Latin letters used in mathematics, science, and engineering

Some common conventions:

• Most symbols are written in italics.
• Vectors can be denoted in boldface.
• Sets of numbers are typically bold or blackboard bold.

• A represents:
  • the first point of a triangle^[1]
  • the digit "ten" in hexadecimal^[2] and other positional numeral systems with a radix of 11 or greater^[3]
  • the unit ampere for electric current in physics^[4]
  • the area of a figure^[5]
  • the mass number or nucleon number of an element in chemistry^[6]
  • the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature^[7]
  • a vector potential, in electromagnetics it can refer to the magnetic vector potential^[8]
  • with a subscript, an alternating group on that many objects
  • an Abelian group in abstract algebra
  • the Glaisher–Kinkelin constant^[9]
  • atomic weight, denoted by A_r ^[10]
  • work in classical mechanics^[10]
  • the pre-exponential factor^[10] in the Arrhenius Equation^[11]
  • electron affinity^[10]
  • A blood type^[12]
• ${\displaystyle \mathbb {A} }$ represents the algebraic numbers^[13] or affine space in algebraic geometry.
  • A spectral type
• a represents:
  • the first side of a triangle (opposite point A)^[1]
  • the scale factor of the expanding universe in cosmology^[14]
  • the acceleration in mechanics equations^[5]
  • the first constant in a linear equation
  • a constant in a polynomial
  • the unit are for area (100 m²)^[15]
  • the unit prefix atto (10⁻¹⁸)^[16]
  • the first term in a sequence or series^[17]
  • Reflectance

• B represents:
  • the digit "11" in hexadecimal^[2] and other positional numeral systems with a radix of 12 or greater^[3]
  • the second point of a triangle^[1]
  • a ball (also denoted by ℬ (${\displaystyle {\mathcal {B}}}$) or ${\displaystyle \mathbb {B} }$)^[18]
  • a basis of a vector space or of a filter (both also denoted by 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 ${\displaystyle {\textbf {B}}}$ or ${\displaystyle {\vec {B}}}$
• 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 meson
  • A blood type
  • Boron
  • Buoyancy
  • Bulk modulus
  • Luminance
  • A spectral type
• b represents:
  • the second side of a triangle (opposite point B)
  • the impact parameter in nuclear scattering
  • the second constant in a linear equation
  • usually with an index, sometimes with an arrow over it, a basis vector
  • a breadth^[10]
  • the molality of a solution^[10]
  • Bottom quark
  • Barn (10⁻²⁴ cm²)

• 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^[10]
  • 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^[10]
  • the circumference of a circle or other closed curve^[19]
  • with a subscript, a cycle on that many vertices
  • with a subscript, a cyclic group of that order
  • the complement of a set (lowercase c and the symbol ∁ are also used)
  • an arbitrary category
  • the number concentration^[10]*
  • Carbon
  • Heat capacity
  • The C programming language
  • Cunningham correction factor
• ${\displaystyle \mathbb {C} }$ 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)^[10]
  • the amount concentration in chemistry^[10]
  • the speed of light in vacuum^[20]
  • the third side of a triangle (opposite corner C)
  • the third constant in a linear equation
  • a constant in a polynomial
  • Charm quark
  • Speed of sound
  • Specific heat capacity
• Lowercase Fraktur ${\displaystyle {\mathfrak {c}}}$ denotes the cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers.

• 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 [distance²/time]
  • the differential operator in Euler's calculus notation
  • with a subscript, a dihedral group of that order or a dihedral group on a regular polygon of that many sides, depending on the convention chosen
  • dissociation energy^[10]
  • Dimension
  • Deuterium
  • Electric displacement
  • D meson
  • Density
• 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^[10]
  • the unit prefix deci (10⁻¹)^[10]
  • a thickness^[10]
  • a distance^[10]
  • Down quark
  • Infinitesimal increment in calculus
  • Density

• 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)^[10]
  • energy in physics^[10]
  • electric field denoted ${\displaystyle {\textbf {E}}}$ or ${\displaystyle {\vec {E}}}$
  • electromotive force (denoted ${\displaystyle {\mathcal {E}}}$ 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, sometimes as ${\displaystyle \mathbb {E} }$
  • E_k represents kinetic energy^[10]
  • (Arrhenius) activation energy, denoted E_a or E_A^[10]
  • ionization energy, denoted E_i^[10]
  • electron affinity, denoted E_ea^[21]
  • dissociation energy, denoted E_d^[10]
• 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
  • In a cartesian coordinate system, a unit vector in notations like ${\displaystyle (\mathbf {\hat {e}} _{x},\mathbf {\hat {e}} _{y},\mathbf {\hat {e}} _{z})}$, or ${\displaystyle (\mathbf {\hat {e}} _{1},\mathbf {\hat {e}} _{2},\mathbf {\hat {e}} _{3})}$

• 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^[10]
  • 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
  • Fluorine
  • A spectral type
• F represents
  • force in mechanics equations^[10]
  • _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 ${\displaystyle {\mathcal {F}}}$
• f represents:
  • the unit prefix femto (10⁻¹⁵)^[10]
• f represents:
  • the generic designation of a function
  • Friction

• G represents
  • an arbitrary graph, as in: G(V,E)
  • an arbitrary group
  • the unit prefix giga (10⁹)^[10]
  • the Newtonian constant of gravitation^[10]
  • the Einstein tensor
  • the Gibbs energy
  • the centroid of a triangle
  • Catalan's constant
  • weight measured in newtons^[10]
  • Green's function
  • a spectral type
• g represents:
  • the generic designation of a second function
  • the acceleration due to gravity on Earth
  • a unit of mass, the gram (also gramme)
  • Gravitational field, denoted g
  • Metric tensor (general relativity)
  • Gluon

• H represents:
  • an arbitrary subgraph
  • an arbitrary subgroup
  • a Hilbert space
  • the unit henry of magnetic inductance^[10]
  • the homology and cohomology functor
  • the enthalpy
  • the (Shannon) entropy of information
  • the orthocenter of a triangle
  • a partial sum of the harmonic series
  • Auxiliary magnetic field, denoted ${\displaystyle {\boldsymbol {H}}}$
  • Hamiltonian in quantum mechanics
  • Hankel function
  • Heaviside step function
  • Higgs boson
  • Hydrogen
  • Set of quaternions
  • Hat matrix
• H₀ is either the Hubble constant; or the Dimensionless Hubble parameter of (100 h km·s⁻¹·Mpc⁻¹, with h being the associated error.
• ${\displaystyle \mathbb {H} }$ represents the quaternions (after William Rowan Hamilton).
• ΔH^‡ represents the standard enthalpy of activation^[10] in the Eyring equation.^[22]
• 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)^[10]
  • the generic designation of a third function
  • the altitude of a triangle
  • a height^[10]
  • Spherical Hankel function

• 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^[10]
  • intensity in physics, typically the vector field I
  • Luminous intensity, typically I_v
  • the incenter of a triangle
  • the electric current^[10]
  • ionization energy, denoted I^[10]
• I represents:
  • the index of an indexed family
  • Iodine

• i represents:
  • the imaginary unit, a complex number that is the square root of −1
  • Imaginary quaternion unit
  • 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, usually bold i

• J represents:
  • the unit joule of energy^[10]
  • the current density in electromagnetism denoted ${\displaystyle {\boldsymbol {J}}}$^[10]
  • the radiosity in thermal mechanics
  • the moment of inertia^[10]
  • Total angular momentum quantum number
  • Bessel function of the first kind
  • Impulse
• 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 principal cube root of 1: ${\displaystyle -{\frac {1}{2}}+{\frac {1}{2}}i{\sqrt {3}}}$
  • the unit vector in Cartesian coordinates going in the y-direction, usually bold j
  • Electrical current density
  • Spherical Bessel function of the first kind
  • Imaginary unit in electrical engineering (where i represents current)
  • Unit vector for the second imaginary dimension in the quaternion number system (bold j)

• K represents:
  • the temperature unit kelvin^[10]
  • the functors of K-theory
  • an unspecified (real) constant
  • a field in algebra
  • with a subscript, a complete graph on that many vertices
  • the area of a polygon
  • kinetic energy^[10]
  • Kaon
  • Potassium
  • Sectional curvature
  • A spectral type
• k represents
  • the unit prefix kilo- (10³)^[10]
  • the Boltzmann constant, often represented as k_B to avoid confusion
  • the angular wavenumber of the wave equation, the magnitude of the wave vector k
  • 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)^[10]
  • the unit vector in Cartesian coordinates going in the z-direction, usually bold k
  • Unit vector for the third dimension in the quaternion number system (bold k)
  • Unit vector in the z direction

• L represents:
  • length, used often in quantum mechanics as the size of an infinite square well^[10]
  • angular momentum^[10]
  • 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 operator creating a line graph
  • the lag operator in statistics
  • a Lucas number
  • the Lagrange function^[10]
  • Inductance in electromagnetism (measured in henries)
  • A spectral type
• l represents:
  • the unit of volume the litre (often avoided due to confusion with the number 1 and uppercase letter I)
  • 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^[23]
• ℒ (${\displaystyle {\mathcal {L}}}$) represents:
  • the Lagrangian (sometimes just L)
  • exposure (in particle physics)
• ℓ represents:
  • Mean free path

• M represents:
  • a manifold
  • a metric space
  • a matroid
  • the unit prefix mega- (10⁶)^[10]
  • the Madelung constant for crystal structures held by ionic bonding
  • the moment of force^[10]
    • Torque when denoted as moment of force
  • molar mass^[10]
  • molar mass constant, denoted M_u^[10]
  • relative molecular mass, denoted M_r ^[10]
  • Magnetization vector field M
  • A spectral type
• m represents:
  • the number of rows in a matrix
  • atomic mass^[10]
  • atomic mass constant denoted m_u^[10]
  • the slope in a linear regression or in any line
  • the mass in mechanics equations^[10]
  • the unit metre of length^[10]
  • the unit prefix milli (10⁻³)^[10]
  • a median of a triangle
  • the overall order of reaction^[10]
  • Magnitude
  • Minute (but the SI abbreviation is "min")
  • Slope
  • Magnetic moment in a magnetization field

• N represents
  • the unit newton of force^[10]
  • the nine-point center of a triangle
  • Bessel function of the second kind (uncommon)
  • Nitrogen
  • Normal distribution
  • Normal vector
• N represents
  • the neutron number^[10]
  • The number of particles of a thermodynamical system^[24]: 57
• N_A represents the Avogadro constant
• ${\displaystyle \mathbb {N} }$ represents the natural numbers.
• n represents
  • A neutron, which may be shown as n, n⁰
    or ¹
    ₀n
  • the unit prefix nano (10⁻⁹)^[10]
• 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^[10]
  • the amount of a given substance^[10]
  • the number concentration^[10]
  • the overall order of reaction^[10]
  • Refractive index of a material
  • Spherical Bessel function of the second kind (uncommon)
  • An integer

• O represents
  • the order of asymptotic behavior of a function (upper bound); see Big O notation^[25]
  • ${\displaystyle (0,0,\ldots ,0)}$ — 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
  • A blood type
  • Oxygen
  • A spectral type
• o represents
  • the order of asymptotic behavior of a function (strict upper bound); see Little o notation (also known as "small o notation")
  • the order of an element in a group
• ${\displaystyle \mathbb {O} }$ represents
  • the octonions^[26]

• P represents:
  • the pressure in physics equations^[24]: 4
  • the unit prefix peta (10¹⁵)^[10]
  • probability in statistics and statistical mechanics^[24]: 35
  • an arbitrary point in geometry
  • with a subscript, a path on that many vertices
  • power, measured in watts^[10]
  • Active power in electrical engineering
  • weight measured in newtons^[10]
  • Legendre polynomial
  • Phosphorus
  • Polarization
• ${\displaystyle \mathbb {P} }$ represents
  • the prime numbers^[27]
  • Projective space^[28]
  • Projection (linear algebra)
  • a probability (as in P(E), which reads "the probability P of event E happening")
• p represents
  • a prime number
  • the numerator of a fraction
  • the unit prefix pico (10⁻¹²)^[10]
  • a proton, often p⁺ or 1
    1 p
  • the linear momentum in physics equations^[10]
  • the perimeter of a triangle or other polygon
  • generalized momentum^[10]
  • the pressure in physics equations^[10]
    • Sound pressure
  • Electric dipole moment

• Q represents:
  • the unit prefix quetta- (10³⁰)^[29]
  • heat energy^[24]: 6
  • electroweak charge, denoted Q_W^[10]
  • Reactive power in electrical engineering
  • Volumetric flow rate
• ${\displaystyle \mathbb {Q} }$ represents the rational numbers^[30]
• q represents:
  • the unit prefix quecto- (10⁻³⁰)^[29]
  • a second prime number
  • the denominator of a fraction
  • the quotient resulting from integer division
  • the deceleration parameter in cosmology
  • electric charge of a particle
  • a generalized coordinate^[10]
  • Quark

• R represents:
  • the unit prefix ronna- (10²⁷)^[29]
  • the Ricci tensor
  • the circumradius of a cyclic polygon such as a triangle
  • an arbitrary relation
  • Riemann curvature tensor
  • Electrical resistance
  • Molar gas constant
• ${\displaystyle \mathbb {R} }$ represents the set of real numbers and various algebraic structures built upon the set of real numbers, such as ${\displaystyle \mathbb {R} ^{n}}$.
• r represents:
  • the unit prefix ronto- (10⁻²⁷)^[29]
  • the radius of a circle or sphere^[10]
  • radial distance in a polar coordinate system or spherical coordinate system
  • the inradius of a triangle or other tangential polygon
  • the ratio of a geometric series (e.g. arⁿ⁻¹)
  • the remainder resulting from integer division
  • the separation of two objects, for example in Coulomb's law
  • a position vector^[10]
  • the rate of concentration change of B (due to chemical reaction) denoted r_B^[31]

• S represents
  • a sum
  • the unit siemens of electric conductance^[10]
  • the unit sphere (with superscript denoting dimension)
  • the scattering matrix
  • entropy
  • action in joule-seconds^[10]
  • Apparent power in electrical engineering
  • Area
  • Spin operator
  • Sulfur
  • Symmetric group
    • with a subscript, a symmetric group on that many objects
• s represents:
  • an arclength^[10]
  • a path length^[10]
  • the displacement in mechanics equations
  • the unit second of time^[10]
  • a complex variable s = σ + i t in analytic number theory
  • the semiperimeter of a triangle or other polygon
  • Strange quark
  • Specific entropy
• 𝒮 (${\displaystyle {\mathcal {S}}}$) represents a system's action in physics
• ${\displaystyle \mathbb {S} }$ represents
  • the sedenions

• T represents:
  • the top element of a lattice
  • a tree (a special kind of graph)
  • temperature in physics equations^[24]: 4
  • the unit tesla of magnetic flux density^[10]
  • the unit prefix tera (10¹²)^[10]
  • the stress–energy tensor
  • tension in physics
  • an arbitrary monad
  • the time it takes for one oscillation^[10]
  • kinetic energy^[10]
  • Torque^[10]
  • A spectral type
  • Tritium
  • Period, the reciprocal of frequency
• t represents:
  • time in graphs, functions or equations^[10]
  • variable of integration
  • 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^[10]
  • Top quark
• ${\displaystyle \mathbb {T} }$ represents
  • the trigintaduonions

• 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
  • Potential energy
  • Uranium
• U(n) represents the unitary group of degree n
• ∪ represents the union operator
• u represents:
  • the initial velocity in mechanics equations^[10][32]
  • Up quark

• V represents:
  • Vanadium
  • the unit volt of voltage^[10]
  • the set of vertices in a graph
  • a vector space
  • potential energy^[10]
  • molar volume denoted by V_m^[10]
• v represents
  • the final velocity in mechanics equations^[10][32]
  • frequency,^[10] especially when referring to electromagnetic waves^[33]
  • a specific volume in classical mechanics^[10]
  • the rate of concentration change of B (due to chemical reaction) denoted v_B^[31]
  • 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

• W represents:
  • the unit watt of power^[10]
  • work, both mechanical and thermodynamical^{[24]: 8–9}
  • in thermodynamics, the number of possible quantum states in Boltzmann's entropy formula
  • weight measured in newtons^[10]
  • Lambert's W function^[34]
  • Tungsten
  • W boson
  • Work function
  • Wiener process
• w represents:
  • the coordinate on the fourth axis in four-dimensional space
  • work in classical mechanics
  • Width

• X represents
  • a random variable
  • a triangle center
  • the first part of a bipartite graph
• Ẋ represents
  • the rate of change of quantity X^[10]
• 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,^[10] or the viewport in a graph or window in computer graphics; the abscissa
    • Axis in the direction of travel of an aerospace vehicle (longitudinal axis)
  • a mole fraction^[10]
  • Variable to be determined in an algebraic equation
  • A vector in linear algebra

• Y represents:
  • the unit prefix yotta- (10²⁴)^[10]
  • Bessel function of the second kind
  • the second part of a bipartite graph
  • Yttrium
  • Gross domestic product
• Y represents:
  • a second random variable
• y represents:
  • the unit prefix yocto- (10⁻²⁴)^[10]
  • 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,^[10] or in the viewport of a graph or window in computer graphics; the ordinate
    • The port-starboard axis (transverse axis) of an aerospace vehicle
  • a mole fraction^[10]

• Z represents:
  • the unit prefix zetta (10²¹)^[10]
  • the atomic number or proton number of an element in chemistry^[10]
  • a standardized normal random variable in probability theory and statistics
  • Partition function
  • in meteorology, the radar reflectivity factor
  • Electrical impedance
  • Z boson
  • Compressibility factor
• ${\displaystyle \mathbb {Z} }$ represents the integers^[35]
• z represents:
  • the unit prefix zepto (10⁻²¹)^[10]
  • the coordinate on the third or vertical axis in three dimensional space^[10]
    • The vertical axis or altitude in an aerospace vehicle
  • 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^[36]: 9
  • a third unknown variable
  • the collision frequency of A with A is denoted z_A(A)^[37]
  • the collision frequency factor is denoted z_AB^[10]

• Blackboard bold letters used in mathematics
• Greek letters used in mathematics, science, and engineering
• List of letters used in mathematics, science, and engineering
• Mathematical Alphanumeric Symbols
• Glossary of mathematical symbols