**Omega** (capital: **Ω**, lowercase: **ω**; Greek Ωμέγα) is the twenty-fourth and last letter of the Greek alphabet. In the Greek numeric system, it has a value of 800. The word literally means "great O" (*ō mega*, mega meaning 'great'), as opposed to omicron, which means "little O" (*o mikron*, micron meaning "little").

In phonetic terms, the Ancient Greek Ω is a long open-mid *o* [ɔː], comparable to the vowel of British English *raw*. In Modern Greek, Ω represents the mid back rounded vowel /o/, the same sound as omicron. The letter omega is transcribed *ō* or simply *o*.

As the last letter of the Greek alphabet, Omega is often used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet. Omega is additionally used in Christianity, as a part of the Alpha and Omega metaphor.

## History

Ω wasn't part of the early (8th century BC) Greek alphabets. It was introduced in the late seventh century BC in the Ionian cities of Asia Minor to denote the long half-open [ɔː]. It is a variant of omicron (Ο), broken up at the side (), with the edges subsequently turned outward (, , , ). The Dorian city of Knidos as well as a few Aegean islands, namely Paros, Thasos and Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long /o/.

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called *ō* (ὦ), whereas the omicron was called *ou* (οὖ). The modern lowercase shape goes back to the uncial form , a form that developed throughout the third century BC in ancient handwriting on papyrus, from a flattened-out form of the letter () that had its edges curved even further upward.

In addition to the Greek alphabet, Omega was additionally adopted into the early Cyrillic alphabet. See Cyrillic omega (Ѡ, ѡ). A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ.

Omega was additionally adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet. It has had little use. See Latin omega.

## The symbol Ω (uppercase letter)

The uppercase letter Ω is used as a symbol:

- In chemistry:
- For oxygen-18, a natural, stable isotope of oxygen.

- In physics:
- For ohm – SI unit of electrical resistance; formerly additionally used upside down (℧) to represent mho, the old name for the inverse of an ohm (now siemens with symbol S) used for electrical conductance. Unicode has a separate code point for the ohm sign (U+2126, Ω), but it is included only for backward compatibility, and the Greek uppercase omega character (U+03A9, Ω) is preferred.
- In statistical mechanics, Ω refers to the multiplicity (number of microstates) in a system.
- The solid angle or the rate of precession in a gyroscope.
- In particle physics to represent the Omega baryons.
- In astronomy (cosmology), Ω refers to the density of the universe, additionally called the density parameter.
- In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.

- In mathematics and computer science:
- In complex analysis, the Omega constant, a solution of Lambert's W function
- In differential geometry, the space of differential forms on a manifold (of a certain degree, usually with a supersrcipt).
- A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral.
- In topos theory, the (codomain of the) subobject classifier of an elementary topos.
- In combinatory logic, the looping combinator,
*(λ x. x x) (λ x. x x)* - In group theory, the omega and agemo subgroups of a
*p*-group, Ω(*G*) and ℧(*G*) - In group theory, Cayley's Ω process as a partial differential operator.
- In statistics, it is used as the symbol for the sample space, or total set of possible outcomes.
- In number theory, Ω(
*n*) is the number of prime divisors of*n*. - In notation related to Big O notation to describe the asymptotic behavior of functions.
- Chaitin's constant.

- As part of logo or trademark:
- The logo of Omega Watches SA.
- Part of the Badge of the Supreme Court of the United Kingdom.
- Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program.
- The logo of the God of War video game series based on Greek mythology.
- The logo of E-123 Omega, a
*Sonic the Hedgehog*character. - The logo of the Heroes of Olympus series, based on Greek mythology.
- the logo of the Ultramarines in Warhammer 40,000
- The logo of Primal Groudon, the version mascot of
*Pokémon Omega Ruby*. - The logo of Darkseid in DC comics

- Other
- The symbol of the resistance movement against the Vietnam-era draught in the United States
- Year or date of death
- Used to refer to the lowest-ranked wolf in a pack
- In eschatology, the symbol for the end of everything
- In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover

## The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

- Biochemistry and chemistry:
- Denotes the carbon atom furthest from the carboxyl group of a fatty acid
- In biochemistry, for one of the RNA polymerase subunits
- In biochemistry, for the dihedral angle associated with the peptide group, involving the backbone atoms Cα-C'-N-Cα
- In biology, for the fitness.
- In genomics, as a measure of evolution at the protein level (also denoted as d
_{N}/d_{S}or K_{a}/K_{s}ratio)

- Physics
- Angular velocity or angular frequency
- In computational fluid dynamics, the specific turbulence dissipation rate
- In meteorology, the change of pressure with respect to time of a parcel of air
- In circuit analysis and signal processing to represent natural frequency, related to frequency
*f*by ω = 2π*f* - In astronomy, as a ranking of a star's brightness within a constellation
- In orbital mechanics, as designation of the argument of periapsis of an orbit
- In particle physics to represent the omega meson

- Computer science:
- In notation related to Big O notation, the asymptotically dominant nature of functions
- In relational database theory to represent NULL, a missing or inapplicable value

- Mathematics:
- The first transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written )
- In set theory, the first uncountable ordinal number (more commonly written as ω
_{1}) - A primitive root of unity, like the complex cube roots of 1
- The Wright Omega function
- A generic differential form
- In number theory, ω(
*n*) is the number of distinct prime divisors of*n* - In number theory, an arithmetic function
- In combinatory logic, the self-application combinator,
*(λ x. x x)* - In mathematical/options finance, the elasticity of financial options
- In analytical investment management, the tracking error of an investment manager

- Other:
- Used in place of ん in Japanese typing shorthand.
- In linguistics, the phonological word
- In textual criticism, the archetype of a manuscript tradition
- In sociology, used to refer to the lowest ranking member of a group
- In shift_JIS art, used to represent the cat's mouth. (e.g. (´･ω･`) ｼｮﾎﾞｰﾝ)

## Character encodings

### Greek Omega/Coptic Oou

Character | Ω | ω | Ⲱ | ⲱ | ||||
---|---|---|---|---|---|---|---|---|

Unicode name | GREEK CAPITAL LETTER OMEGA | GREEK SMALL LETTER OMEGA | COPTIC CAPITAL LETTER OOU | COPTIC SMALL LETTER OOU | ||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 937 | U+03A9 | 969 | U+03C9 | 11440 | U+2CB0 | 11441 | U+2CB1 |

UTF-8 | 206 169 | CE A9 | 207 137 | CF 89 | 226 178 176 | E2 B2 B0 | 226 178 177 | E2 B2 B1 |

Numeric character reference | Ω | Ω | ω | ω | Ⲱ | Ⲱ | ⲱ | ⲱ |

Named character reference | Ω | ω | ||||||

DOS Greek | 151 | 97 | 224 | E0 | ||||

DOS Greek-2 | 213 | D5 | 250 | FA | ||||

Windows 1253 | 217 | D9 | 249 | F9 | ||||

TeX | Omega | omega |

### Cyrillic Omega

Character | Ѡ | ѡ | ꙻ | |||
---|---|---|---|---|---|---|

Unicode name | CYRILLIC CAPITAL LETTER OMEGA | CYRILLIC SMALL LETTER OMEGA | COMBINING CYRILLIC LETTER OMEGA | |||

Encodings | decimal | hex | decimal | hex | decimal | hex |

Unicode | 1120 | U+0460 | 1121 | U+0461 | 42619 | U+A67B |

UTF-8 | 209 160 | D1 A0 | 209 161 | D1 A1 | 234 153 187 | EA 99 BB |

Numeric character reference | Ѡ | Ѡ | ѡ | ѡ | ꙻ | ꙻ |

Character | Ѻ | ѻ | Ꙍ | ꙍ | ||||
---|---|---|---|---|---|---|---|---|

Unicode name | CYRILLIC CAPITAL LETTER ROUND OMEGA | CYRILLIC SMALL LETTER ROUND OMEGA | CYRILLIC CAPITAL LETTER BROAD OMEGA | CYRILLIC SMALL LETTER BROAD OMEGA | ||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 1146 | U+047A | 1147 | U+047B | 42572 | U+A64C | 42573 | U+A64D |

UTF-8 | 209 186 | D1 BA | 209 187 | D1 BB | 234 153 140 | EA 99 8C | 234 153 141 | EA 99 8D |

Numeric character reference | Ѻ | Ѻ | ѻ | ѻ | Ꙍ | Ꙍ | ꙍ | ꙍ |

### Latin/IPA Omega

Character | ɷ | Ꞷ | ꞷ | |||
---|---|---|---|---|---|---|

Unicode name | LATIN SMALL LETTER CLOSED OMEGA | LATIN CAPITAL LETTER OMEGA | LATIN SMALL LETTER OMEGA | |||

Encodings | decimal | hex | decimal | hex | decimal | hex |

Unicode | 631 | U+0277 | 42934 | U+A7B6 | 42935 | U+A7B7 |

UTF-8 | 201 183 | C9 B7 | 234 158 182 | EA 9E B6 | 234 158 183 | EA 9E B7 |

Numeric character reference | ɷ | ɷ | Ꞷ | Ꞷ | ꞷ | ꞷ |

### Technical Omega symbols

Character | ⍵ | ⍹ | Ω | ℧ | ||||
---|---|---|---|---|---|---|---|---|

Unicode name | APL FUNCTIONAL SYMBOL OMEGA | APL FUNCTIONAL SYMBOL OMEGA UNDERBAR | OHM SIGN | INVERTED OHM SIGN | ||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 9077 | U+2375 | 9081 | U+2379 | 8486 | U+2126 | 8487 | U+2127 |

UTF-8 | 226 141 181 | E2 8D B5 | 226 141 185 | E2 8D B9 | 226 132 166 | E2 84 A6 | 226 132 167 | E2 84 A7 |

Numeric character reference | ⍵ | ⍵ | ⍹ | ⍹ | Ω | Ω | ℧ | ℧ |

### Mathematical Omega

Character | 𝛀 | 𝛚 | 𝛺 | 𝜔 | 𝜴 | 𝝎 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Unicode name | MATHEMATICAL BOLD CAPITAL OMEGA | MATHEMATICAL BOLD SMALL OMEGA | MATHEMATICAL ITALIC CAPITAL OMEGA | MATHEMATICAL ITALIC SMALL OMEGA | MATHEMATICAL BOLD ITALIC CAPITAL OMEGA | MATHEMATICAL BOLD ITALIC SMALL OMEGA | ||||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 120512 | U+1D6C0 | 120538 | U+1D6DA | 120570 | U+1D6FA | 120596 | U+1D714 | 120628 | U+1D734 | 120654 | U+1D74E |

UTF-8 | 240 157 155 128 | F0 9D 9B 80 | 240 157 155 154 | F0 9D 9B 9A | 240 157 155 186 | F0 9D 9B BA | 240 157 156 148 | F0 9D 9C 94 | 240 157 156 180 | F0 9D 9C B4 | 240 157 157 142 | F0 9D 9D 8E |

UTF-16 | 55349 57024 | D835 DEC0 | 55349 57050 | D835 DEDA | 55349 57082 | D835 DEFA | 55349 57108 | D835 DF14 | 55349 57140 | D835 DF34 | 55349 57166 | D835 DF4E |

Numeric character reference | 𝛀 | 𝛀 | 𝛚 | 𝛚 | 𝛺 | 𝛺 | 𝜔 | 𝜔 | 𝜴 | 𝜴 | 𝝎 | 𝝎 |

Character | 𝝮 | 𝞈 | 𝞨 | 𝟂 | 𝟔 | |||||
---|---|---|---|---|---|---|---|---|---|---|

Unicode name | MATHEMATICAL SANS-SERIF BOLD CAPITAL OMEGA | MATHEMATICAL SANS-SERIF BOLD SMALL OMEGA | MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL OMEGA | MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL OMEGA | MATHEMATICAL SANS-SERIF BOLD ITALIC P.OOO OMEGA | |||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 120686 | U+1D76E | 120712 | U+1D788 | 120744 | U+1D7A8 | 120770 | U+1D7C2 | 120788 | U+1D7D4 |

UTF-8 | 240 157 157 174 | F0 9D 9D AE | 240 157 158 136 | F0 9D 9E 88 | 240 157 158 168 | F0 9D 9E A8 | 240 157 159 130 | F0 9D 9F 82 | 240 157 159 148 | F0 9D 9F 94 |

UTF-16 | 55349 57198 | D835 DF6E | 55349 57224 | D835 DF88 | 55349 57256 | D835 DFA8 | 55349 57282 | D835 DFC2 | 55349 57300 | D835 DFD4 |

Numeric character reference | 𝝮 | 𝝮 | 𝞈 | 𝞈 | 𝞨 | 𝞨 | 𝟂 | 𝟂 | 𝟔 | 𝟔 |

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.