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| 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.
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| 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.
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| ==Aa==
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| *A represents:
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| **the first corner of a [[triangle]]
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| **the digit "10" in [[hexadecimal]] and other positional numeral systems with a radix of 11 or greater
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| **the unit [[ampere]] for electrical current
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| **the [[Area]]
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| **the [[Mass number]] of an element
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| **the [[Helmholtz free energy]] of a closed thermodynamic system of constant Pressure & Temperature
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| **a [[Vector potential]], in Electromagnetics it can refer to the [[magnetic vector potential]]
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| **an [[Abelian group]] in abstract algebra
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| *𝔸 (<math>\mathbb{A}</math>) represents the [[algebraic numbers]] or affine space in [[Algebraic Geometry]]
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| *a represents:
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| **the first side of a triangle (opposite corner A)
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| **the [[Scale factor (Universe)|scale factor]] of the expanding universe in [[cosmology]]
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| **the [[acceleration]] in [[Equations of motion|mechanics equations]]
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| **the ''x''-intercept of a line using the [[Linear equation|line equation]]
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| **the unit [[Hectare#Are|are]] for area (100 m²)
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| **the unit prefix [[Atto-|atto]] (10<sup>−18</sup>)
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| **the first term in a sequence or series (e.g. ''S''<sub>''n''</sub> = ''n''(''a''+l)/2)
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| ==Bb==
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| *B represents:
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| **the digit "11" in [[hexadecimal]] and other positional numeral systems with a radix of 12 or greater
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| **the second corner of a triangle
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| **a [[Ball (mathematics)|ball]] (also denoted by ℬ (<math>\mathcal{B}</math>) or 𝔹 (<math>\mathbb{B}</math>))
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| ** a [[basis (linear algebra)|basis]] of a vector space or of a [[filter (mathematics)|filter]] (both also denoted by ℬ (<math>\mathcal{B}</math>))
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| ** in econometrics and time-series statistics it is often used for the (back)lag operator, the formal parameter of the lag polynomial
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| *''B'' with various [[subscript]]s represents several variations of [[Brun's constant]] and [[Betti number]]s
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| *b represents:
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| **the second side of a triangle (opposite corner B)
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| **The [[Impact parameter]] in Nuclear [[scattering]]
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| **the ''y''-intercept of a line using the [[Linear equation|line equation]]
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| **(usually with an index, sometimes with an arrow over it) a [[basis vector]]
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| ==Cc==
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| *C represents:
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| **the third corner of a triangle
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| ** the digit "12" in [[hexadecimal]] and other positional numeral systems with a radix of 13 or greater
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| ** the unit [[coulomb]] of electrical charge
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| ** [[capacitance]] in electrical theory
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| ** with indices denotes the number of combinations, a binomial coefficient
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| ** together with a degree symbol (°) represents the [[Celsius]] measurement of temperature = °C
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| *ℂ (<math>\mathbb{C}</math>) represents the [[Set (mathematics)|set]] of [[complex numbers]]
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| *A vertically elongated C with an integer subscript n sometimes denotes the n-th coefficient of a formal [[power series]].
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| *c represents:
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| **the unit prefix centi (10<sup>−2</sup>)
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| ** the [[Molar concentration]] in Chemes
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| *''c'' represents:
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| **the [[speed of light]] in vacuum
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| **the third side of a triangle (opposite corner C)
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| *Small bold C denotes the cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers
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| ==Dd==
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| *D represents the digit "13" in [[hexadecimal]] and other positional numeral systems with a radix of 14 or greater
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| **[[diffusion]] coefficient or diffusivity in dimensions of [length^2 / time]
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| *d represents
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| **the [[differential operator]]
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| **the unit day of time (86,400 s)
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| **the difference in an arithmetic sequence (e.g. ''S''<sub>''n''</sub> = ''n''(2''a''+(''n''-1)''d'')/2)
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| **a metric operator/function
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| ==Ee==
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| *E represents:
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| **the digit "14" in [[hexadecimal]] and other positional numeral systems with a radix of 15 or greater
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| **an exponent in decimal numbers 1.2E3 is 1.2×10³ or 1200
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| **the set of edges in a [[graph (mathematics)|graph]] or [[matroid]]
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| **the unit prefix [[exa]] (10<sup>18</sup>)
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| **[[Energy]] in physics
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| **[[Electric field]] denoted <math>\boldsymbol{E}</math>.
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| ** [[Electromotive force]], (denoted <math>\mathcal{E}</math> and measured in [[volts]]), refers to [[voltage]].
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| **an [[event (probability theory)|event]] (as in P('''E'''), which reads "the probability P of event '''E''' happening")
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| *e represents:
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| **[[e (mathematical constant)|Euler's number]], a transcendental number equal to 2.71828182845... which is used as the base for natural logarithms
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| **a vector of unit length, especially in the direction of one of the coordinates axes
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| **the [[elementary charge]] in [[physics]]
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| **an [[electron]], usually donated e<sup>-</sup> to distinguish against a [[positron]] e<sup>+</sup>
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| **the eccentricity of an ellipse
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| ==Ff==
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| *F represents
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| **the digit "15" in [[hexadecimal]] and other positional numeral systems with a radix of 16 or greater
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| **the unit [[farad]] of electrical capacity
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| **The [[Helmholtz free energy]] of a closed thermodynamic system of constant pressure & temperature
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| ** together with a degree symbol (°) represents the [[Fahrenheit]] measurement of temperature = °F
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| *''F'' represents
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| **force in mechanics equations
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| **''<sub>p</sub>F<sub>q</sub>'' is a [[hypergeometric series]]
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| **the [[probability distribution]] [[function (mathematics)|function]] in [[statistics]]
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| *f represents:
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| **the unit prefix [[femto]] (10<sup>−15</sup>)
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| *''f'' represents:
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| **the generic designation of a [[function (mathematics)|function]]
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| ==Gg==
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| *G represents
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| **an arbitrary [[graph (mathematics)|graph]], as in: ''G''(''V'',''E'')
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| **an arbitrary [[group (mathematics)|group]]
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| **the unit prefix [[giga]] (10<sup>9</sup>)
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| **[[Gravitational constant|Newton's gravitational constant]]
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| **the [[Einstein tensor]]
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| **the [[Gibbs free energy]]
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| *g represents:
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| **the generic designation of a second function
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| **the acceleration due to [[Free fall|gravity on Earth]]
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| ==Hh==
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| *H represents:
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| **a [[Hilbert space]]
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| **the unit [[henry (unit)|henry]] of magnetic inductance
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| **the [[homology (mathematics)|homology]] and [[cohomology]] [[functor]]s
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| **the (Shannon) [[entropy (information theory)|entropy of information]]
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| *H<sub>0</sub> represents [[Dimensionless Hubble parameter|Hubble's parameter]] as measures today (100 h km·[[second|s]]<sup>−1</sup>·[[megaparsec|Mpc]]<sup>−1 </sup> with h being the associated error)
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| *ℍ (<math>\mathbb{H}</math>) represents the [[quaternion]]s (after [[William Rowan Hamilton]])
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| *ℋ (<math>\mathcal{H}</math>) represents the Hamiltonian in [[Hamiltonian mechanics]]
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| *h represents:
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| **the [[class number (number theory)|class number]] in [[algebraic number theory]]
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| **a small increment in the argument of a function
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| **the unit [[hour]] for [[time]] (3600 s)
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| **the [[Planck constant]] (6.624 608 96(33) × 10<sup>−34</sup> J·s)
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| **the unit prefix [[hecto]] (10²)
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| ==Ii==
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| *I represents:
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| **the closed unit interval, which contains all real numbers from 0 to 1, inclusive
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| **the [[identity matrix]]
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| **the [[Irradiance]]
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| **[[Moment of inertia]]
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| **[[Intensity (physics)|Intensity]]
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| *i represents:
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| **the [[imaginary number|imaginary unit]], a complex number that is the square root of −1
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| **a subscript to denote the ''i''th term (that is, a general term or index) in a sequence or list
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| **the index to the elements of a vector, written as a subscript after the vector name
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| **the index to the rows of a matrix, written as the first subscript after the matrix name
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| **an index of summation using the [[Summation#Capital-sigma notation|sigma notation]]
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| **the [[Unit vector#Cartesian coordinates|unit vector]] in [[Cartesian coordinates]] going in the X-direction, usual bold '''''i'''
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| ''
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| ==Jj==
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| *J represents:
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| **the unit [[joule]] of energy
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| **the [[current density]] in [[electromagnetism]]
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| **the [[Radiosity (heat transfer)|Radiosity]] in thermal mechanics
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| *j represents:
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| **the index to the columns of a matrix, written as the second subscript after the matrix name
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| **in [[electrical engineering]], the square root of −1, instead of i
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| **in [[electrical engineering]], the principal cube root of 1: <small><math>-\frac{1}{2}+\frac{1}{2}i \sqrt 3</math></small>
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| ==Kk==
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| *K represents:
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| **the unit [[kelvin]] of temperature
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| **the [[functor]]s of [[k theory|K-theory]]
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| **an unspecified (real) constant
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| **a [[field (mathematics)|field]] in algebra
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| *k represents
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| ** the unit prefix [[kilo-]] (10³)
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| ** the [[Boltzmann constant]], this is often represented as k<sub>B</sub> to avoid confusion with
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| ** the [[Wavenumber]] of the [[wave equation]]
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| ** an [[integer]], e.g. a [[bound variable|dummy variable]] in [[summation]]s, or an index of a [[matrix (mathematics)|matrix]].
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| ** an unspecified (real) constant
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| ** the spring constant of [[Hooke's law]]
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| ** the spacetime [[Curvature]] from the [[Friedmann equations]] in cosmology
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| ==Ll==
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| *L represents:
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| **[[Length]], used often in quantum mechanics as the size of an [[infinite square well]]
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| **[[Angular momentum]]
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| **the unit of volume the [[litre]]
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| **the [[radiance]]
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| **the space of all integrable real (or complex) functions
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| **the space of linear maps, as in ''L''(''E'',''F'') or ''L''(''E'') = [[endomorphism|End]](''E'')
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| **the [[Likelihood function]]
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| **a [[formal language]]
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| *l represents:
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| **the unit of volume the [[litre]]
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| **the length of a side of a rectangle or a rectangular prism (e.g. V = lwh; A = lw)
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| **the last term of a sequence or series (e.g. S<sub>n</sub> = n(a+l)/2)
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| *ℒ (<math>\mathcal{L}</math>) represents:
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| **the [[Lagrangian]] (sometimes just L)
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| **[[Particle beam|Exposure]] (in particle physics)
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| ==Mm==
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| *M represents:
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| ** a [[manifold]]
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| ** a [[metric space]]
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| ** a [[matroid]]
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| **the unit prefix [[mega-]] (10<sup>6</sup>)
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| ** the [[Madelung constant]] for crystal structures held by [[ionic bonding]]
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| *m represents:
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| **the number of rows in a [[matrix (mathematics)|matrix]]
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| **the [[gradient|slope]] in a linear regression or in any [[Linear equation|line]]
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| **the [[mass]] in mechanics equations
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| **the unit [[metre]] of length
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| **the unit prefix [[milli]] (10<sup>−3</sup>)
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| ==Nn==
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| *N represents
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| **the unit [[Newton (unit)|newton]] of force
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| **the [[Neutron number]]
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| **the [[Particle number]] in thermodynamics
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| **The [[particle number|number of particles]] of a thermodynamical system
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| *N<sub>A</sub> 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,<sup>23</sup> mol <sup>−1</sup>
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| *ℕ (<math>\mathbb{N}</math>) represents the [[natural number]]s
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| *n represents
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| **the number of columns in a [[matrix (mathematics)|matrix]]
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| **the "number of" in [[algebra]]ic equations.
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| **A [[neutron]], often shown as <sup>1</sup><sub>0</sub>n
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| **the [[Number density]] of particles in a Volume
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| **the unit prefix [[Nano-|nano]] (10<sup>−9</sup>)
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| **the nth term of a sequence or series (e.g. t<sub>n</sub> = a+(n-1)d)
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| **the principal quantum number
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| | |
| ==Oo==
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| *O represents
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| **the order of asymptotic behavior of a function (upper bound); see [[Big O notation]]
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| **<math>(0,0,\ldots,0)</math> — the origin of the coordinate system in [[Cartesian coordinates]]
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| *o represents
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| **the order of asymptotic behavior of a function (strict upper bound); see [[Big O notation]]
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| **the [[group (mathematics)#order of an element|order of an element]] in a [[group (mathematics)|group]]
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| | |
| ==Pp==
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| *P represents:
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| **the [[pressure]] in physics equations
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| **the unit prefix [[Peta (prefix)|peta]] (10<sup>15</sup>)
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| **[[Probability]] in Statistics and Statistical Mechanics
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| *ℙ (<math>\mathbb{P}</math>) represents
| |
| **the [[prime number]]s
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| **[[projective space]]
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| **a [[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>)
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| **a [[proton]], often p<sup>+</sup> or <sup>1</sup><sub>1</sub>p
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| **the linear [[momentum]] in physics equations
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| | |
| ==Qq==
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| *Q represents:
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| ** [[Heat]] energy
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| *ℚ (<math>\mathbb{Q}</math>) represents the [[rational number]]s
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| *q represents:
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| ** the [[Deceleration parameter]] in Cosmology
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| | |
| ==Rr==
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| *R represents:
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| **the [[Ricci tensor]]
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| *ℝ (<math>\mathbb{R}</math>) represents the set of real numbers and various [[algebraic structure]]s built upon the set of real numbers, such as <math>\mathbb{R}^n</math>
| |
| *r represents:
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| **the [[radius]] of a circle or sphere
| |
| **the ratio of a geometric series (e.g. ar<sup>n-1</sup>)
| |
| **the separation of two objects, for example in [[Coulomb's law]]
| |
| | |
| ==Ss==
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| *S represents
| |
| **a [[sum]]
| |
| **the unit [[siemens (unit)|siemens]] of electric conductance
| |
| **the unit [[sphere]] (with superscript denoting dimension)
| |
| **the [[scattering matrix]]
| |
| ** [[entropy]]
| |
| *s represents:
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| **an [[arclength]]
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| **the [[displacement (vector)|displacement]] in [[Equations of motion|mechanics equations]]
| |
| **the unit [[second]] of time
| |
| **a [[complex number|complex]] variable ''s'' = σ + ''i'' ''t'' in [[analytic number theory]]
| |
| *𝒮 (<math>\mathcal{S}</math>) represents a system's [[Action (physics)|action]] in physics
| |
| | |
| ==Tt==
| |
| *T represents:
| |
| **the [[Greatest element|top element]] of a [[lattice (order)|lattice]]
| |
| **a [[tree (graph theory)|tree]] (a special kind of graph)
| |
| **[[temperature]] in physics equations
| |
| **the unit [[tesla (unit)|tesla]] of magnetic flux density
| |
| **the unit prefix [[Tera-|tera]] (10<sup>12</sup>)
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| **the [[stress-energy tensor]]
| |
| *t represents:
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| **[[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]]
| |
| **the sample statistic resulting from a Student's t-test
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| | |
| ==Uu==
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| *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
| |
| *{{Unicode|∪}} represents the [[Union (set theory)|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==
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| *W represents the unit [[watt]] of power
| |
| **In physics is also represents the work, both the [[Work (physics)|mechanical]] & [[Work (thermodynamics)|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]].
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| | |
| ==Xx==
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| *''x'' represents
| |
| **an unknown [[Variable (mathematics)|variable]], most often (but not always) from the set of [[real number]]s, while a [[complex number|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]]{{dn|date=November 2012}} in a [[computer graphics|graph]] or [[window (computer)|window]] in computer graphics.
| |
| | |
| ==Yy==
| |
| *Y represents:
| |
| **the unit prefix [[yotta-]] (10<sup>24</sup>)
| |
| *y represents:
| |
| **the unit prefix [[yocto-]] (10<sup>−24</sup>)
| |
| *''y'' represents:
| |
| **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]]{{dn|date=November 2012}} of a [[computer graphics|graph]] or [[window (computing)|window]] in computer graphics.
| |
| | |
| ==Zz==
| |
| *Z represents:
| |
| **the unit prefix [[zetta]] (10<sup>21</sup>)
| |
| **the [[atomic number]] in Chemistry and Physics
| |
| **a standarized normal [[random variable]] in [[Probability Theory]] and [[Statistics]]
| |
| **The [[Partition function (statistical mechanics)|Partition function]] in statistical mechanics
| |
| *ℤ (<math>\mathbb{Z}</math>) represents the [[integer]]s
| |
| *z represents:
| |
| **the unit prefix [[zepto]] (10<sup>−21</sup>)
| |
| **the coordinate on the third or vertical axis in three [[dimension]]al space
| |
| **the view depth in [[computer graphics]], see also "[[z-buffering]]"
| |
| **the argument of a [[Complex analysis|complex function]], or any other variable used to represent a complex value
| |
| ** in astronomy, it can donate wavelength [[redshift]]
| |
| | |
| ==See also==
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| * [[Greek letters used in mathematics]]
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| * [[Latin alphabet]]
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| * [[Mathematical alphanumeric symbols]]
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| * [[Table of mathematical symbols]]
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| * [[Typographical conventions in mathematical formulae]]
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| | |
| {{DEFAULTSORT:Roman Letters Used In Mathematics}}
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| [[Category:Elementary mathematics]]
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| [[Category:Mathematical notation| ]]
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| [[Category:Latin letters| ]]
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