A stardate is a type of date expressed as a decimal number, e.g. 7412.6.
Stardates were used in certain cultures as far back as the 2150s, although the United Earth government had not adopted the system yet. In 2154, Degra, a Xindi-Primate, sent a coded message to Enterprise containing a stardate for when Enterprise should rendezvous with Degra's ship. T'Pol was able to calculate that the given stardate was three days away, indicating that Vulcans also had an understanding of stardates at that time. (ENT: "Damage")
When adopted by Earth during the next hundred years, stardates began to be used in many contexts instead of Gregorian calendar dates. At the time of Richard Robau's murder, the digits to the left of the decimal separator were equal to the Gregorian calendar year: Robau died in 2233 on stardate 2233.04. This method was used in the alternate reality at least through 2258. (Star Trek) By 2265 in the prime reality, a more complex relationship had been established between stardates and the Gregorian calendar. (TOS: "Where No Man Has Gone Before")
Stardates did not replace clock time or everyday units for expressing larger timespans, such as days, weeks, months, years, centuries, or millennia, and tend not to apply retroactively instead of Gregorian or Julian calendars either. (TOS: "The Naked Time" remastered) The following table outlines the progress of stardates over time:
In an alternate timeline, the combat date replaced the stardate as the dating system used by Starfleet during their war with the Klingon Empire. This was indicative of the militaristic nature of Starfleet in this timeline. (TNG: "Yesterday's Enterprise")
Stardates were first portrayed in TOS: "Where No Man Has Gone Before", the second pilot for the series. Dave Eversole notes that the first draft of the teleplay (dated May 27, 1965) contains no stardates, although there is a reference to "Captain's Log, Report 197."  Kirk mentions "stardate 1312.4" by the final revised draft (July 8, 1965), which also asks for "C-1277.1 to 1313.7" to appear on his gravestone. (The letter "C" and the regular increase of other stardates in the script raise the possibility that 1277.1 was intended to be the date Kirk was promoted to captain and/or assumed command of the Enterprise, not his date of birth.)
Gene Roddenberry: The Myth and the Man Behind Star Trek
The pilot was written by Samuel A. Peeples, who was interviewed by journalist Joel Engel for Gene Roddenberry: The Myth and the Man Behind Star Trek.  Replying to a newsgroup question on stardates, Engel quoted information from his book:
"For the starship captain's log entry narrations, Roddenberry wanted to devise a futuristic measurement of time reference. He called (Sam) Peeples (whom Roddenberry had contacted early on for help in learning about science fiction, a subject he knew nothing about; it was Peeples who wrote "Where No Man Has Gone Before," the pilot that sold ST). The two men had a few drinks while brainstorming, and soon began chuckling over their imaginative 'stardate' computations. 'We tried to set up a system that would be unidentified unless you knew how we did it,' Peeples says.
"They marked off sections on a pictorial depiction of the known universe and extrapolated how much earth time would elapse when traveling between given points, taking into account that the Enterprise's warp engines would be violating Einstein's theory that nothing could exceed the speed of light. They concluded that the 'time continuum' would therefore vary from place to place, and that earth time may actually be lost in travel. 'So the stardate on Earth would be one thing, but the stardate on Alpha Centauri would be different,' Peeples says. 'We thought this was hilarious, because everyone would say, "How come this date is before that date when this show is after that show?" The answer was because you were in a different sector of the universe.' 
The Star Trek Guide
The following instructions to writers were transcribed from the series bible Star Trek Guide, third revision, dated April 17, 1967 (page 25). Their original date of composition and the author are unclear, but the sample stardates are consistent with the range from the second pilot.
We invented "Stardate" to avoid continually mentioning Star Trek's century (actually, about two hundred years from now), and getting into arguments about whether this or that would have developed by then. Pick any combination of four numbers plus a percentage point, use it as your story's stardate. For example, 1313.5 is twelve o'clock noon of one day and 1314.5 would be noon of the next day. Each percentage point (sic) is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode.
What is called a "percentage point" is actually the tenths digit. While this 24-hour increasing stardate with noon at .5 wasn't always adhered to within episodes, the initial four digits weren't selected quite as randomly as described here. An overall increase with time can be observed in the above table of stardates, from 1312.4 in the second pilot to 5928.5 in the final episode of the series. The Animated Series and the movies continued the general trend, despite a number of variations in the rates of increase.
The Making of Star Trek
Although much of the information from the Star Trek Guide was used in Stephen E. Whitfield's book The Making of Star Trek (conceived in May 1967 and published in September 1968), the above specifics of selecting stardate numbers weren't included. However, the author did interview Gene Roddenberry on the subject, who provided a more elaborate rationalization for stardate behavior:
In the beginning, I invented the term "star date" simply to keep from tying ourselves down to 2265 A.D., or should it be 2312 A.D.? I wanted us well into the future but without arguing approximately which century this or that would have been invented or superseded. When we began making episodes, we would use a star date such as 2317 one week, and then a week later when we made the next episode we would move the star date up to 2942, and so on. Unfortunately, however, the episodes are not aired in the same order in which we filmed them. So we began to get complaints from the viewers, asking, "How come one week the star date is 2891, the next week it's 2337, and then the week after it's 3414?"
In answering these questions, I came up with the statement that "this time system adjusts for shifts in relative time which occur due to the vessel's speed and space warp capability. It has little relationship to Earth's time as we know it. One hour aboard the U.S.S. Enterprise at different times may equal as little as three Earth hours. The star dates specified in the log entry must be computed against the speed of the vessel, the space warp, and its position within our galaxy, in order to give a meaningful reading." Therefore star date would be one thing at one point in the galaxy and something else again at another point in the galaxy.
I'm not quite sure what I meant by that explanation, but a lot of people have indicated it makes sense. If so, I've been lucky again, and I'd just as soon forget the whole thing before I'm asked any further questions about it.
Star Trek 30 Years Special Collector's Edition
Star Trek 30 Years Special Collector's Edition, published in 1996 by Paramount Pictures, states on page 81:
Few Star Trek topics generate as much heated debate as the stardate system, the time calculation used by the United Federation of Planets which was introduced to the classic series by Gene Roddenberry, who borrowed the notion from the Julian date currently used by astronomers. Developed by Joseph Scaliger (who named his dating system after his father, Julius Caesar Saliger), the Julian time calculation measures the number of days elapsed since 1 Jan. 4713 BC, the date derived by Joseph Justus. In the case of the 30th anniversary of the air date for the original series (8 Sept. 1996), that's 2,450,335 days. To make it easier, astronomers only use the last five digits - making 50335 the Julian date for the Star Trek anniversary. For Star Trek, Roddenberry added a single digit after the decimal point (50335.2) to represent one of the 10 time measurements in a 24-hour period...Roddenberry borrowed the five-digit Julian date, shortening it to four digits and renaming it "stardate."
The Next Generation era
The teleplay of TNG: "Encounter at Farpoint" dated April 13, 1987 contains stardates ranging from 42353.7 to 42372.5. (Star Trek: The Next Generation Companion CD) This was changed to 41153.7-41174.2 on the air, consistent with the following description in Star Trek: The Next Generation Writer's/Director's Guide of March 23, 1987 (page 13):
A stardate is a five-digit number followed by a decimal point and one more digit. Example: "41254.7." The first two digits of the stardate are always "41." The 4 stands for 24th century, the 1 indicates first season. The additional three leading digits will progress unevenly during the course of the season from 000 to 999. The digit following the decimal point is generally regarded as a day counter.
Under this system, 1,000 stardate units elapse in approximately one year, since that was the normal timespan between two seasons of TNG. The 'century' digit was elaborated upon as early as TNG: "Future Imperfect", where the imaginary Jean-Luc Riker asks the computer to display his birthday party of stardate 58416, less than sixteen years in the future of 2367. While the '4' may have been inspired by the 24th century, in-universe it changes once a decade.
The writers of the Star Trek Chronology further developed the system by having a calendar year start at 000 and end at 999, although this does not fit all references in the show, such as a Diwali celebration around stardate 44390, too early in the year according to the simplified system. (TNG: "Data's Day") Stardate 41986.0 was in 2364 according to TNG: "The Neutral Zone", hence the simplified system assumes that stardates 41xxx.x covered the entire year 2364, stardates 42xxx.x the entire year 2365 and so forth. As stated in Star Trek Chronology (page 95):
The year 2323 works out as the zero point for the system of stardates developed for Star Trek: The Next Generation, assuming that the beginning of year 2364 (the first season of Star Trek: The Next Generation) was stardate 41000, and that stardates progress at 1000 units per year. In other words, under the Next Generation system of stardates, January 1, 2323 would seem to correspond to stardate 0. This probably shouldn't be taken too seriously, because Star Trek's stardates have never been too internally consistent, but we're mentioning it here because it's kinda fun.
The second digit increased every TV season in other spin-offs as well, even after TNG had ended. Since DS9 premiered during the sixth season of TNG and was set in exactly the same year (2369), stardates on DS9 ranged from 46379.1 to 52861.3. Likewise, the first season of Voyager (2371) would have been the eighth season of TNG had it continued, so Voyager stardates ranged from 48315.6 to 54973.4. In at least one draft of the script, Star Trek Nemesis had a stardate of 47844.9, but the initial digits were changed to '56' for the film, consistent with Riker having been Picard's "trusted right arm for fifteen years." However, stardates of events prior to TNG: "Encounter at Farpoint", but not so far back as the time of TOS, do not always conform to this method of counting. For example, in TNG: "Dark Page", the stardate for an event which took place 42 years before 47254.1 is given as 30620.1, which, according to the standard method of counting used after "Encounter at Farpoint", should only be 17 years earlier.
In addition to the overall rate of approximately 1,000 units per year, many episodes confirm the 24-hour stardate unit which was first mentioned in the TOS bible, with midnight at .0 and noon at .5. According to Appendix I of Star Trek Chronology, "As with the original series, an increase of a single unit within an episode corresponds to about 24 hours, even though this is inconsistent with a 365-day year." It is especially noticeable when the time of day is shown next to a stardate fraction, as demonstrated in the table below:
|Stardate and time||Fraction converted to h:m:s||Source|
|42605.57 13:40:23||13:40:48||Donald Varley's log (TNG: "Contagion")|
|42592.72 17:16||17:16:48||Log from the future Enterprise (TNG: "Time Squared")|
|44673.9 22:30:59||21:36 to midnight||Captain Chantal Zaheva's log (TNG: "Night Terrors")|
|40164.7 17:29:46 (19:29, 22:15)||16:48 to 19:12||Logs of the USS Victory (TNG: "Identity Crisis")|
|44623.9 22:26:09||21:36 to midnight||A video showing Pardek (TNG: "Unification I")|
|46154.4 10:37:41||09:36 to noon||Riker's clock (TNG: "Schisms")|
|2823.6 16:23:00||14:24 to 16:48||TOS: "The Galileo Seven" (remastered)|
Although the vast majority of stardates are given with only one digit following the decimal point, the captain's log in TNG: "Code of Honor" is recorded with two digits (41235.25 and 41235.32) and other references have two, three or even four digits, as in TNG: "The Child", where a stardate of 42073.1435 is seen on a viewscreen in the Observation Lounge. Commenting on the graphic, Mike Okuda explained: "I always thought that the numbers after the decimal were fractions of a 24 hour day, meaning that .1435 would be about 3:20 in the morning. Which is really early in the day for a doctor's appointment..."  In VOY: "Relativity", Seven of Nine travels back in time from 52861.274 to 49123.5621. Occasionally there are no digits, such as when "today's date" is given as stardate 47988. (TNG: "All Good Things...")
There are also cases in TNG where stardates appear to be non-linear or that can be reverted to previous values. In one noticeable example Tasha Yar's death occurs around 41601.3 (TNG: "Skin of Evil") however she was alive in episodes with greater stardates such as "The Big Goodbye", set in stardate 41997.7. Such episodes were of course filmed before Skin of Evil and Denise Crosby's departure from the show.
The stardate format from the latest film series is credited to screenwriters Roberto Orci and Alex Kurtzman. According to Orci, they "used the system where, for example, 2233.45 or whatever means 23rd century, 33rd year of that century, and the .45 indicates the day of the year out of 365 days."  During a Q&A session, Orci restated that a stardate is "the year, as in 2233, with the month and day expressed as a decimal point from .1 to .365 (as in the 365 days of the year)."  A similar reply was posted on his Twitter account: "star date=standard year, with decimal representing day of year from 1-365." 
Orci never said whether leap years end at .366, which would be expected if the digits before the decimal point correspond to Gregorian calendar years. When asked about the scripted stardates 2230.06 and 2233.04, with only one leading zero instead of two or none, he replied that it could have been an error.  IDW's Star Trek: Timelines show the latter number as 2233.4. Except for the separator and uncertain leading zeroes, the new stardates are similar to the ordinal dates of ISO 8601. According to that standard, the first day of 2259 would be written as 2259-001.
The alternate reality adaptation of "Where No Man Has Gone Before" began with a stardate in the new style, but the second part of that comic reverted to 1313.1, consistent with the range of its prime reality counterpart, and the same approach was taken with "The Galileo Seven" reimagining, which began on stardate 2821.5. After that story was finished, writer Mike Johnson commented at TrekMovie.com: "Speaking of typos... Going forward we are using the new Stardate system."  The year-based stardates have also been used with the prime reality; according to Star Trek: Timelines, Sisko assumed command of DS9 on stardate 2369. The table below shows only new-style stardates from the films and other sources, along with their calculated equivalents in the Gregorian calendar.
|2063.95||April 5||Vulcans contact Zefram Cochrane. (Star Trek: Timelines) The date of April 5 was established in Star Trek: First Contact.|
|2151.102||April 12||Jonathan Archer assumes command of Enterprise. (Star Trek: Timelines) The first starlog entry from ENT: "Broken Bow" was made on April 16.|
|2161||The United Federation of Planets is founded. (Star Trek: Timelines)|
|2230.06||January 6?||Spock's birth in a deleted scene which opens with the superimposed stardate. The number is also in the script and in the comic adaptation. The year is from the Star Trek Chronology.|
|2231||"Star Trek Ongoing, Issue 19": Scotty is a child at this time.|
|2233.(0)4||January 4||Shortly after Nero's arrival. Robau says "2233-zero-four," written as 2233.04 in the script and in the official comic adaptation. Star Trek: Timelines, on the other hand, display the number as 2233.4. The year is from the Star Trek Chronology.|
|2256||"Star Trek Ongoing, Issue 20". (Star Trek: Timelines)|
|2257||"Star Trek Ongoing, Issue 18" and after that, "Star Trek Ongoing, Issue 19". (Star Trek: Timelines)|
|2258.42||February 11||Shortly after the destruction of Vulcan.|
|2258.56||February 25||"Mirrored, Part 1"|
|2258||"Star Trek Ongoing, Issue 1": Scotty isn't sure about the decimals, but comments that the Nero incident was "ages" ago. In the second part of the story, Kirk has "been a starship captain for less than a year". Star Trek: Timelines give 2258 and set the comic after "Mirrored, Part 2"|
|2258||"Star Trek Ongoing, Issue 2" through "Vulcan's Vengeance, Part 2". Star Trek: Timelines place the issues in this order, setting all of them before the following entry.|
|2258.241||August 29||"The Return of the Archons, Part 1"|
|2258.247||September 4||"Star Trek Ongoing, Issue 17"|
|2258||"Star Trek Ongoing, Issue 14". (Star Trek: Timelines)|
|2259||"The Truth About Tribbles, Part 1": The Delta Vega events of Star Trek are captioned "several months ago," but stardate 2259.155 from the main story is actually 15 months and 24 days later than 2258.42. In addition, the comic is mentioned in the video game below and set by Star Trek: Timelines in 2259, after Issue 14 but before "Countdown to Darkness".|
|2259.23||January 23||"The Redshirt's Tale". Star Trek: Timelines use 2258 and order the story between Issues 17 and 14, but 2259.23 is displayed in reverse on a transparent viewscreen from the comic.|
|2259||~January 24||"Star Trek: Countdown to Darkness". According to Star Trek Into Darkness, the Mudd Incident occurred a month before.|
|2259.32, .33||February 1, 2||Star Trek (video game)|
|2259.55||February 24||Star Trek Into Darkness|
|2259||Star Trek Ongoing 21 to Star Trek Ongoing, Issue 24. The year is from Star Trek: Timelines. These events occurred in the late fall or winter of that year, as the USS Enterprise was rechristened nearly a year later after Star Trek Into Darkness|
|2264||Kirk's five-year mission begins in the prime reality. (Star Trek: Timelines)|
|2364||The first season of TNG in the prime reality. (Star Trek: Timelines)|
|2369||The first season of DS9 in the prime reality. (Star Trek: Timelines)|
|2371||The first season of VOY in the prime reality. (Star Trek: Timelines)|
|2387||The Jellyfish is commissioned according to the ship's computer. Stardates in the 643xx range are used in "Countdown, Number One".|
|2409||Star Trek Online. (Star Trek: Timelines)|
Deviations from production norms
Stardates would occassionally deviate from the prevailing production norm throughout all of the Star Trek incarnations. Examples include:
- In TOS: "Where No Man Has Gone Before", the stardates within the episode progress by 1.4, from 1312.4 to 1313.8, in what could not be more than a few days, yet the birth stardates of Gary Mitchell and Elizabeth Dehner are given as 1087.7 (onscreen dossier age: 23) and 1089.5 (onscreen dossier age: 21), respectively.
- The animated episode "The Magicks of Megas-Tu" set in 2269 has a stardate of 1254.4. This is lower than any of the TOS episodes, including the first Kirk-era episode, TOS: "Where No Man Has Gone Before" set in 2265 which had a stardate of 1312.4.
- In TNG: "Datalore", Riker dropped one of the numbers in his log, stating "Stardate 4124.5".
- In VOY: "Unimatrix Zero, Part II", set during stardate 54014.4, Tuvok mentions that his date of birth is stardate 38774, but he was born in 2264.
- VOY: "Homestead" gives a stardate of 54868.6, which would suggest a date sometime in late 2377, but in fact the episode is set on the 315th anniversary of the first contact with Vulcans, which works out to April 5, 2378.
Franz Joseph stardates
Most of the stardates in Star Fleet Technical Manual are calendar dates of the 1970s, formatted YYMM.DD. This can be inferred by comparing the stated dates of first printing (November 1975) and the 20th anniversary edition (September 1986) with the corresponding stardates, 7511.01 and 8609.01. According to StarTrek.com, "By using the year, month, day approach, the day the first episode of Star Trek aired, September 8, 1966, would appear as 6609.08." wbm The Star Trek (Stardate) Calendar also used this format.
FASA Reference Stardates
FASA's Star Trek: The Role Playing Game released in the early 1980s used "reference stardates" (β) similar to those used by Franz Joseph. However, they prefixed a digit and a slash to represent the century, starting with the year 2000, so January 1, 2000, was 0/0001.01 and the Organian Peace Treaty was signed on 2/0801.24, or January 24, 2208 (β), according to Star Trek Spaceflight Chronology. Preceding centuries are negative, so the first episode of TOS aired -1/6609.08.
- Stardate at Memory Beta, the wiki for licensed Star Trek works
- The Stardate FAQ - primarily develops one particular theory of stardates that has gained some currency
- Determining Calendar Dates from Stardates - has calculations and calculators based upon information from the television series' and movies
- Star Trek logs - database of stardates and logs from the Star Trek films and television series