View source for Latin letters used in mathematics

Many letters of the Latin alphabet, both capital and small, are used in [[Mathematics|mathematics]], [[Science|science]], and [[Engineering:Engineering|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|triangle]]
**the digit "10" in [[Hexadecimal|hexadecimal]] and other positional numeral systems with a radix of 11 or greater
**the unit [[Ampere|ampere]] for electric current in [[Physics:Physics|physics]]
**the [[Area|area]] of a figure
**the [[Chemistry:Mass number|mass number]] of an element in [[Chemistry:Chemistry|chemistry]]
**the [[Physics:Helmholtz free energy|Helmholtz free energy]] of a closed thermodynamic system of constant pressure and temperature
**a [[Physics:Vector potential|vector potential]], in electromagnetics it can refer to the [[Physics:Magnetic vector potential|magnetic vector potential]]
**an [[Abelian group]] in abstract algebra
**the [[Glaisher–Kinkelin constant]]
*<math>\mathbb{A}</math> 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 [[Astronomy:Cosmology|cosmology]]
**the [[Physics:Acceleration|acceleration]] in [[Physics:Equations of motion|mechanics equations]]
**the ''x''-intercept of a line using the [[Linear equation|line equation]]
**the unit [[Hectare#Are|are]] for area (100 m<sup>2</sup>)
**the unit prefix [[Atto-|atto]] (10<sup>−18</sup>)
**the first term in a [[Sequence|sequence]] or [[Series (mathematics)|series]]

==Bb==
*B represents:
**the digit "11" in [[Hexadecimal|hexadecimal]] and other positional numeral systems with a radix of 12 or greater
**the second point of a triangle
**a [[Ball (mathematics)|ball]] (also denoted by ℬ (<math>\mathcal{B}</math>) or <math>\mathbb{B}</math>)
** a [[Basis (linear algebra)|basis]] of a vector space or of a [[Filter (mathematics)|filter]] (both also denoted by ℬ (<math>\mathcal{B}</math>))
** in econometrics and time-series statistics it is often used for the backshift or [[Lag operator|lag operator]], the formal parameter of the lag polynomial
**the [[Physics:Magnetic field|magnetic field]], denoted <math>\textbf{B}</math> or <math>\vec{B}</math>
*''B'' with various subscripts represents several variations of [[Brun's constant]] and [[Betti number]]s; it can also be used to mean the [[Bernoulli number|Bernoulli numbers]]
*b represents:
**the second side of a triangle (opposite point B)
**The [[Physics:Impact parameter|impact parameter]] in nuclear [[Physics:Scattering|scattering]]
**the ''y''-intercept of a line using the [[Linear equation|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|hexadecimal]] and other positional numeral systems with a radix of 13 or greater
** the unit [[Coulomb|coulomb]] of electrical charge
** [[Physics:Capacitance|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|circumference]] of a circle or other closed curve
** the [[Complement (set theory)|complement]] of a set (lowercase ''c'' and the symbol ∁ are also used)
* ''C'' represents:
** an arbitrary [[Category (mathematics)|category]]
* <math>\mathbb{C}</math> represents the [[Set (mathematics)|set]] of complex numbers
* A vertically elongated C with an integer subscript n sometimes denotes the n-th coefficient of a formal [[Power series|power series]].
* c represents:
** the unit prefix centi (10<sup>−2</sup>)
** the [[Physics:Molar concentration|molar concentration]] in chemistry
* ''c'' represents:
** the [[Physics:Speed of light|speed of light]] in a vacuum
** the third side of a triangle (opposite corner C)
* Lower case Fraktur <math>\mathfrak{c}</math> denotes the [[Cardinality of the continuum|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|hexadecimal]] and other positional numeral systems with a radix of 14 or greater
**[[Physics:Diffusion|diffusion]] coefficient or diffusivity in dimensions of [length^2 / time]
**the [[Differential operator|differential operator]] in Euler's calculus notation
*d represents
**the [[Differential operator|differential operator]]
**the unit day of time (86,400 s)
**the difference in an arithmetic sequence
**a metric operator/function
**the [[Diameter|diameter]] of a circle

==Ee==
*E represents:
**the digit "14" in [[Hexadecimal|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<sup>3</sup> or 1200
**the set of edges in a [[Graph (discrete mathematics)|graph]] or [[Matroid|matroid]]
**the unit prefix exa (10<sup>18</sup>)
**[[Physics:Energy|energy]] in physics
**[[Physics:Electric field|electric field]] denoted <math>\textbf{E}</math> or <math>\vec{E}</math>
** [[Physics:Electromotive force|electromotive force]] (denoted <math>\mathcal{E}</math> and measured in volts), refers to [[Physics:Voltage|voltage]].
**an [[Event (probability theory)|event]] (as in P('''E'''), which reads "the probability P of event '''E''' occurring")
**in statistics, the [[Expected value|expected value]] of a random variable
*e represents:
**[[E (mathematical constant)|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 [[Physics:Elementary charge|elementary charge]] in [[Physics:Physics|physics]]
**an [[Physics:Electron|electron]], usually denoted e<sup>−</sup> to distinguish against a [[Physics:Positron|positron]] e<sup>+</sup>
**the eccentricity of a conic section
**the identity element in a [[Group (mathematics)|group]]

==Ff==
*F represents
**the digit "15" in [[Hexadecimal|hexadecimal]] and other positional numeral systems with a radix of 16 or greater
**the unit [[Farad|farad]] of electrical capacity
**the [[Physics:Helmholtz free energy|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
**''<sub>p</sub>F<sub>q</sub>'' is a hypergeometric series
**the [[Probability distribution|probability distribution]] [[Function (mathematics)|function]] in [[Statistics|statistics]]
**a [[Fibonacci number]]
** an arbitrary functor
*f represents:
**the unit prefix femto (10<sup>−15</sup>)
*''f'' represents:
**the generic designation of a [[Function (mathematics)|function]]

==Gg==
*G represents
**an arbitrary [[Graph (discrete mathematics)|graph]], as in: ''G''(''V'',''E'')
**an arbitrary [[Group (mathematics)|group]]
**the unit prefix giga (10<sup>9</sup>)
**[[Physics:Gravitational constant|Newton's gravitational constant]]
**the [[Physics:Einstein tensor|Einstein tensor]]
**the Gibbs energy
**the [[Centroid|centroid]] of a triangle
**[[Catalan's constant]]
*g represents:
**the generic designation of a second function
**the acceleration due to [[Physics:Free fall|gravity on Earth]]
**a unit of mass, the gramme

==Hh==
*H represents:
**a [[Hilbert space]]
**the unit [[Henry (unit)|henry]] of magnetic inductance
**the [[Homology (mathematics)|homology]] and [[Cohomology|cohomology]] [[Functor|functor]]
**the [[Physics:Enthalpy|enthalpy]]
**the (Shannon) [[Entropy (information theory)|entropy of information]]
**the orthocenter of a triangle
**a partial sum of the [[Harmonic series (mathematics)|harmonic series]]
**[[Physics:Magnetic field|magnetic field]], denoted <math>\boldsymbol{H}</math>.
*H<sub>0</sub> represents Hubble's parameter as measures today (100 h km·[[Second|s]]<sup>−1</sup>·Mpc<sup>−1 </sup> with h being the associated error)
*<math>\mathbb{H}</math> represents the [[Quaternion|quaternion]]s (after [[Biography:William Rowan Hamilton|William Rowan Hamilton]])
*ℋ (<math>\mathcal{H}</math>) represents the Hamiltonian in [[Physics:Hamiltonian mechanics|Hamiltonian mechanics]]
*h represents:
**the class number in [[Algebraic number theory|algebraic number theory]]
**a small increment in the argument of a function
**the unit [[Hour|hour]] for [[Time|time]] (3600 s)
**the [[Physics:Planck constant|Planck constant]] (6.626 069(57)× 10<sup>−34</sup> J·s)
**the unit prefix hecto (10{{sup|2}})
**the generic designation of a third function
**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|identity matrix]]
**the [[Physics:Irradiance|Irradiance]]
**the [[Physics:Moment of inertia|moment of inertia]]
**[[Physics:Intensity|Intensity]] in physics
**the incenter of a triangle
*''I'' represents:
** the index of an [[Indexed family|indexed family]]
*i represents:
**the [[Imaginary number|imaginary unit]], a complex number that is the square root of −1
**a subscript to denote the ''i''th 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 [[Summation#Capital-sigma notation|sigma notation]]
**the [[Unit vector#Cartesian coordinates|unit vector]] in Cartesian coordinates going in the X-direction, usual bold '''''i'''
''

==Jj==
*J represents:
**the unit [[Joule|joule]] of energy
**the [[Physics:Current density|current density]] in [[Physics:Electromagnetism|electromagnetism]] denoted <math>\boldsymbol{J}</math>.
**the Radiosity in thermal mechanics
*''J'' represents:
** the scheme of a [[Diagram (category theory)|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|electrical engineering]], the square root of −1, instead of i
**in [[Electrical engineering|electrical engineering]], the principal cube root of 1: <small><math>-\frac{1}{2}+\frac{1}{2}i \sqrt 3</math></small>

==Kk==
*K represents:
**the unit [[Kelvin|kelvin]] of temperature
**the [[Functor|functor]]s of K-theory
**an unspecified (real) constant
**a [[Field (mathematics)|field]] in algebra
**the area of a [[Polygon|polygon]]
*k represents
** the unit prefix [[Kilo-|kilo-]] (10<sup>3</sup>)
** the [[Physics:Boltzmann constant|Boltzmann constant]], this is often represented as k<sub>B</sub> to avoid confusion with
** the [[Physics:Wavenumber|Wavenumber]] of the [[Physics:Wave equation|wave equation]]
** an [[Integer|integer]], e.g. a dummy variable in [[Summation|summation]]s, or an index of a [[Matrix (mathematics)|matrix]].
** an unspecified (real) constant
** the spring constant of [[Physics:Hooke's law|Hooke's law]]
** the spacetime [[Curvature]] from the [[Friedmann equations]] in cosmology

==Ll==
*L represents:
**[[Physics:Length|Length]], used often in quantum mechanics as the size of an infinite square well
**[[Physics:Angular momentum|Angular momentum]]
**the unit of volume the [[Litre|litre]]
**the [[Physics:Radiance|radiance]]
**the space of all integrable real (or complex) functions
**the space of linear maps, as in ''L''(''E'',''F'') or ''L''(''E'') = [[Endomorphism|End]](''E'')
**the [[Likelihood function|likelihood function]]
**a [[Formal language|formal language]]
**the [[Lag operator|lag operator]] in statistics
**a [[Lucas number]]
*l represents:
**the unit of volume the [[Litre|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. S<sub>n</sub> = n(a+l)/2)
*ℒ (<math>\mathcal{L}</math>) represents:
**the [[Lagrangian mechanics|Lagrangian]] (sometimes just L)
**[[Physics:Particle beam|Exposure]] (in particle physics)

==Mm==
*M represents:
** the unit of length the [[Metre|metre]]
** a [[Manifold|manifold]]
** a [[Metric space|metric space]]
** a [[Matroid|matroid]]
**the unit prefix [[Mega-|mega-]] (10<sup>6</sup>)
** the [[Physics:Madelung constant|Madelung constant]] for crystal structures held by [[Chemistry:Ionic bonding|ionic bonding]]
*m represents:
**the number of rows in a [[Matrix (mathematics)|matrix]]
**the [[Gradient|slope]] in a linear regression or in any [[Linear equation|line]]
**the [[Physics:Mass|mass]] in mechanics equations
**the unit [[Metre|metre]] of length
**the unit prefix milli (10<sup>−3</sup>)
**a [[Median (geometry)|median]] of a triangle

==Nn==
*N represents
**the unit [[Newton (unit)|newton]] of force
**the [[Physics:Neutron number|Neutron number]]
**the [[Physics:Particle number|Particle number]] in thermodynamics
**The [[Physics:Particle number|number of particles]] of a thermodynamical system
**the nine-point center of a triangle
*N<sub>A</sub> represents the [[Physics:Avogadro constant|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,<sup>23</sup> mol <sup>−1</sup>
*<math>\mathbb{N}</math> represents the [[Natural number|natural number]]s
*n represents
**the number of columns in a [[Matrix (mathematics)|matrix]]
**the "number of" in [[Algebra|algebra]]ic equations.
**A [[Physics:Neutron|neutron]], often shown as <sup>1</sup><sub>0</sub>n
**the [[Physics:Number density|Number density]] of particles in a Volume
**the unit prefix [[Nano-|nano]] (10<sup>−9</sup>)
**the nth term of a sequence or series (e.g. t<sub>n</sub> = 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]]
**<math>(0,0,\ldots,0)</math>&nbsp;— 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 [[Group (mathematics)#order of an element|order of an element]] in a [[Group (mathematics)|group]]

==Pp==
*P represents:
**the [[Physics:Pressure|pressure]] in physics equations
**the unit prefix peta (10<sup>15</sup>)
**[[Probability|probability]] in statistics and statistical mechanics
**an arbitrary point in [[Geometry|geometry]]
*<math>\mathbb{P}</math> represents
**the [[Prime number|prime number]]s
**[[Projective space|projective space]]
**a [[Probability|probability]] (as in '''P'''(E), which reads "the probability '''P''' of event E happening")
*p represents
**the unit prefix [[Pico-|pico]] (10<sup>−12</sup>)
**a [[Physics:Proton|proton]], often p<sup>+</sup> or {{subsup||1|1}}p
**the linear [[Physics:Momentum|momentum]] in physics equations
**the [[Perimeter|perimeter]] of a triangle or other polygon

==Qq==
*Q represents:
** [[Physics:Heat|heat]] energy
*<math>\mathbb{Q}</math> represents the [[Rational number|rational number]]s
*q represents:
** the [[Astronomy:Deceleration parameter|deceleration parameter]] in cosmology
** [[Physics:Electric charge|electric charge]] of a particle

==Rr==
*R represents:
**the Ricci tensor
**the circumradius of a cyclic polygon such as a triangle
**an arbitrary [[Relation (mathematics)|relation]]
*<math>\mathbb{R}</math> represents the set of real numbers and various [[Algebraic structure|algebraic structure]]s built upon the set of real numbers, such as <math>\mathbb{R}^n</math>
*r represents:
**the [[Radius|radius]] of a circle or sphere
**the inradius of a triangle or other tangential polygon
**the ratio of a geometric series (e.g. ar<sup>n-1</sup>)
**the separation of two objects, for example in [[Physics:Coulomb's law|Coulomb's law]]

==Ss==
*S represents
**a [[Summation|sum]]
**the unit [[Siemens (unit)|siemens]] of electric conductance
**the unit [[Sphere|sphere]] (with superscript denoting dimension)
**the scattering matrix
** [[Physics:Entropy|entropy]]
*s represents:
**an arclength
**the [[Displacement (vector)|displacement]] in [[Physics:Equations of motion|mechanics equations]]
**the unit [[Second|second]] of time
**a [[Complex number|complex]] variable ''s'' = σ + ''i'' ''t'' in [[Analytic number theory|analytic number theory]]
**the [[Semiperimeter|semiperimeter]] of a triangle or other polygon
*𝒮 (<math>\mathcal{S}</math>) represents a system's [[Physics:Action|action]] in physics

==Tt==
*T represents:
**the top element of a [[Lattice (order)|lattice]]
**a [[Tree (graph theory)|tree]] (a special kind of graph)
**[[Physics:Temperature|temperature]] in physics equations
**the unit [[Tesla (unit)|tesla]] of magnetic flux density
**the unit prefix [[Tera-|tera]] (10<sup>12</sup>)
**the [[Stress–energy tensor|stress–energy tensor]]
**tension in physics
**an arbitrary [[Monad (category theory)|monad]]
*t represents:
**time in graphs, functions or equations
**a term in a sequence or series (e.g. t<sub>n</sub> = t<sub>n−1</sub>+5)
**the imaginary part of the [[Complex number|complex]] variable ''s'' = σ + ''i'' ''t''  in [[Analytic number theory|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|set of uniqueness]]
**a [[Unitary operator|unitary operator]]
**in thermodynamics, the [[Physics:Internal energy|internal energy]] of a system
**a [[Forgetful functor|forgetful functor]]
*U(''n'') represents the [[Unitary group|unitary group]] of degree ''n''
*∪ represents the [[Union (set theory)|union]] operator

==Vv==
*V represents:
**[[Physics:Volume|volume]]
**the unit [[Volt|volt]] of [[Physics:Voltage|voltage]]
**the set of vertices in a graph
**a vector space
*v represents the [[Physics:Velocity|velocity]] in mechanics equations

==Ww==
*W represents:
**the unit [[Watt|watt]] of power
**work, both [[Physics:Work|mechanical]] & [[Physics:Work (thermodynamics)|thermodynamical]]
**in thermodynamics, the number of possible quantum states in [[Physics:Boltzmann's entropy formula|Boltzmann's entropy formula]]
*''w'' represents:
** the coordinate on the fourth axis in [[Four-dimensional space|four-dimensional space]].

==Xx==
*''X'' represents
**a [[Random variable|random variable]]
**a [[Triangle center|triangle center]] 
*''x'' represents
**a realized value of a random variable
**an unknown [[Variable (mathematics)|variable]], most often (but not always) from the set of [[Real number|real number]]s, while a [[Complex number|complex]] unknown would rather be called ''z'', and an [[Integer|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|viewport]] in a [[Computer graphics|graph]] or window in computer graphics.

==Yy==
*Y represents:
**the unit prefix [[Yotta-|yotta-]] (10<sup>24</sup>)
*''Y'' represents:
**a second [[Random variable|random variable]]
*y represents:
**the unit prefix [[Yocto-|yocto-]] (10<sup>−24</sup>)
*''y'' represents:
**a realized value of a second random variable
**a second unknown [[Variable (mathematics)|variable]]
**the coordinate on the second or [[Cartesian coordinate system|vertical axis]] (backward axis in three dimensions) in a linear coordinate system, or in the [[Viewport|viewport]] of a [[Computer graphics|graph]] or [[Window (computing)|window]] in computer graphics.

==Zz==
*Z represents:
**the unit prefix zetta (10<sup>21</sup>)
**the [[Physics:Atomic number|atomic number]] in chemistry and physics
**a standardized normal [[Random variable|random variable]] in [[Probability theory|probability theory]] and [[Statistics|statistics]]
**The [[Physics:Partition function (statistical mechanics)|partition function]] in statistical mechanics
**in meteorology, the [[Astronomy:DBZ (meteorology)|radar reflectivity factor]]
*<math>\mathbb{Z}</math> represents the [[Integer|integer]]s
*z represents:
**the unit prefix zepto (10<sup>−21</sup>)
**the coordinate on the third or vertical axis in three [[Physics:Dimension|dimension]]al space
**the view depth in [[Computer graphics|computer graphics]], see also "[[Z-buffering|z-buffering]]"
**the argument of a [[Complex analysis|complex function]], or any other variable used to represent a complex value
** in astronomy, wavelength [[Astronomy:Redshift|redshift]]
**a third unknown [[Variable (mathematics)|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]]

{{Latin alphabet}}

{{DEFAULTSORT:Roman Letters Used In Mathematics}}
[[Category:Elementary mathematics]]
[[Category:Mathematical notation|*]]

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