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 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 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 𝔸 ( A {\displaystyle \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 m²)

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 ( B {\displaystyle {\mathcal {B}}}

) or 𝔹 ( B {\displaystyle \mathbb {B} }

)) a basis of a vector space or of a filter (both

also denoted by ℬ ( B {\displaystyle {\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 B {\displaystyle {\textbf {B}}}

or B

→ {\displaystyle {\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==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 denotes the number of combinations, a binomial coefficient

together with a degree symbol (°) represents the Celsius measurement of temperature=°C

the circumference of a circle or other closed curve

C represents: an arbitrary category

ℂ ( C {\displaystyle \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 chemistry c represents:

the speed of light in a vacuum the third side of a triangle (opposite corner

C) Lower case Fraktur c {\displaystyle {\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 [length^2 / time] the differential operator in Euler’s calculus

notation 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==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 1.2×10³ or 1200 the set of edges in a graph or matroid

the unit prefix exa (1018) energy in physics

electric field denoted E {\displaystyle {\textbf {E}}}

or E

→ {\displaystyle {\vec {E}}} electromotive force (denoted E {\displaystyle {\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 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 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 pFq is a hypergeometric series

the probability distribution function in statistics a Fibonacci number

an arbitrary functor 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 energy the centroid of a triangle

Catalan’s constant 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 the orthocenter of a triangle

a partial sum of the harmonic series magnetic field, denoted H {\displaystyle {\boldsymbol {H}}}

. H0 represents Hubble’s parameter as measures

today (100 h km·s−1·Mpc−1 with h being the associated error)

ℍ ( H {\displaystyle \mathbb {H} }

) represents the quaternions (after William Rowan Hamilton)

ℋ ( H {\displaystyle {\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 (102) the altitude of a triangle==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

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 J {\displaystyle {\boldsymbol {J}}}

. the Radiosity in thermal mechanics

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: − 1

2 + 1

2 i 3 {\displaystyle -{\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 the area of a polygon

k represents the unit prefix kilo- (10³)

the Boltzmann constant, this is often represented as kB 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

the lag operator in statistics a Lucas number

l represents: the unit of volume the litre

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. Sn=n(a+l)/2)

ℒ ( L {\displaystyle {\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)

a median of a triangle==Nn==

N represents the unit newton of force

the Neutron number the Particle number in thermodynamics

The number of particles of a thermodynamical system

the nine-point center of a triangle NA 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 ( N {\displaystyle \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.

tn=a+(n-1)d) the principal quantum number==Oo==

O represents the order of asymptotic behavior of a function

(upper bound); see Big O notation (

0 ,

0 ,

… ,

0 ) {\displaystyle (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

the unit prefix peta (1015) probability in statistics and statistical

mechanics an arbitrary point in geometry

ℙ ( P {\displaystyle \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 11 p

the linear momentum in physics equations the perimeter of a triangle or other polygon==Qq==

Q represents: heat energy

ℚ ( Q {\displaystyle \mathbb {Q} }

) represents the rational numbers q represents:

the deceleration parameter in cosmology electric charge of a particle==Rr==

R represents: the Ricci tensor

the circumradius of a cyclic polygon such as a triangle

an arbitrary relation ℝ ( R {\displaystyle \mathbb {R} }

) represents the set of real numbers and various algebraic structures built upon the set of

real numbers, such as R n {\displaystyle \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. arn-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 the semiperimeter of a triangle or other polygon

𝒮 ( S {\displaystyle {\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 tension in physics

an arbitrary monad t represents:

time in graphs, functions or equations a term in a sequence or series (e.g. tn=tn−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 a forgetful functor

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

a vector space v represents the velocity in mechanics equations==Ww==

W represents: the unit watt of power

work, both mechanical & thermodynamical in thermodynamics, 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 a random variable

a triangle center 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.==Yy==

Y represents: the unit prefix yotta- (1024)

Y represents: a second random variable

y represents: the unit prefix yocto- (10−24)

y represents: 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 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 standardized normal random variable in probability

theory and statistics The partition function in statistical mechanics

in meteorology, the radar reflectivity factor ℤ ( Z {\displaystyle \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 a third unknown variable==See also==

Blackboard bold letters used in mathematics Greek letters used in mathematics

List of letters used in mathematics and science Mathematical alphanumeric symbols

Table of mathematical symbols Typographical conventions in mathematical

formulae