The original usage of quadrant occurs in episodes such as "The Deadly Years" and "The Squire of Gothos", where numbered quadrants (448 and 904) are given. In other episodes it appears to refer to an entire quarter of the galaxy. The season 3 Star Trek: The Next Generation Writers' Technical Manual asserts that there are four quadrants in each sector (which seem to vary in size).
The exact quadrant borders are not clearly established in the series canon. Episodes often contradict each other. Art staff explanations also contradict each other.
The Star Trek: The Next Generation episode "The Price" (1988) introduced the concept of four quadrants of the galaxy, named the Alpha, Beta, Gamma, and Delta quadrants, respectively.
Star Trek VI: The Undiscovered Country implies that the Alpha/Beta border runs through, or is relatively close to, Federation space. The Star Trek Encyclopedia attributes this decision to a desire to rationalize a line in Star Trek II: The Wrath of Khan, in which James T. Kirk claimed that the Enterprise was the only ship in a Quadrant. Most of the maps produced by the art staff for the series (both on-screen and published) show that the Solar system is roughly in the center of the Alpha Quadrant, but some of the maps show that the Solar system is at the edge of the Alpha and Beta Quadrants.
Assuming the galactic meridian runs from the center of the galaxy through the Solar System, then the Alpha Quadrant is between 180 degrees and 270 degrees, and the Beta Quadrant is between 90 degrees and 180 degrees.
The Alpha Quadrant and the nearby areas of the Beta Quadrant are the primary setting of Star Trek, Star Trek: The Next Generation, Star Trek: Deep Space Nine, and Star Trek: Enterprise. According to the Encyclopedia, the Federation is largely on the Alpha Quadrant side, but with parts in the Beta Quadrant; whereas the Klingon and Romulan Empires are mainly in the Beta Quadrant but extend in part into the Alpha Quadrant. The Star Trek Star Charts have the Romulans and Klingons entirely within the Beta Quadrant, as well as the Gorn Hegemony, the Son'a Solidarity, and the Metron Consortium. Star Trek Star Charts further located the First Federation, Breen, Ferengi, Tzenkethi, Cardassians, Bajorans, Talarians, and Tholians in the Alpha Quadrant.
Of core worlds, Star Trek Star Charts claims that Vulcan (40 Eridani), Andoria (Procyon), Risa, and the Rigel (Beta Rigel) systems are in the Beta Quadrant, with Tellar (61 Cygni), Trill, and Betazed in the Alpha Quadrant.
Star Trek Star Charts has the Romulans corewards and counterclockwise from the Federation core, with the Klingons rimwards of the Romulans. Federation territory is shown to expand around the backs of the Klingon and Romulan Empires, further into the Beta Quadrant. Other powers such as the Cardassians, Tholians, and Ferengi are on the clockwise side of the Federation. The Star Fleet Technical Manual (1975) by Franz Joseph also has a galactic meridian running through Sol, but depicted the Romulans as being counterclockwise, and the Klingons as being clockwise.
Although the Romulans and Klingons are shown by maps as part of the Beta Quadrant, Star Trek: Deep Space Nine did not use this terminology, referring to them as Alpha Quadrant powers. Ronald D. Moore noted that the "Alpha quadrant is firmly planted in the audience's mind as where the Federation, the Klingons, and the Romulans all live so I think we'll stick with that nomenclature".
About 600,000 years ago, the Alpha Quadrant was dominated by the Tkon Empire, which has long since vanished by the time of the Star Trek series.
The Gamma Quadrant is situated between 270 degrees and 0 degrees.
It is the home of the Changelings, or Founders. The majority of it is ruled by the Dominion.
In the Star Trek universe, the Bajoran wormhole is a unique spatial anomaly located within 160,000,000 kilometres (99,000,000 mi) of the planet Bajor (per DS9 S1Ep2: "Emissary (Part 2)"), which is a little more than the distance from Earth to the Sun. The Bajoran religion refers to the wormhole as the "Celestial Temple". It is an aperture of swirling golden light surrounded by blue clouds, which appears when a vessel approaches and disappears when the vessel enters it; it also appears when discharging a vessel. The wormhole can only be traversed by ships traveling at impulse (sub-light speed) velocities.
The wormhole is discovered in the first episode of Star Trek: Deep Space Nine. It is found to lead from the Bajor-B'Hava'el system in the Alpha Quadrant to the Idran system in the Gamma Quadrant, 70,000 light-years away and on the other side of the galaxy. Due to the strategic importance of such a phenomenon, the Deep Space Nine space station is moved out of Bajor's orbit and repositioned 15 kilometres (9.3 mi) from the wormhole.
Starfleet Commander Benjamin Sisko and Lt. Jadzia Dax are the first to make contact with the wormhole and its creators, noncorporeal beings known as the Prophets in Bajoran religion; they are simply referred to as "wormhole aliens" by the Federation. It is they who provided the Orb-like energy artifacts (or "Tears of the Prophets") to the Bajorans and these artifacts are the basis of Bajoran religion.
The wormhole becomes a point of conflict throughout the series, since it permits travel between the Alpha Quadrant and the Gamma Quadrant controlled by the Dominion, a militaristic interstellar state led by the race of shapeshifters known as the Changelings. Neither the Dominion nor the major powers of the Alpha Quadrant wish the other to gain a foothold in their relative quadrants, which explains the strategic importance of the wormhole running between them. The wormhole closes at one point, as a result of one of the Tears of the Prophets being temporarily rendered inert by the Pah Wraiths. It is later restored by the discovery of an additional orb by Benjamin Sisko.
The Delta Quadrant is situated between 0 degrees and 90 degrees.
Most of the information about the Delta Quadrant and its inhabitants comes from the show Star Trek: Voyager. Apart from the voyages of the USS Voyager, the USS Equinox, the USS Raven, briefly the USS Enterprise-D, and the Federation citizens assimilated or de-assimilated from the Borg, the Federation has not explored this quadrant.
The Delta Quadrant is home to the Borg Collective, the Kazon, the Vidiians, the Talaxians, the Ocampa, the Hirogen, the Malon, the Devore, and the Ankari. Species 8472, beings from "fluidic space", are first encountered in this quadrant, although they are not native to this region or physical dimension.
On some maps the center of the galaxy is regarded as its own area, not part of any of the four quadrants. The Great Barrier is here as are the Cytherians from the TNG episode, "The Nth Degree".