Latin letters used in mathematics, science, and engineering explained
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, 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.
Typographical variation
Some common conventions:
Typographical variations of Latin letters in UnicodeName | Sub-type | Alphabet |
---|
Double-struck | Mathematical | |
|
Italic | ⅆ ⅇ ⅈ ⅉ ⅅ |
Script/Calligraphy | Mathematical | ℬ ℰ ℱ ℋ ℐ ℒ ℳ ℛ |
ℯ ℊ ℴ |
Mathematical Bold | |
|
Fraktur | Mathematical | ℭ ℌ ℑ ℜ ℨ |
|
Mathematical Bold | |
|
Mono-space | Mathematical | |
| |
Aa
represents the
algebraic numbers[11] or affine space in
algebraic geometry.
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
)
[16] - a basis of a vector space or of a filter (both also denoted by 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
or
Cc
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:
denotes the
cardinality of the set of real numbers (the "continuum"), or, equivalently, of the power set of natural numbers.
Dd
- D represents
- d represents
Ee
- E represents:
- the digit "14" in hexadecimal and other positional numeral systems with a radix of 15 or greater
- an exponent in decimal numbers. For example, 1.2E3 is 1.2×103 or 1200
- the set of edges in a graph or matroid
- the unit prefix exa (1018)
- energy in physics
- electric field denoted
or
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
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
- Fluorine
- A spectral type
- F represents
- f represents:
- the unit prefix femto (10−15)
- f represents:
Gg
- G represents
- g represents:
Hh
-
- 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.
represents the
quaternions (after
William Rowan Hamilton).
) represents the Hamiltonian in
Hamiltonian mechanics.
Ii
- I represents:
- I represents:
- 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
Jj
-
- J represents:
- the scheme of a diagram in category theory
- j represents:
- 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)
Kk
- K represents:
- k represents
Ll
- L represents:
- 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. Sn = n(a+l)/2)
- the orbital angular momentum quantum number[21]
- ℒ (
) represents:
Mm
- M represents:
- m represents:
Nn
represents the
natural numbers.
- n represents
- A neutron, which may be shown as, or n
- the unit prefix nano (10−9)
- n represents
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
- 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
Pp
represents
Qq
represents the
rational numbers
Rr
represents the set of real numbers and various
algebraic structures built upon the set of real numbers, such as
.
Ss
- S represents
- s represents:
- (
) represents a system's
action in physics
Tt
- T represents:
- t represents:
Uu
- U represents:
- U(n) represents the unitary group of degree n
- ∪ represents the union operator
- u represents:
Vv
- V represents:
- v represents
Ww
- W represents:
- w represents:
Xx
- X represents
- x represents
Yy
- Y represents:
- Y represents:
- y represents:
Zz
represents the
integers
See also
Notes and References
- Web site: Weisstein . Eric W. . Triangle . 2022-03-21 . mathworld.wolfram.com . en.
- Web site: Hexadecimal - Hexadecimal and character sets - GCSE Computer Science Revision . 2022-03-21 . BBC Bitesize . en-GB.
- Web site: DECIMAL function . 2022-03-22 . support.microsoft.com.
- Web site: 2014-10-07 . BIPM - SI base units . bipm.org . https://web.archive.org/web/20141007203046/http://www.bipm.org/en/publications/si-brochure/section2-1.html . 2014-10-07.
- Web site: 2014-10-07 . BIPM - SI derived units . 2022-03-22 . bipm.org . https://web.archive.org/web/20141007193455/http://www.bipm.org/en/publications/si-brochure/section2-2.html . 2014-10-07.
- Jensen . William B. . December 2005 . The Origins of the Symbols A and Z for Atomic Weight and Number . Journal of Chemical Education . en . 82 . 12 . 1764 . 10.1021/ed082p1764 . 2005JChEd..82.1764J . 0021-9584.
- News: 2014-06-21 . 22.1: Helmholtz Energy . 2022-03-23 . Chemistry LibreTexts . en.
- Web site: The magnetic vector potential . 2022-03-21 . farside.ph.utexas.edu.
- Web site: Weisstein . Eric W. . Glaisher-Kinkelin Constant . 2022-03-21 . mathworld.wolfram.com . en.
- Web site: 2013-10-02 . 6.2.3.1: Arrhenius Equation . 2022-04-03 . Chemistry LibreTexts . en.
- Web site: Weisstein . Eric W. . Algebraic Number . 2022-03-22 . mathworld.wolfram.com . en.
- Book: Liebscher, Dierck-Ekkehard . Cosmology . Springer . 2005 . 9783540232612 . Berlin . 53–77 .
- Book: Conversion factors and tables. Part 1. Basis of tables. Conversion factors. . 1974 . BSI . British Standards Institution . 0-580-08471-X . 3rd revision . London . 7 . 32212391.
- Book: Conversion factors and tables. Part 1. Basis of tables. Conversion factors. . 1974 . BSI . British Standards Institution . 0-580-08471-X . 3rd revision . London . 4 . 32212391.
- Web site: Arithmetic Progression - Formula, Examples AP Formula . 2022-03-24 . Cuemath . en.
- Web site: Weisstein . Eric W. . Ball . 2022-03-24 . mathworld.wolfram.com . en.
- Stohner . Jürgen . Quack . Martin . 2011 . A Concise Summary of Quantities, Units, and Symbols in Physical Chemistry . Chemistry International . . 33 . 4 . Centerfold . y.
- Book: Prasad . Paras N. . Introduction to Biophotonics . 16 January 2004 . John Wiley & Sons . 978-0-471-46539-3 . 12 . en.
- Book: Quantities, Units and Symbols in Physical Chemistry . International Union of Pure and Applied Chemistry . 1993 . 0-632-03583-8 . 20 . En.
- Web site: 2013-10-02 . 6.4.1: Eyring equation . 2022-04-03 . Chemistry LibreTexts . en.
- Web site: 2013-10-02 . Quantum Numbers for Atoms . 2022-04-07 . Chemistry LibreTexts . en.
- Book: Kardar, Mehran . Statistical Physics of Particles . Statistical Physics of Particles . . 2007 . 978-0-521-87342-0 . 860391091 . Mehran Kardar.
- Web site: Analytical Compendium . https://web.archive.org/web/20170505235542/https://media.iupac.org/publications/analytical_compendium/Cha01sec39.pdf . May 5, 2017 . October 5, 2023.
- Web site: Velocity, acceleration and distance - Motion - Edexcel - GCSE Physics (Single Science) Revision - Edexcel . 2022-03-26 . BBC Bitesize . en-GB.
- Web site: frequency Definition, Symbols, & Formulas Britannica . 2022-03-26 . www.britannica.com . en.
- Book: Durrer, Ruth . The cosmic microwave background . 2021 . Cambridge University Press . 978-1-316-47152-4 . 2nd . Cambridge, United Kingdom . 1182021387 . Ruth Durrer.
- Book: Quantities, Units and Symbols in Physical Chemistry . International Union of Pure and Applied Chemistry . 1993 . 0-632-03583-8 . 56.