit second of time
  • a complex variable s = σ + i t in analytic number theory
• 𝒮 ($\mathcal{S}$) represents a system's action in physics

Tt

• T represents:
  • the top element of a lattice
  • a tree (a special kind of graph)
  • temperature in physics equations
  • the unit tesla of magnetic flux density
  • the unit prefix tera (10¹²)
  • the stress-energy tensor
• t represents:
  • time in graphs, functions or equations
  • a term in a sequence or series (e.g. t_n = t_n-1+5)
  • the imaginary part of the complex variable s = σ + i t in analytic number theory
  • the sample statistic resulting from a Student's t-test

Uu

• U represents:
  • a U-set which is a set of uniqueness
  • a unitary operator
  • In thermodynamics, the internal energy of a system
• U(n) represents the unitary group of degree n
• ∪ represents the union operator

Vv

• V represents:
  • volume
  • the unit volt of voltage
  • the set of vertices in a graph
• v represents the velocity in mechanics equations

Ww

• W represents the unit watt of power
  • In physics is also represents the work, both the mechanical & thermodynamical
  • Also in thermodynamics, it can represent the number of possible quantum states in Boltzmann's entropy formula

• w represents
  • the coordinate on the fourth axis in four-dimensional space.

Xx

• x represents
  • an unknown variable, most often (but not always) from the set of real numbers, while a complex unknown would rather be called z, and an integer by a letter like m from the middle of the alphabet.
  • the coordinate on the first or horizontal axis in a cartesian coordinate system, or the viewport in a graph or window in computer graphics.

Yy

• Y represents:
  • the unit prefix yotta- (10²⁴)
• y represents:
  • the unit prefix yocto- (10⁻²⁴)
• y represents:
  • a second unknown variable
  • the coordinate on the second or vertical axis (backward axis) in three dimensions) in a linear coordinate system, or in the viewport of a graph or window in computer graphics.

Zz

• Z represents:
  • the unit prefix zetta (10²¹)
  • the atomic number in Chemistry and Physics
  • a standarized normal random variable in Probability Theory and Statistics
  • The Partition function in statistical mechanics
• ℤ ($\mathbb{Z}$) represents the integers
• z represents:
  • the unit prefix zepto (10⁻²¹)
  • the coordinate on the third or vertical axis in three dimensional space
  • the view depth in computer graphics, see also "z-buffering"
  • the argument of a complex function, or any other variable used to represent a complex value
  • in astronomy, it can donate wavelength redshift

See also

• Greek letters used in mathematics
• Latin alphabet
• Mathematical alphanumeric symbols
• Table of mathematical symbols
• Typographical conventions in mathematical formulae