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In Star Trek: Voyager, there is a big deal made about them warping far beyond contact with any Federation bases, beause they're all the way out in "the Delta Quadrant".

To me, this indicates that there is a finite area of space that has been explored in the Star Trek universe up to this point.

So, including for the sake of this question the Delta Quadrant that they were lost in, and all of explored Space up to that point in the series, how much of Space is included in the Federation-explored region of the Star Trek Universe?

Actual units of measurement would be ideal, but are not required if a general idea would better describe the size of the known universe.

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    People will (hopefully) come along and do proper answers, but in short, it’s meant to be a percentage of our real-world galaxy. “Quadrant”, as in Delta Quadrant, refers to a quarter of our galaxy.
    – Paul D. Waite
    Feb 14, 2014 at 16:20
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    pretty much. This wasn’t quite so nailed down in The Original Series (“quadrant” was used more loosely there, the idea of four galactic quadrants didn’t come up until TNG), and I think there was an episode there about the edge of our galaxy. But yes.
    – Paul D. Waite
    Feb 14, 2014 at 16:54
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    There were also two examples of aliens from the Andromeda Galaxy in the original series, and in the episode "By Any Other Name" where one of these alien races appeared, it was mentioned that the Enterprise would take thousands of years to reach Andromeda: en.memory-alpha.org/wiki/Andromeda_Galaxy ...on the other hand, Star Trek V had them reaching a planet at the center of the galaxy in a very short time, but maybe that movie is best forgotten (or maybe "center of the galaxy" just meant "in some very broadly-defined central region of the galaxy")
    – Hypnosifl
    Feb 14, 2014 at 18:00
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    @PaulD.Waite In later series Quadrant as one of the 4 quadrants of the galaxy is the primary meaning, but minor quadrants were retained in TNG - such as Morgana Quadrant and Quadrant 448
    – Izkata
    Feb 14, 2014 at 22:40
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    The Star Trek universe is a spheroid region 705 meters in diameter.
    – user14349
    Feb 15, 2014 at 8:47

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Star Trek takes place in our galaxy, in the late 24th century. (with the most-distant movie set in 2379.) The Milky Way Galaxy is absurdly big -- some 120,000 light-years in diameter, with a center some 27,000 light years away from Earth. The nearest galaxy is the Small Magellanic Cloud, some 200,000 light-years away.

Since Voyager found themselves 70,000 light-years from home, and projected their time to get home at 75 years, we can infer an effective cruising speed of 933 ly/y, or 2-3 ly/day. Considering that they weren't stocked for it, and had to scavenge along the way, one can presume that a well-stocked round-trip vessel with custom-designed engines would, at best, match their speed.

Taken together, that means that a Federation Expedition to reach the closest galaxy and return home would take over 400 years. Which means that, if they left today with 24th-century technology, such an expedition wouldn't return until some thirty years after the star trek canon ends.

So, Star Trek's "universe" is really just a portion of our current galaxy.

It's worth noting that, although not closely followed in the show itself, the official star trek separation of "quadrants" uses a meridian pretty close to Sol, the star around which Earth orbits. So, the federation encompasses some territory in both the "alpha" and "beta" quadrants, as do the major and minor powers with which it can negotiate, plus some special-case exploration to the "delta" and "gamma" quadrants, from Voyager's journey plus the DS9 wormhole.

Of course, this only explores the Federation's domain of exploration and influence. Several other powers, such as the Borg, the Fluidic-space aliens, and cosmic-level powers such as Q have unmeasured spheres of dominion, and have probable access to whole galaxies that the Federation does not.

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    Of course, the reported time of several journeies call into question the validity of a "cruising speed", due to the high variance in stated times. (The Enterprise-E made it from the Romulan neutral zone to Earth in less than a day, the Defiant went from Earth to DS9 in about a week, and Kirk's Enterprise traveled to both the galactic core and the edge of the galaxy). I'm of the opinion that actual travel time in explored space can be orders of magnitude faster than Voyager's quote due to improved navigation, but the stated explored area is still significantly less than half of our galaxy.
    – DougM
    Feb 14, 2014 at 16:48
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    Ha, but what is "the edge of the galaxy"? Its shape resembles a disk rather than a sphere, so if you look at it sideways, the way out of the galaxy from Earth is not that far at all!
    – Mr Lister
    Feb 14, 2014 at 21:01
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    Distances and travel speeds in Star Trek are so inconsistent that they are pretty much bullshit. For example the Defiant makes a trip to the badlands in around 6 hours at warp 7. This is equivalent to about 2 lj/day, but warp 7 is several orders of magnitude slower than the Voyager's typical cruise speed. At other occasions, shuttles are able to travel distances of 1-2 light years in a matter of minutes.
    – Damon
    Feb 14, 2014 at 22:07
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    Example: O'Brian and Bashir travel to Risa both for holiday and for conventions. Direct path is about 90lj, but that'd be very close to the Cardassian border (so it's more like 100lj). Assuming 3lj/day it would be over 1 month one way, but they do it in shuttles capable of only warp 5. They gotta have a hell lot of holiday in starfleet! OTOH, the Destiny, a Sovereign-class starship capable of warp 9.99, isn't able to bring the Dex symbiont to Trill (or close to a trained host anywhere in range) in time although Trill is a mere 20lj away. There is no reasonable explanation but "plot".
    – Damon
    Feb 16, 2014 at 22:08
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    @Damon: Sorry but what is a lj?
    – Lightness Races in Orbit
    Oct 27, 2016 at 16:44
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In "The Dauphin" (tenth episode of the second season of Next Generation") Wesley Crusher states: "Only 19% of the galaxy has been explored. The rest it out there, waiting."

This equates to around 70'000 sq lightyears of the galaxy (If we make the incorrect but simplifying assumption that the galaxy is "flat").

If we assume Earth is at the centre of the Federation (and assume that exploration has progress in all directions at the same rate) the furthest distance the Federation has explored is out to about 10'000 light years...

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Known/explored universe raises the question of how well explored. If we include everything that has ever been directly looked at (and thus excluding cosmic background radiation - the echo of the big bang - which we can observe today):

These two are the most significant references:

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