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.
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Transcription
In the 16th century, the mathematician Robert Recorde wrote a book called "The Whetstone of Witte" to teach English students algebra. But he was getting tired of writing the words "is equal to" over and over. His solution? He replaced those words with two parallel horizontal line segments because the way he saw it, no two things can be more equal. Could he have used four line segments instead of two? Of course. Could he have used vertical line segments? In fact, some people did. There's no reason why the equals sign had to look the way it does today. At some point, it just caught on, sort of like a meme. More and more mathematicians began to use it, and eventually, it became a standard symbol for equality. Math is full of symbols. Lines, dots, arrows, English letters, Greek letters, superscripts, subscripts. It can look like an illegible jumble. It's normal to find this wealth of symbols a little intimidating and to wonder where they all came from. Sometimes, as Recorde himself noted about his equals sign, there's an apt conformity between the symbol and what it represents. Another example of that is the plus sign for addition, which originated from a condensing of the Latin word et meaning and. Sometimes, however, the choice of symbol is more arbitrary, such as when a mathematician named Christian Kramp introduced the exclamation mark for factorials just because he needed a shorthand for expressions like this. In fact, all of these symbols were invented or adopted by mathematicians who wanted to avoid repeating themselves or having to use a lot of words to write out mathematical ideas. Many of the symbols used in mathematics are letters, usually from the Latin alphabet or Greek. Characters are often found representing quantities that are unknown, and the relationships between variables. They also stand in for specific numbers that show up frequently but would be cumbersome or impossible to fully write out in decimal form. Sets of numbers and whole equations can be represented with letters, too. Other symbols are used to represent operations. Some of these are especially valuable as shorthand because they condense repeated operations into a single expression. The repeated addition of the same number is abbreviated with a multiplication sign so it doesn't take up more space than it has to. A number multiplied by itself is indicated with an exponent that tells you how many times to repeat the operation. And a long string of sequential terms added together is collapsed into a capital sigma. These symbols shorten lengthy calculations to smaller terms that are much easier to manipulate. Symbols can also provide succinct instructions about how to perform calculations. Consider the following set of operations on a number. Take some number that you're thinking of, multiply it by two, subtract one from the result, multiply the result of that by itself, divide the result of that by three, and then add one to get the final output. Without our symbols and conventions, we'd be faced with this block of text. With them, we have a compact, elegant expression. Sometimes, as with equals, these symbols communicate meaning through form. Many, however, are arbitrary. Understanding them is a matter of memorizing what they mean and applying them in different contexts until they stick, as with any language. If we were to encounter an alien civilization, they'd probably have a totally different set of symbols. But if they think anything like us, they'd probably have symbols. And their symbols may even correspond directly to ours. They'd have their own multiplication sign, symbol for pi, and, of course, equals.
Contents
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 () 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 xintercept 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 () or 𝔹 ())
 a basis of a vector space or of a filter (both also denoted by ℬ ())
 in econometrics and timeseries statistics it is often used for the backshift or lag operator, the formal parameter of the lag polynomial
 the magnetic field, denoted or
 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 yintercept 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 () represents the set of complex numbers
 A vertically elongated C with an integer subscript n sometimes denotes the nth 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 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 (10^{18})
 energy in physics
 electric field denoted or
 electromotive force (denoted 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
 _{p}F_{q} 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 (10^{9})
 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_{0} represents Hubble's parameter as measures today (100 h km·s^{−1}·Mpc^{−1 } with h being the associated error)
 ℍ () represents the quaternions (after William Rowan Hamilton)
 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 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 Xdirection, usual bold i
Jj
 J represents:
 the unit joule of energy
 the current density in electromagnetism denoted .
 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:
Kk
 K represents:
 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
 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. S_{n} = n(a+l)/2)
 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
 m represents:
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 ninepoint center of a triangle
 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 () represents the natural numbers
 n represents
 the number of columns in a matrix
 the "number of" in algebraic equations.
 A neutron, often shown as ^{1}_{0}n
 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+(n1)d)
 the principal quantum number
Oo
 O represents
 the order of asymptotic behavior of a function (upper bound); see Big O notation
 — 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 (10^{15})
 probability in statistics and statistical mechanics
 an arbitrary point in geometry
 ℙ () represents
 the prime numbers
 projective space
 a probability (as in P(E), which reads "the probability P of event E happening")
 p represents
 Q represents:
 heat energy
 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 () represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as
 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^{n1})
 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 () 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 (10^{12})
 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. 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 ttest
Uu
 U represents:
 a Uset 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:
 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 fourdimensional space.
Xx
 X represents
 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 (10^{24})
 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 (10^{21})
 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 () 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 "zbuffering"
 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