Sigma (upper case Σ, lower case σ; Greek Σιγμα, lower case in word-final position ς) is the eighteenth letter of the Greek alphabet, and carries the /s/ sound. In the system of Greek numerals it has a value of 200. When used at the end of a word, and the word is not all upper case, the final form (ς) is used. (e.g. (Odysseus) - Note the two sigmas in the center of the name, and the word-final sigma at the end.) It is not to be confused with the cedilla ç.

The letter is ultimately derived from Phoenician Šin . However, its name derives from Samekh.

The uppercase form of sigma was borrowed into the Latin alphabet to serve as the uppercase of esh (lowercase: ).

Disigma, or "double sigma", is a non-current term for the character Sampi. 1

Lunate sigma

In Eastern forms of Greek writing (as opposed to the Western Greek alphabet used in the European Greek colonies) and in the Middle Ages, the lunate sigma (upper case , lower case ) — which resembles, but which is not at all related to, the Latin letter C — was often used. Lunate sigma was frequently used for writing Medieval Greek, and can still be seen in inscriptions in Greek Orthodox churches, and also in certain printed editions of classical authors.

The form of the Cyrillic letter С 2 and Coptic letter sima are derived from lunate sigma.

On coins from the Hellenistic period in India, the script of later coins sometimes use lunate sigma. This sigma continued to be written this way also in Medieval Greek.

A dotted lunate sigma (sigma periestigmenon, encoded at U+03FE ) was used by Aristarchus of Samothrace as an editorial sign indicating that the line so marked is at an incorrect position. Similarly, an antisigma (encoded at U+03FD ) may mark a line that is out of place. A dotted antisigma (antisigma periestigmenon, encoded at U+03FF ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.

Science and mathematics

Upper case Σ is used as a symbol for:

• the summation operator
• a class of baryons in particle physics
• macroscopic cross sections in nuclear and particle physics
• in economics this letter is for the balance of the invoice classes, the overall amount of the debts and demands
• in linguistics and computer science it is used to refer to the set of symbols that form an alphabet

Lower case σ is used for:

• sigma bonds in chemistry
• the Sigma receptor
• the parametric standard deviation of a population (as opposed to a sample) in statistics
• a quality model for business, Six Sigma, based on the standard deviation, often referred to as "6σ"
• sigma-algebras, sigma-fields and sigma-finiteness in measure theory; more generally, the symbol σ serves as a shorthand for "countably", e.g. a σ-compact topological space is one that can be written as a countable union of compact subsets.
• the sum-of-divisors function in number theory
• the Stefan-Boltzmann constant
• the "sigma factor" of RNA polymerase
• a measure of electrical conductivity
• the Surface charge density in electrostatics
• Normal stress in continuum mechanics
• volatility of a stock generally needed for options pricing
• a syllable in phonology
• the spectrum of a matrix $A$, denoted as $\backslash sigma(A)$, in applied mathematics
• surface tension
• the unary operation of selection on a database relation in relational algebra
• the standard deviation of a bell curve in statistics