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Fantastic Measurement System

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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.
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. Compare 20% More Awesome, for abstractions that can't really be numerically quantified. See Microts for units relating to time and Alternative Calendar for different ways of arranging time units.
Note: This article does not necessarily deal with exceptionally good measurement systems, though a fictional measurement system that's well-defined and easy to understand would be pretty fantastic.
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In Trials & Trebuchets, magic is measured in Cows.
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Batman: Arkham Knight: The Riddler, proud genius that he is, claims that he invented an entirely new unit of measurement for pressure, called the "deadbat", purely for one of his crusher traps. Given his neurosis, it's hard to tell whether he's being actually serious about itnote and if so, what is he basing his "scale" off of and how does it differentiate from kPa or psi? or he's just making it up to troll you.
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Cyberchase had "cyber" as their prefix. But it has been pointed out this isn't consistent.
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Sharing the Night: In addition to the standard hooves instead of feet, Twilight measures things in bookshelves and bookshelf-heights.
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In Back Arrow, height is measured in "gents", with appears to be an equivalent of meters, since a character of average build states that he's 1,78 gent tall.
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Twitch Plays Pokémon measures the difficulty of a specific boss in Wattsons, calculated as attempts taken to beat divided by 23, after the gym leader in question walled them out for over a day in Emerald. A separate measure called WAHAs tales time into account; WAHA is calculated as (Wattson Rating)(Days taken)/1.55, set such that Wattson himself again had a rating of exactly 1. Entire Elite Fours have taken less than 1 Wattson, and as of the 25th run, only two other trainers (outside of Elite Four members, whose rankings are calculated differently) have broken the 1 Wattson barrier.
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Saturday Morning Breakfast Cereal does this sometimes, including using "kiloweiners" at at least one point to measure shame/embarrasment.
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Dragon Ball:
Though it's never named, there obviously is a unit to measure one's strength in. In the games it's often referenced as B.P. (Battle Power), and the English dub of the anime just calls it one's "Power Level". In this system, the average human would rate 2-5 and a master martial artist would top out around 100. By the middle of Dragon Ball Z, the numbers we're dealing with are in the millions. According to Word of God, power and potential cannot be measured in numbers, and power levels become totally meaningless early on.
Babidi uses his own scale to measure power, in "kilis". According to him, 300 kilis is necessary to destroy a planet, and Goku as a Super Saiyan has 3000. Due to the difference between those two numbers not making much sense (Goku has far more than ten times the energy to blow up a planet), some have assumed it's a logarithmic scale.
Dragon Ball Super: The gods measure time in "tiks" (8 hours) and "taks" (an exact equivalence is never given, but it's slightly more than 2 minutes).
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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 5th, 2010, one Galleon is worth about 5 British Pounds, or 7.82 U.S. Dollars.
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Toriko manages to go along with and avert this by using (kilo)calories to describe maximum energy levels, or the amount of energy that attacks use up. Although the kilocalorie is a real and quantifiable unit of measurement of energy, the numbers reach the hundreds of millions of kilocalories (the energy an average person would exert in 140 years or so) so frequently and without the backlashes that would come from the real-life use of these real units that the actual units bear little meaning whatsoever.
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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).
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The Space Empires games, much like Spelljammer as mentioned above, measure everything in kilotons, which thus can be a measure of volume, mass, or even structural integrity—you might have a freighter hull with a mass of 400kT, which can carry 1000kT in volume of cargo, and has 650kT of structural integrity!
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The SCP Foundation frequently deals in Humes, which is a unit used to measure baseline reality in the event of reality warping. They also measure religious faith in terms of "Akiva radiation" (using centiakivas).
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The Broken Earth Trilogy: The Advanced Ancient Humans of Syl Anagist have standard units of measurement for generating, storing, and transferring their Sufficiently Analyzed Magic. However, their scientific approach overlooks that the magic comes from a planet that's alive, aware, and furious.
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In Anarchy Reigns, upon starting a cage match, both characters' statistics are shown, which are Type (for example, Cyborg), Age, Height and Weight. If the player has Guest Fighter Bayonetta as one of the fighters, her height and weight statistics are displayed as "uwh" and "uww". They both have "(Magical Unit of Measurement)" next to them. These aren't in Bayonetta's game of origin, so these were likely invented as a means of filling in the height and weight for Bayonetta.
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Discworld
The 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. (Thaums are also the fundamental particles of magic, as described in Lords and Ladies and The Science of Discworld. Given the haphazard nature of Discworld metaphysics, it's not clear if these are two seperate meanings). Continuing the temperature parody theme, younger wizards use a "thaumometer" (sounds like "thermometer") 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 colored aura which lets them judge the background magic strength.
Parodied in Nanny Ogg's Cookbook, in which the "editors" explain that they've helpfully translated the quantities in the recipe into metric since Nanny used "the very specialised unit of measure known as the 'some', as in 'take some flour and some sugar'". They also note that "some" is very flexible, in that "some pepper" is almost certainly less than "some butter", but may or may not be less than "some flour".
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In 21st Century Fox computer speeds have accelerated to the point where they've needed to add new metric prefixes, Zeppoflopsnote not to be confused with zettaflops were achieved in the 2040s while in the 2060s they've moved onto Harpoflops and Grouchoflops and are working on Yankovicflops.
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Triptych Continuum:
To measure unicorn's magical capability, with the Celestia Meter (Adjusted) for raw power and the Luna Meter (Adjusted) for manipulative ability. Basically, strength and dexterity for horns. Both range from 0 (nonexistent) to 10 (alicorn).
There are also several more mundane measurements, including Celests (a unit of length equal to the distance from the ground to the top of Celestia's shoulder), bale-weights and bale-tons (smaller and larger units of weight), and gallops (a unit of distance equal to the approximate distance an average pony can trot in a day on a clear track).
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The Keys Stand Alone: The Soft World: Problematic for a lot of people, since, with so many people from different worlds, hardly anyone has any measurements in common. For example, when Ringo is trying to provide Mindy with an estimate of how far he can reach with his telekinesis, she's puzzled by his "feet" and "miles", and he ends up having to say "From here to the jump gate."
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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.
The Keys Stand Alone: The Soft World: Problematic for a lot of people, since, with so many people from different worlds, hardly anyone has any measurements in common. For example, when Ringo is trying to provide Mindy with an estimate of how far he can reach with his telekinesis, she's puzzled by his "feet" and "miles", and he ends up having to say "From here to the jump gate."
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The Order of the Stick introduces 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.
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In Red Dwarf, distances are measured in "gigooks", though how far this is is never indicated.
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Xenoblade Chronicles has done this in a few places. Xenoblade 2 had characters measuring distance in "peds", which appear analogous to meters or feet (the name suggests they are based on the size of a specific Titan's foot). Xenoblade 3 mentions "metris" and "cetris", which would again appear to be similar to meters and centimeters.
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The xkcd physics blog "What If?":
It uses "megayoda" as a unit of energy, in reference to a previous entry which calculated Yoda's energy output when he lifted Luke's X-Wing out of the swamp in The Empire Strikes Back.
Unusual measurements are often found in the notes of "What If?" Giraffes make a regular appearance as a measure of height, and the author once described an object's mass in "yoctomoons".
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Issue #33 of MAD had the "Potrzebie System of Weights and Measures", sent in by a 19-year-old Donald Knuth, who later became a computer scientist. The base unit was the thickness of Mad issue #26, or 2.263348517438173216473 millimeters.
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The Next Frontier: A footnote briefly mentions that the Kerbal "Astronomical Unit" is slightly shorter than its human equivalent. At all other times, either Translation Convention applies or they use the same measurement system as humans.
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In Slayers, a spellcaster's magical prowess is determined by two of these applied to mana: pool capacity and bucket capacity. Pool capacity is how much mana a caster can safely store at one time, and this increases with practice and regular use of spells. Bucket capacity is how much mana a caster can actually take from their pool at any one time, and this limit is fixed from birth. For this reason, bucket capacity is what really defines how powerful a spellcaster is, since all spells have a minimum amount of mana that they need before they can be cast. The most powerful Fire Shamanism spell, Blast Bomb, has effectively been lost to humanity because no person in centuries has had a bucket capacity high enough to cast it. To put this in perspective, Lina Inverse doesn't have the bucket capacity to cast Blast Bomb without wearing power-booster talismans!
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Marvel Cinematic Universe: Distance in space is measured in larger "jumps" and smaller "clicks" between them. In Guardians of the Galaxy Vol. 2, the Guardians travel 47 "clicks" to the nearest jumping point to make one "jump" and thus escape the Sovereign fleet. Later in the film, Rocket and Yondu quickly do 700 "jumps" in a row, with Yondu complaining that it is unhealthy for a mammalian body to hop more than 50 "jumps" at a time. In Avengers: Infinity War, the unknown Asgardian who sends the distress signal says they are 22 "jump points" out of Asgard.
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Early editions of Advanced Dungeons & Dragons rated 'encumbrance' in 'coins'. Encumbrance, itself, was a vaguely-defined combination of actual weight and the awkwardness of carrying something. More recent systems use pounds, but the unit is still measuring ungainliness rather than weight proper. After all, density and molar weight are both secondary considerations to the principal question, "Is it worth looting this object?"
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Dwarf Fortress uses the Urist scale of temperature, where temperature in Urist is equal to temperature in Fahrenheit plus 9968. Water freezes at 10000 ºU.
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Max Blaster and Doris de Lightning Against the Parrot Creatures of Venus: Xavians measure temperature in ziknoks. Or the other standard units, yelpips.
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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. (But then why aren't they just translated into units Chrichton/the viewers can understand?)
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In an episode of The Life and Times of Juniper Lee, June is brewing a potion from a recipe that calls for a "smidgen" of dustroot. (Monroe claims a "smidgen" is "a bit less than a dash" and "a tad more than a pinch".
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A "kellicam" (QelIqam) is a unit of length used by Klingons which is similar in magnitude to a kilometre. (It also sounds like the name of a web cam clandestinely set up in Kelly's room.) The Star Trek: Vanguard novels build on this, introducing the Qam and MenIqam.
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Gulliver's Travels has many. The protagonist claims that Lilliput is 5,000 blustrugs in circumference (equal to about 12 British miles, by Gulliver's estimation) while Brobdingnag's capital is three glonglungs (about fifty four English miles) and two and a half wide.
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The Scholomance: Magical Society measures Mana in "lilim". Although any single wizard's mana generation and consumption are too unique to quantify, projects like the Scholomance's Pocket Dimension demand enough mana from enough different sources to average out a unit of measurement.
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In Traveller the "ton" is a unit of volume, equal to the volume of 1000kg (a metric ton) of liquid hydrogen.
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The Lord of the Rings: The Numenoreans have the "ranga," which is roughly equivalent to a meter (approximately 38 inches). Two rangar makes an informal unit of measurement called "man-high," the height of the average Dunedain male (they were pretty tall).
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Star Trek:
A "kellicam" (QelIqam) is a unit of length used by Klingons which is similar in magnitude to a kilometre. (It also sounds like the name of a web cam clandestinely set up in Kelly's room.) The Star Trek: Vanguard novels build on this, introducing the Qam and MenIqam.
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). Most notably, warp field strength is measured often in thousands of cochranes for higher-end warp drives; each cochrane is the field strength needed for one multiple of light-speed.
Star Trek: Voyager is fond of using the unit "isoton" for mass and explosive yield.
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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). XIV also uses onze, ponze, and tonze in approximate place of ounce, pound, and ton respectively, alongside bells (hours) and moons (months).
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Many fantastic settings have things like Challenge Ratings, but Girl Genius has a competing set of Monster Scales, with antiquated, living, and somewhat-antiquated-but-still-in-use varieties. The older measurement systems are even decried as Aristotlean, which fits well when the name of one scale is the Perseus-Beowulf system.
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In The Familiar of Zero, a mage's power level is based on a scale of one to four, with higher numbers being more powerful. Level 1 is Dot, level 2 is Line, level 3 is Triangle and level 4 is Square. Mages need to be at least Line rank to be able to use two kinds of Elemental Powers, though it's unclear if this is a matter of training or natural affinity, and even single-element mages are exponentially more powerful in that element depending on their rank. It's unclear if rank is simply something a mage is born with or if it can be trained to make them stronger.
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In Tegami Bachi: Letter Bee, hours are generally referred to as "bells"; for example, the 15th bell seems to be 3:00 in the afternoon.
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In The Furthest Station, he has also defined a scale to measure the "intensity" of a ghost, from a vague feeling in the air to easily mistaken for a real person. The unit of measurement is the annie.
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Superman:
According to The Hunt for Reactron, in old Krypton, distances were measured in "sesats".
Adventures of Supergirl: The titular Kryptonian heroine mentions that her sister weighs 31 Sulls, but she is too busy at the time to calculate the equivalent in pounds.
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ReBoot: Megabyte offhandedly mentions that Bob will erase if he gets within five bits of a magnet.
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The Wheel of Time has its own system of measuring distances and areas: 10 inches make three hands, which make one foot. There are also paces, spans, miles and leagues. The series also uses new weight measurements, including 10 ounces to a pound, 10 pounds to a stone, etc.
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Beyond Heroes: Of Sunshine and Red Lyrium: When Varric meets the Iron Bull, he estimates that Bull is "at least two Varrics tall, probably closer to three."
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Mystery Science Theater 3000: In "Angels Revenge", Tom Servo's shame-o-meter measures the shame of famous or talented actors doing a B-movie in Lawfords (after Peter Lawford, who was in that week's experiment).
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Dragon Ball Super: The gods measure time in "tiks" (8 hours) and "taks" (an exact equivalence is never given, but it's slightly more than 2 minutes).
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The 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. (Thaums are also the fundamental particles of magic, as described in Lords and Ladies and The Science of Discworld. Given the haphazard nature of Discworld metaphysics, it's not clear if these are two seperate meanings). Continuing the temperature parody theme, younger wizards use a "thaumometer" (sounds like "thermometer") 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 colored aura which lets them judge the background magic strength.
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In The Good Place the time in the afterlife is measured in Jeremy Bearimy, since in both the bad place and the good place time is not linear, but cyclical and describes curves.
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When fans ask One Piece writer 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. When someone asked him how Gomu-Gomus convert into litres, Oda responded that you can't really put it in those terms but 1 Gomu-Gomu is about 10 "Fairy Tale Gomu-Gomus" which are each about about 10 "Funky Gomu-Gomus". 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.
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In The Cold Moons, badgers measure distances in rough equivalents such as a "badger leap", "frog's leap", and "fox's leap".
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Futurama uses the fonzie to measure coolness. It's a metric unit, with the most commonly-seen scale being the megafonzie.
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Adventures of Supergirl: The titular Kryptonian heroine mentions that her sister weighs 31 Sulls, but she is too busy at the time to calculate the equivalent in pounds.
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James May's 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".
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In Death Note, the Shinigami keep time in their own system, which we see as numbers floating above people's heads, which measure the time left until that person's natural death. These numbers are apparently not random: the author claims to have had a mathematical formula for converting between human and Shinigami timekeeping systems, but he's forgotten it.
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hololive: after several incidents of the group's members oversleeping and missing their scheduled streams, Fubuki started defining "measurements of oversleeping". 1 "Mio" is oversleeping by 1 hour, 1 "Shion" is 2 Mios, and 1 "baba" ("old lady" in Japanese) is 2 Shions.
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The Incredible Hulk: 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.
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Shadowrun measures the size of computer memory in "megapulses". That might be for the better, as when science fiction gives measurements for computer performance using proper units, it tends to get superceded by real-world technology way too soon.
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Grace in El Goonish Shive measures sadness in Seymours — using the "Jurassic Bark" episode of Futurama as a baseline.
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In Unsounded, the Old Tainish Language of Magic has lots of units of measurement to describe things like the quantities of Aspects involved in a spell, the dimensions of how the spell manifests through the Background Magic Field, and the volume of spellwork "code" for when it's enchanted into a First Material. Those units are quite important, since magic is very literal and Magic Misfires, like misstating the origin point of a spell, tend to involve the caster getting messily dissolved.
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Sagittarius: The Cabal measure distances using units of chrens.
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My Little Pony: Friendship Is Magic:
Pegasi measure the power of their wings in "wing power", which is apparently related not to their top speed but to the amount of wind they can generate at a fixed speed. A combined 800 wing power is both sufficient and necessary to generate a tornado powerful enough to suck water out of a lake and hurl it hundreds of yards into the air, all to get it to the Cloudsdale weather factory so they can make storm-clouds for the rainy season.
Ponies and others occasionally measure time in "moons" — which might just be another way of saying month, but this a world where the lunar orbit is perfectly synced with the sun, so who knows? It's basically a way for the writers to imply a great length of time (like a portal to another world that only opens for three days every thirty moons) without giving anything too specific. Moons apparently aren't converted into years, which implies that they don't have a set ratio of moons to years, but that still doesn't answer how long they are relative to anything.note  And this is if you’re not trying to tie it into the lunar calendar which uses the phases of the moon to mark time, which would make it all the more confusing.
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Doctor Who:
The Daleks measure time in "rels". Which, when we actually hear them using it, turns out to be exactly equal to one second. Canonically, a rel is 1.2 seconds.
"Planet of the Dead": The UNIT scientist discussing the episode's situation with the Doctor reveals that he named a unit of measurement for something after himself.
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According to The Hunt for Reactron, in old Krypton, distances were measured in "sesats".
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NationStates statistics are full of these, including "Pineapple Fondness Rating" for recreational drug use and "Milli-Stalins" for measurement of authorianism.
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The parsecs thing from Star Wars is parodied in Star Wreck, where the "twist of a maggothole" is expressed as megaparsecseconds (Finnish original) or googol-fluxoms (English translation). Neither of those make any sense.
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The speedometer in SuperTuxKart uses "tf/s". What are those? Tux feet per second?
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Battlestar Galactica (1978): According to its The Other Wiki article, the only distance unit that wasn't an Earth name was "metron" (1 meter). However, the fact something had the same name as an Earth unit didn't mean it had the same meaning as the Earth unit: "microns", for example, were time units in BG (as opposed to distance units on Earth).
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The John Carter of Mars stories have their own take on the metric system. In the series' Wikipedia article, distance units are as follows, from shortest to longest: sofad (11.68 inches), ad (10 sofads, 9.75 feet), haad (100 sofads, 10 ads, 32.44 yards), and karad (1,000 sofads, 100 ads, 10 haads, 36.92 miles). The difference is that the karad is based on the length of an arc-degree on the Barsoomian equator, whereas the real-life meter/metre was originally based on a ten-millionth of the length of the Earth's circumference from the Equator to the poles as measured through the Paris meridian.
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In Spelljammer, all ships and equipment are measured in space tons. We know it's not the same as a "groundling" ton. Unit Confusion in some sourcebooks raises to the level when it's not clear even whether a space ton is a unit of mass or volume. This may indicate the authors don't get units, but it may also be an intentional reflection of real-life naval usage. Depending on nation, year, and the other words in the phrase, a naval measurement with the word "ton" in it may reference a weight, mass, volume, or even a dimensionless quantity!
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In South Park, the official unit of measure for fecal mass is the couric, which is approximately 2.5 pounds.
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Rivers of London
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 "yap", a "yap" being the amount of magic need to make a small dog bark. Not just any small dog, mind you, but one specific small dog which had previously been exposed to magic and was known to react to it.
In The Furthest Station, he has also defined a scale to measure the "intensity" of a ghost, from a vague feeling in the air to easily mistaken for a real person. The unit of measurement is the annie.
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The world of Zemuria in the Trails Series uses rege/rige for centimeter, arge for meter, selge for kilometer, and torim for tonne.
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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).
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The Martian: Mark gets tired of calculating the power needs of his survival gear in kilowatt-hours per sol note Martian solar day, so he dubs that unit the "pirate-ninja". Defictionalization: Andy Weir comments in this interview that the team monitoring the Curiosity rover has started referring to watt-hours per sol as milli-pirate-ninjas.
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Star Carrier: The Turusch use units such as g'nyuu'm for time and lurm'm for distance. 12,000 lurm'm = 5 light-g'nyuu'm. Meanwhile g'ri is a unit used for mass, with several vessels in the America battlegroup described as massing more than 28,000 g'ri.
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Mario & Luigi: Bowser's Inside Story: Kilamoles
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The Zork series had a number of these. The only explicitly defined one was the bloit, which was defined as the distance the king's favorite pet can travel in one hour (Which caused much trouble when a king with a pet turtle died, leaving a successor with a pet leopard). Others, whose definition must be inferred rather than being explicitly defined, are the gloop (A measure of volume, apparently the amount of liquid that comes out when the container goes gloop) and the ugh (A measure of weight, apparently the amount of mass to make a man of a given size say "ugh" when lifting it).
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Star Control 2 references this:
Most of the time the alien races conveniently give you measurements and units in Earth units, but they apparently are doing this consciously. The Zoq-Fot-Pik mess up at one point:
Likewise the Slylandro, who have had extremely limited interstellar contact, are unaware of how to convert to Earth time units and use units based on the rotation of their homeworld: "Dranhasa" and "Drahn". You never actually get to scan their planet in-game so you can't calculate the durations either, but they correspond roughly to "few years" and "several millenia" respectively.
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Though it's never named, there obviously is a unit to measure one's strength in. In the games it's often referenced as B.P. (Battle Power), and the English dub of the anime just calls it one's "Power Level". In this system, the average human would rate 2-5 and a master martial artist would top out around 100. By the middle of Dragon Ball Z, the numbers we're dealing with are in the millions. According to Word of God, power and potential cannot be measured in numbers, and power levels become totally meaningless early on.
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The Underworld in Sword Art Online Alicization uses cels and mels in place of centimeters and meters.
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The Last Dragonslayer: Magical power in the series is measured in units called "shandars," named after the famous wizard Shandar. Devices called "Shandargraphs" can measure background levels of ambient magical energy, while "Shandarmeters" can measure the amount of shandars that certain acts of magic take to cast — it takes about 200 shandars to make a toad burp and 1000 shandars to boil an egg. All children in the UnUnited Kingdom are tested for magical aptitude with a national average hovering around 150 shandars. Protagonist Jennifer rated at 159.3 shandars, while her apprentice Tiger got 162.8; neither is able to perform magic.
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Star Trek: Voyager is fond of using the unit "isoton" for mass and explosive yield.
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On Gor, distances are measured in "passangs", which are 7/10ths of a mile.
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How I Met Your Mother had Barney spending a lot of money on suits, so much so that Future Ted told his kids that he spent a "crap-load" of money per year on suits. Later, when we see a flashback to Barney's job interview, he is offered "15 crap-loads" of money for a salary. This means that he spends roughly 1/15 the annual salary of an executive level position solely on suits, per year.
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Horizon Zero Dawn has the so-called "Turing Scale" for A.I.s. 1 Turing is defined as an AI that is indistinguishable from a human by the Turing Test. After the AI "VAST SILVER", measured at 1.38 Turing, went rogue, regulations were put in place to limit A.I.s to reach at most 0.6 Turing. However, out of necessity, both CYAN, the AI created by Project Firebreak, and GAIA, created by Project Zero Dawn, surpassed this limit. CYAN had around 0.61 Turing, but this had to be hidden, while GAIA surpassed the 1.38 Turing record. Of course, by the time GAIA was created, no one who could enforce consequences for breaking the 0.6 Turing limit was going to be around anymore.
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Handyman Saitou in Another World: "maderaca" is a unit of measurement used in the story. Morlock explains that the first ruler of Maderaca had a Gag Penis and its length was used as said measurement.
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In Quantum Vibe Huoxing (Chinese Mars) has its own names for the silver and gold grams used by almost everyone in the solar system as currency (yinke and jinke), and they measure time in huofen and huoke. In the second series the isolationist planet Zytemonde measures distance in "peters" instead of meters, though they still use SI prefixes.
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The Transformers of the eponymous metaseries have a staggering variety of not-at-all-internally-consistent Cybertronian units of length and time.
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In Dairugger XV, distances are measured in "space kilometers." Exactly how big a space kilometer is varies widely from one episode to the next.
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The following is a list of statements referring to the current page from other pages.

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Language Tropes
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Speculative Fiction Tropes
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