Fantastic Measurement System

Instead of going with normal measurement unit names, fiction will make up their own. Expect a guide to have conversions between them and real units unless the entire point is to avert Technology Marches On and Sci-Fi Writers Have No Sense of Scale by simply never giving a unit comparable to real world objects in the first place.

In some cases, especially Science Fiction or Sufficiently Analyzed Magic, units will have to be invented where they do not exist in normal speech. Magical energy is likely to have some unit. Particularly well developed settings may even specify what the unit is, for example, one Merlin might be defined as the magical energy required to push a specific object a specific distance.

Compare Hiroshima as a Unit of Measure, where a unit is scaled to a specific object. See Microts for units relating to time.

Anime and Manga

 * Though it's never named, there obviously is a unit to measure one's strength in Dragon Ball. In the games it's often referenced as B.P. (Battle Power). In this system, the average human would rate 2-3. By the middle of Dragonball Z, the numbers we're dealing with are in the 'millions'. So yeah.
 * And as we all know, over 9000 of this unit is already... a lot.
 * In Trigun, distances are measured in "Iles," which are just "miles" with one letter removed.
 * Not to mention, the unit of money is called "Double Dollars", represented, of course, with "$$" (seems like just a waste of time and ink really)
 * When fans ask Eiichiro Oda things like the extent that someone who ate the Gomu-Gomu fruit can stretch, Oda's response is something along the lines of "100 Gomu-Gomus" without telling us how long a Gomu-Gomu is. He does the same thing for the Bara-Bara fruit and the Hana-Hana fruit, except the measures are in Bara-Baras and Hana-Hanas.
 * In the Crest of the Stars universe, some distances are measured in daj. Other distances are measured in wesdaj, which appear to be longer than daj.

Comic Books

 * When Amadeus Cho studies magical phenomena, he measures the reality-warping field strength in "hercs", one herc being equal to the field strength of his friend Hercules. It sounds like "hertz" so it's pretty natural to tack on SI prefixes like megahercs or gigahercs, but most of the measurements he gives are between zero and five hercs.
 * The various Transformers franchises use various units of length and time. While they used generic "cycles" a lot, the earliest Cybertronian units of measurement had such names as "breem," "vorn," and "orn."

Fan Works

 * In With Strings Attached, the Baravadans have “longsteps”; how long these units are is never explained. Also, John's Kansael doesn't understand any Earth measurements and can't tell him how distant Ehndris is from Ta'akan; he figures out that the distance is roughly comparable to that between London and Glasgow. On the other hand, the Hunter's world uses miles.

Literature

 * On Gor, distances are measured in "passangs", which are 7/10ths of a mile.
 * Edgar Rice Burroughs' Barsoom stories. According to The Other Wiki article, distance units were as follows:
 * 1 sofad = 11.68 inches
 * 1 ad = 9.75 feet
 * 1 haad = .3692 miles
 * 1 karad = 36.92 miles
 * In Harry Potter, the Wizarding world uses a different system of money than the rest of the world, which consists of Galleons, Sickles and Knuts. There are 17 Sickles in a Galleon, and 29 Knuts in a Sickle. As of December 5, 2010, one Galleon is worth about 5 British Pounds, or 7.82 U.S. Dollars.
 * The Star Wars Expanded Universe uses the metric system - called Imperial measurements, confusingly enough - in the Republic, New Republic, and the Empire. Others may use other systems - the Adumari use "keps", which are about .8 kilometers. In Outbound Flight, the Chiss use "visvia", which are about 1.6 kilometers. There are others.
 * In Moon Over Soho, Peter Grant is depressed that, despite being codified by Isaac Newton himself, the rules of magic have no proper unit of measurement. He decides to invent one and call it the a "yap", a "yap" being the amount of magic need to make a small dog bark.
 * Similarly, the Discworld unit of magic is the thaum, defined as the amount of magic needed to create a white pigeon or three standard-sized billiard balls. There is also the prime, an attempt at a more rational unit created by the wizard Augustus Prime, which is defined as the amount of magic needed to move one pound of lead one foot. In a bit of a parody of how British scientists and academics act with Centigrade/Fahrenheit, it's mentioned in the Discworld Companion that any young wizard attempting to use primes will immediately face the question from his superiors "What's that in Old Money?" Perhaps because of this, thaums are nearly always cited as the unit in the books.
 * The Science of Discworld uses "splitting the thaum" as a fantastic version of splitting the atom, implying the thaum is actually a real distinct particle or entity rather than just an arbitrary measurement.
 * Continuing the temperature parody theme, younger wizards use a "thaumometer" (sounds like "thermomemter") to measure the strength of a magical field, while older wizards dismiss these modern gadgets and just lick their finger and hold it up—which causes it to sprout a coloured aura which lets them judge the background magic strength.
 * In Warrior Cats, the most common unit of measurement is a "tail-length", which is equivalent to about a foot. "Foxlength" - about a yard - is used occasionally as well, and on very rare occasions they'll use "kittenstep" (about an inch).
 * Pern used "dragonlength" as a measure of, well, length and distance. The Dragonlover's Guide to Pern by Jody Lynn Nye said a length was the size of a green dragon, approximately 40 feet.
 * In the Destroyermen series, the 'Cats normally measure length/distance by the "tail," which is about the same as one yard.
 * Played for Laughs in the 1985 humor book Science Made Stupid by Tom Weller, in which a table in its appendix lists such units as the "arg" (the unit of work done incorrectly), the "galumph" (unit of waste motion), the "lumpen" (unit of resistance to getting out of bed in the morning), and the "melvin" (unit of temperature, "as measured from absolutely perfect to absolutely awful"). A separate table of conversions for weights and measures on the same page listed equivalencies such as "325 cubebs = 1 furbish; 6 furbishes = 1 nautical smile; 20 nautical smiles = 1 minor league; 3 minor leagues = 1 major league" and "24 carrots = 1 pickelweight; 30 pickelweights = 1 tuna; 1000 tuna = 1 short ton; 1.37 short tons = 1 tall ton".

Live Action TV

 * The original Battlestar Galactica (1970s): according to its article at The Other Wiki, the only distance unit that wasn't an Earth name was "metron" (1 meter).
 * In Star Trek, a "kellicam" is a unit of length used by Klingons which is similar in magnitude to a kilometre.
 * Bajoran units of measurement include hecapate, kellipate, kerripate, linnipate, tessijen and tessipate.
 * Computer capacity is measured in "kiloquads", which are very carefully never defined to avoid looking outdated when Tech Marches On.
 * Star Trek has also had the forethought to come up with units for things that present-day science is physically incapable of measuring. "Cochranes" is apparently the metric unit for subspace flux (named for Zefram Cochrane, obviously). Except when it isn't.
 * In Red Dwarf, distances are measured in "gigooks", though how far this is is never indicated.
 * The Daleks of Doctor Who measure time in "rels".
 * Which, when we actually hear them using it, turns out to be exactly equal to one second.
 * James Mays Man Lab parodied the BBC's tendencies for using objects to express units of measure (see the Real Life section), at one point measuring the ascent of two weather balloons in "Mount Everests" and "Oz Clarkes".
 * Farscape is an excellent example, as apparently everyone in Peacekeeper space, as well as the Uncharted Territories uses "klance" (temperature); "dench", "henta", "samat", "milon", "metron", "motra" and "zacron" (distance); "hetch" (speed); "micron", "microt", "arn", "solar day", "weeken" and "cycle" (time). The fact that everyone seems to use these, even outside Peacekeeper space, might just be due to the Translator Microbes converting foreign measurements into units everyone can understand.

Magazines

 * "The Potrzebie System of Weights and Measurements", described in Mad #33, is largely similar to the metric system, but with different base units. The standard unit of length, the potrzebie, is defined as the thickness of Mad Magazine #26 (2.263348517438173216473 mm).

Oral Tradition

 * Helen from Greek Mythology is said to be the face that launched a thousand ships (to rescue her when she was kidnapped). Thus, beauty is measured in millihelens - the amount of beauty needed to launch a single ship.

Tabletop Games

 * Early editions of Advanced Dungeons and Dragons rated encumbrance in "coins". Encumbrance, itself, was a vaguely-defined combination of actual weight and the awkwardness of carrying something.
 * In Spelljammer, all ships and equipment are measured in space tons. We know it's not the same as a landlubber "groundling" ton. Sadly, Unit Confusion in some sourcebooks raises to the level when it's not clear even whether a space ton is an unit of mass or volume.
 * In Traveller the "ton" is a unit of volume, equal to the volume of 1000 kg (a metric ton) of liquid hydrogen.
 * To avoid the problems of Technology Marches On, Shadowrun rates the memory capacity of cyberdecks and other computing equipment in "megapulses", which are undefined in terms of real-world units.

Toys

 * Bionicle: "bios", "kios", and "mios" are units for distance used in the Matoran Universe. The distance units are as follows:
 * 1 bio = 4.5 feet = 1.37 meters
 * 1 kio = 1,000 bio = 4,500 feet/0.85 miles = 1.37 kilometers
 * 1 mio = 1,000 kio = 850 miles = 1,370 kilometers
 * Fridge Logic ensues when you wonder what they ever needed to measure in mio. The various islands of the setting are hundreds of kio in size at most.

Video Games

 * The force of the final Climax move in Bayonetta is measured in "Infinitons" (most other moves are measured in "Megatons" and "Gigatons"). Serial Escalation indeed, and possible Fridge Brilliance since the idea of different values of infinity is a real concept in mathematics. Or, y'know it just sounds cool.
 * Mario & Luigi: Bowser's Inside Story: Kilamoles
 * The Source Engine uses "Hammer Units"
 * Majority of Game Engines use some sort of map unit to measure distances. A Physics Engine might also use its own unit.
 * Whereas many MMOs will measure the distance of attacks (and thus, implicitly, all distances) in a unit that audiences would recognize, like meters, Final Fantasy XI and Final Fantasy XIV have "ilms", "fulms", "yalms", and "malms" as their units of measure. These may be "inches", "feet", "yards", and "miles", respectively, or else just have the same relations with each other as those real measurements do (without being the actual equivalent in length).
 * In Hyperdimension Neptunia, you can get memory upgrades for the CPUs (a.k.a. goddesses) in your party, which are measured in megamibytes, natch.

Web Comics

 * The Order of the Stick introduced measurement of villainy in kilonazi. Presumably 1 Nz equals the output of an average (from "rabid" to "nodding freeloader") member of National Socialistic party. The estimated evildoing level for a hypothetical offspring of Cruella de Vil and Sauron was 4.8±0.4 kNz.
 * Grace in El Goonish Shive measured sadness in Seymours—using the "Jurassic Bark" episode of Futurama as a baseline.
 * Saturday Morning Breakfast Cereal does this sometimes, including using "kiloweiners" at at least one point to measure shame/embarrasment.

Western Animation

 * The Transformers of the eponymous metaseries have a staggering variety of not-at-all-internally-consistent Cybertronian units of length and time.
 * ReBoot: Megabyte offhandedly mentions that Bob will erase if he gets within five bits of a magnet.
 * They also use the term, "nano", instead of "second". Presumably this is just short for the actual unit of a "nanosecond" but it's not explicit and short of some additional explanation would seem to conflict with the scale of time passing when the User plays a game.
 * "Nanosecond" is the most likely example, given that in one episode, Enzo complains that studying could take "One whole second" in much the same way we could say "This is taking forever!"
 * When Dot gets partially deleted by a magnet, Phong tells Bob that he doesn't have a lot of time to save her: "You don't have all second you know!"
 * Cyberchase had "cyber" as their prefix. But it has been pointed out this isn't consistent.
 * In My Little Pony: Friendship Is Magic, pegasi measure the power of their wings in "wing power" which apparently is a measure for their ability to create wind by flying really fast than the speed itself.