List of mathematical uses of Latin letters
# List of mathematical uses of Latin letters

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, or 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 point of a triangle
   * the digit "10" in hexadecimal and other positional numeral systems with a radix of 11 or greater
   * the unit ampere for electric current in physics
   * the area of a figure
   * the mass number or nucleon number of an element in chemistry
   * the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature
   * a vector potential, in electromagnetics it can refer to the magnetic vector potential
   * an Abelian group in abstract algebra
   * the Glaisher–Kinkelin constant
   * atomic weight, denoted by $A_r$
   * work in classical mechanics
   * the pre-exponential factor in the Arrhenius Equation
   * electron affinity
* $\mathbb {A}$ represents the algebraic numbers or affine space in algebraic geometry.
* a represents:
   * the first side of a triangle (opposite point 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 $m^2)$
   * the unit prefix atto $(10^{−18})$
   * the first term in a sequence or series

## Bb

* B represents:
   * the digit "11" in hexadecimal and other positional numeral systems with a radix of 12 or greater
   * the second point of a triangle
   * a ball (also denoted by ℬ (${\mathcal {B}}$) or $\mathbb {B}$)
   * 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 backshift or lag operator, the formal parameter of the lag polynomial
   * the magnetic field, denoted ${\textbf {B}}$ or ${\vec {B}}$
* B with various subscripts represents several variations of Brun's constant and Betti numbers; it can also be used to mean the Bernoulli numbers.
* b represents:
   * the second side of a triangle (opposite point 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
   * a breadth
   * the molality of a solution

## Cc

* C represents:
   * the third point 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 denoting the number of combinations, a binomial coefficient
   * together with a degree symbol (°), the Celsius measurement of temperature = °C
   * the circumference of a circle or other closed curve
   * the complement of a set (lowercase c and the symbol ∁ are also used)
   * an arbitrary category
   * the number concentration
* $\mathbb {C}$ 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 amount concentration in chemistry
   * the speed of light in vacuum
   * the third side of a triangle (opposite corner C)
* Lowercase Fraktur ${\mathfrak {c}}$ 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
   * diffusion coefficient or diffusivity in dimensions of $[distance^2/time]$
   * the differential operator in Euler's calculus notation
   * dissociation energy
   * Dimension
* d represents
   * the differential operator
   * the unit day of time (86,400 s)
   * the difference in an arithmetic sequence
   * a metric operator/function
   * the diameter of a circle
   * the unit prefix deci $(10^{−1})$
   * a thickness
   * a distance

## 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. For example, 1.2E3 is $1.2×10^3$ or 1200
   * the set of edges in a graph or matroid
   * the unit prefix exa $(10^{18})$
   * energy in physics
   * electric field denoted ${\textbf {E}}$ or ${\vec {E}}$
   * electromotive force (denoted ${\mathcal {E}}$ and measured in volts), refers to voltage
   * an event (as in P(E), which reads "the probability P of event E occurring")
   * in statistics, the expected value of a random variable, sometimes as $\mathbb {E}$
   * $E_k$ represents kinetic energy
   * (Arrhenius) activation energy, denoted $E_a$ or $E_A$
   * ionization energy, denoted $E_i$
   * electron affinity, denoted $E_{ea}$
   * dissociation energy, denoted $E_d$
* 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 denoted $e^−$ to distinguish against a positron $e^+$
   * the eccentricity of a conic section
   * the identity element in a group

## 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 and 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
   * a Fibonacci number
   * an arbitrary functor
   * a field
   * an event space sigma algebra as part of a probability space, often as ${\mathcal {F}}$
* 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 $(10^9)$
   * the Newtonian constant of gravitation
   * the Einstein tensor
   * the Gibbs energy
   * the centroid of a triangle
   * Catalan's constant
   * weight measured in newtons
* g represents:
   * the generic designation of a second function
   * the acceleration due to gravity on Earth
   * a unit of mass, the gramme

## Hh

* H represents:
   * a Hilbert space
   * the unit henry of magnetic inductance
   * the homology and cohomology functor
   * the enthalpy
   * the (Shannon) entropy of information
   * the orthocenter of a triangle
   * a partial sum of the harmonic series
   * magnetic field, denoted ${\boldsymbol {H}}$
   * the Hamilton function
* $H_0$ represents Hubble's parameter as measured today (100 h $km·s^{−1}·Mpc^{−1}),$ with h being the associated error.
* $\mathbb {H}$ represents the quaternions (after William Rowan Hamilton).
* $ΔH^‡$ represents the standard enthalpy of activation in the Eyring equation.
* 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 (6.626 069(57)× $10^{−34}$ J·s)
   * the unit prefix hecto $(10^2)$
   * the generic designation of a third function
   * the altitude of a triangle
   * a height

## Ii

* I represents:
   * the closed unit interval, which contains all real numbers from 0 to 1, inclusive
   * the identity matrix
   * the Irradiance
   * the moment of inertia
   * intensity in physics
   * the incenter of a triangle
   * the electric current
   * ionization energy, denoted I
* I represents:
   * the index of an indexed family
* 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 denoted ${\boldsymbol {J}}$
   * the radiosity in thermal mechanics
   * the moment of inertia
* J represents:
   * the scheme of a diagram in category theory
* 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 temperature unit kelvin
   * the functors of K-theory
   * an unspecified (real) constant
   * a field in algebra
   * the area of a polygon
   * kinetic energy
* k represents
   * the unit prefix kilo- $(10^3)$
   * 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
   * the rate constant (coefficient)

## 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
   * the lag operator in statistics
   * a Lucas number
   * the Lagrange function
* l represents:
   * the unit of volume the litre
   * the length of a side of a rectangle or a cuboid (e.g. V = lwh; A = lw)
   * the last term of a sequence or series (e.g. $S_n$ = n(a+l)/2)
   * the orbital angular momentum quantum number
* 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- $(10^6)$
   * the Madelung constant for crystal structures held by ionic bonding
   * the moment of force
   * molar mass
   * molar mass constant, denoted $M_u$
   * relative molecular mass, denoted $M_r$
* m represents:
   * the number of rows in a matrix
   * atomic mass
   * atomic mass constant denoted $m_u$
   * the slope in a linear regression or in any line
   * the mass in mechanics equations
   * the unit metre of length
   * the unit prefix milli $(10^{−3})$
   * a median of a triangle
   * the overall order of reaction

## Nn

* N represents
   * the unit newton of force
   * the nine-point center of a triangle
* N represents
   * the neutron number
   * The number of particles of a thermodynamical $system^{:57}$
* $N_A$ represents the Avogadro constant
* $\mathbb {N}$ represents the natural numbers.
* n represents
   * A neutron, which may be shown as n , $n^0$ or $^1$ $_0n$
   * the unit prefix nano $(10^{−9})$
* n represents
   * the number of columns in a matrix
   * the "number of" in algebraic equations
   * the number density of particles in a volume
   * the index of the nth term of a sequence or series (e.g. $t_n$ = a + (n − 1)d)
   * the principal quantum number
   * the amount of a given substance
   * the number concentration
   * the overall order of reaction

## 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
   * the circumcenter of a triangle or other cyclic polygon, or more generally the center of a circle
* o represents
   * the order of asymptotic behavior of a function (strict upper bound); see Little o notation
   * the order of an element in a group

## Pp

* P represents:
   * the pressure in physics $equations^{:4}$
   * the unit prefix peta $(10^{15})$
   * probability in statistics and statistical $mechanics^{:35}$
   * an arbitrary point in geometry
   * power in watts
   * weight measured in newtons
* $\mathbb {P}$ 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 1 1 p
   * the linear momentum in physics equations
   * the perimeter of a triangle or other polygon
   * generalized momentum
   * the pressure in physics equations

## Qq

* Q represents:
   * heat $energy^{:6}$
   * electroweak charge, denoted $Q_W$
* $\mathbb {Q}$ represents the rational numbers
* q represents:
   * the deceleration parameter in cosmology
   * electric charge of a particle
   * a generalized coordinate

## Rr

* R represents:
   * the Ricci tensor
   * the circumradius of a cyclic polygon such as a triangle
   * an arbitrary relation
* $\mathbb {R}$ 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 inradius of a triangle or other tangential polygon
   * the ratio of a geometric series (e.g. $ar^{n−1})$
   * the separation of two objects, for example in Coulomb's law
   * a position vector
   * the rate of concentration change of B (due to chemical reaction) denoted $r_B$

## Ss

* S represents
   * a sum
   * the unit siemens of electric conductance
   * the unit sphere (with superscript denoting dimension)
   * the scattering matrix
   * entropy
   * action in joule-seconds
* s represents:
   * an arclength
   * a path length
   * the displacement in mechanics equations
   * the unit second of time
   * a complex variable s = σ + i t in analytic number theory
   * the semiperimeter of a triangle or other polygon
* 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 $equations^{:4}$
   * the unit tesla of magnetic flux density
   * the unit prefix tera $(10^{12})$
   * the stress–energy tensor
   * tension in physics
   * an arbitrary monad
   * the time it takes for one oscillation
   * kinetic energy
   * Torque
* 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 + it in analytic number theory
   * the sample statistic resulting from a Student's t-test
   * the half life of a quantity, denoted as $t_{1⁄2}$

## Uu

* U represents:
   * a U-set which is a set of uniqueness
   * a unitary operator
   * in thermodynamics, the internal energy of a system
   * a forgetful functor
* U(n) represents the unitary group of degree n
* ∪ represents the union operator
* u represents the initial velocity in mechanics equations

## Vv

* V represents:
   * the unit volt of voltage
   * the set of vertices in a graph
   * a vector space
   * potential energy
   * molar volume denoted by $V_m$
* v represents
   * the final velocity in mechanics equations
   * frequency, especially when referring to electromagnetic waves
   * a specific volume in classical mechanics
   * the rate of concentration change of B (due to chemical reaction) denoted $v_B$
   * the rate of reaction based on amount concentration denoted v or $v_c$
   * the rate of reaction based on number concentration denoted v or $v_C$

## Ww

* W represents:
   * the unit watt of power
   * work, both mechanical and $thermodynamical^{:8–9}$
   * in thermodynamics, the number of possible quantum states in Boltzmann's entropy formula
   * weight measured in newtons
* w represents:
   * the coordinate on the fourth axis in four-dimensional space
   * work in classical mechanics

## Xx

* X represents
   * a random variable
   * a triangle center
* Ẋ represents
   * the rate of change of quantity X
* x represents
   * a realized value of a random variable
   * 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
   * a mole fraction

## Yy

* Y represents:
   * the unit prefix yotta- $(10^{24})$
* Y represents:
   * a second random variable
* y represents:
   * the unit prefix yocto- $(10^{−24})$
   * a realized value of a second random variable
   * a second unknown variable
   * the coordinate on the second or vertical axis (backward axis in three dimensions) in a Cartesian coordinate system, or in the viewport of a graph or window in computer graphics
   * a mole fraction

## Zz

* Z represents:
   * the unit prefix zetta $(10^{21})$
   * the atomic number or proton number of an element in chemistry
   * a standardized normal random variable in probability theory and statistics
   * The partition function in statistical $mechanics^{:111}$
   * in meteorology, the radar reflectivity factor
* $\mathbb {Z}$ 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, wavelength $redshift^{:9}$
   * a third unknown variable
   * the collision frequency of A with A is denoted $z_A(A)$
   * the collision frequency factor is denoted $z_{AB}$
