The world we know has many measurement systems. The most prominent are SI units (kg, m, s) and US customary units (lb, ft, s), but there are many others, up to and including the FFF system (furlong-firkin-fortnight). None of them, with the possible exception of Imperial measurements (lb, ft, s, but with different definitions to the US), are particularly suited to Middle-earth.
So: is it possible to design a measurement system which could be used in Middle-earth? For example, one defined entirely in Quenya?
Of course it is. Welcome to Netilardo. :)
There are seven basic SI units - s, m, kg, A, K, mol, cd - and while it is perfectly possible to build a system on a different foundation, they're probably the best basis to start from.
Length: Far and away the easiest unit. Tolkien directly defines a useful base unit in Unfinished Tales.
1 ranga = 38 inches. The 'Númenórean yard', measuring the length of a full-grown Númenórean man's stride.
5000 rangar = 1 lár. A 'league' of approximately 3 miles. Plural: lári.
Time: The only other unit precisely defined by Tolkien, though not in an entirely useful form.
1 coronar = 365 days, 5 hours, 48 minutes, 46 seconds. A solar year, as defined in Appendix D. Plural: coronari.
More useful units are the lúmë (hour, plural lúmi) and the ré (24 lúmi, 1 day, plural ri). Useful only in specific contexts is the yén (144 coronari, plural yéni).
Weight: Tolkien did not define a unit of weight. However, he did provide a unit of currency: the Gondorian Mirian, or silver penny. 'Mirian' is Sindarin, but can be translated into Quenya:
1 mírim = approx. 1.555 g, or precisely 1/20 Troy ounces. Plural: mírimi. This is the obsolete English pennyweight, which did indeed mean the weight of one silver penny. Following the example of 'pounds', I am allowing a single word to serve as both currency and weight.
1/24 mírim = 1 milin. The English pennyweight is 24 grains, and Tolkien kindly provided a word of the same meaning. Plural: milini.
Luminous Intensity: The unit people are least familiar with, a candela is a measurement of how much light an object puts out. Obviously, Tolkien has a lot of light-emitting objects, but the best one to use as a unit is:
1 lícuma = 0.981 cd. 'Candle'. The candlepower is another obsolete English unit. Plural: lícumar.
Temperature: A tricky one. Tolkien doesn't give us the words for temperature, so the best way to go seems to be to return to the definitions of our degrees.
1 miculallo-welelanna = 100 °C (or K). A Quenya phrase meaning 'from freezing to boiling'. This is not terribly satisfactory, particularly since 'wele' is an early Qenya verb, and may not even be valid in late Quenya. But it's the best I can do. Plural: miculallo-welelannar.
Quantity of Substance: I'm still not convinced that the mole is really a unit, but the SI says so. We can't translate it, since the word derives from 'molecule'... but we can be silly.
1 noldare = 6.022 140 76×1023. Early Qenya for 'mole' (ie, the small animal). Plural: noldari.
Current: There is no Quenya base unit of current, or anything relating to electricity; most electromagnetic units are people's names, which makes them impossible to translate. However... electrostatic units provide a way in. The franklin, or electrostatic current unit, is equal to about 3.3 x 10-10 coulombs - and is defined in terms of electrostatic force. It is equal to 1 g1/2 . cm3/2 / s2, and with a little unit juggling, we can conjure up an amps/Quenya translation:
1 ranga3/2.mírim1/2 = 0.0118 A.
Information: "But information doesn't have an SI unit!" No, it doesn't. But in this world of computers, we all spend a lot of time dealing with bits and bytes, so it seemed only appropriate.
1 notesset = 1 bit. 'Natural pair of digits'. This would normally be a nonsense term in Quenya - numerals don't form a natural pair, because there are 10 or 12 of them. The only way it makes sense is if you're thinking in binary, and thus, the bit.
1 toldo = 1 byte. 'Eight'. The bit > byte pun doesn't work in Quenya, but an 8-bit byte is also known as an octet. We shall simply have to trust our Quenya-speaking IT managers not to confuse 8 (the number) with 8 (the unit).
Magic: "But magic doesn't have units!" Incorrect! The magnificent Sir Terry Pratchett has provided two: the thaum (the amount of magic needed to create one small pigeon, or three billiard balls) and the much more useful prime (the amount needed to move one pound of lead by one foot).
1 milin.lár (canu) = 2.2 prime.
It would be possible to define other units. For example, the phrase 'poldore rocco' translates as 'strength of a horse', so could be used to mean 'horsepower' (the Imperial horsepower is around 745.7 watts). But the units above have a much firmer foundation in Tolkien, and so should be preferred.
A few common or familiar values and units, translated into QMS:
The speed of light (ca. 3 x 108 m/s) = 2.2 x 108 lári/lúmë.
1J = 358 mírim.lár2/lúmë2
1 food calorie = 2 milin.lár2/lúmë2
50 mph = 16.7 lári/lúmë.
1 sievert = 0.55 lári2/lúmë2 (unit of radioactivity)