Etymology
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capacity (n.)

early 15c., "ability to contain; size, extent;" also "ability" in a legal, moral, or intellectual sense, from Old French capacité "ability to hold" (15c.), from Latin capacitatem (nominative capacitas) "breadth, capacity, capability of holding much," noun of state from capax (genitive capacis) "able to hold much," from capere "to take" (from PIE root *kap- "to grasp").

Sense of "power to store electricity" is from 1777; industrial sense of "ability to produce" is from 1931. Meaning "power of containing a certain quantity" is from 1885, hence "largest audience a place can hold" (1908).

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measure (n.)

c. 1200, "moderation, temperance, abstemiousness;" c. 1300, "instrument for measuring," from Old French mesure "limit, boundary; quantity, dimension; occasion, time" (12c.), from Latin mensura "a measuring, a measurement; thing to measure by," from mensus, past participle of metiri "to measure," from PIE root *me- (2) "to measure." The native word was Old English cognate mæð "measure."

Meaning "size or quantity as ascertained by measuring" is from early 14c. Meanings "action of measuring; standard measure of quantity; system of measuring; appointed or allotted amount of anything" are from late 14c. Also from late 14c. are the senses "proper proportion; balance." Sense of "that to which something is compared to determine its quantity" is from 1570s.

In music, from late 14c. as "air, tune;" 1570s as "rhythmic pattern." Specifically as "a group of tones indicated between two primary beats" is from 1660s. From mid-15c. as "rhythmic pattern in poetry;" c. 1500 in dance. Meaning "treatment 'meted out' to someone" is from 1590s; that of "plan or course of action intended to obtain some goal" is from 1690s; sense of "legislative enactment" is from 1759. Figurative phrase for good measure is from good measure as "ample in quantity in goods sold by measure" (late 14c.).

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measure (v.)

early 14c., mesuren, "to exercise moderation;" mid-14c., "to deal out or divide up by measure," also "to ascertain spatial dimensions, quantity, or capacity of by comparison with a standard;" from Old French mesurer "measure; moderate, curb" (12c.), from Late Latin mensurare "to measure," from Latin mensura "a measuring, a measurement; thing to measure by," from mensus, past participle of metiri "to measure," from PIE root *me- (2) "to measure." The native verb is mete. Intransitive sense of "to be of a (specified) measure" is from 1670s. To measure up "have the necessary abilities" is 1910, American English. Related: Measured; measuring.

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half-measure (n.)
"incomplete effort," 1798, from half + measure (n.).
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omer (n.)

Hebrew measure of capacity (a little over 5 pints), 1610s, from Hebrew 'omer.

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liter (n.)
unit of capacity in the metric system, 1797, from French litre (1793), from litron, name of an obsolete French measure of capacity for grain (16c.), from Medieval Latin litra, from Greek litra "pound" (unit of weight), which apparently is from the same Sicilian Italic source as Latin libra (see Libra).
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dimension (n.)
Origin and meaning of dimension

late 14c., dimensioun, "measurable extent, magnitude measured along a diameter," from Latin dimensionem (nominative dimensio) "a measuring," noun of action from past-participle stem of dimetri "to measure out," from dis- (see dis-) + metiri "to measure," from PIE root *me- (2) "to measure."

Sense of "bulk, size, extent, or capacity" is from 1520s, Meaning "any component of a situation" is from 1929. Related: Dimensional; dimensions.

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gallon (n.)
English measure of capacity (containing four quarts), usually for liquids, late 13c., from Old North French galon, corresponding to Old French jalon, name of a liquid measure roughly equivalent to a modern gallon," which is related to (perhaps augmentative of) jale "bowl," from Medieval Latin or Vulgar Latin diminutive form galleta "bucket, pail," also "a measure of wine," a word of unknown origin, perhaps from Gaulish galla "vessel."
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quart (n.)

liquid measure of capacity equal to one-fourth of a gallon, early 14c., from Old French quarte "a fourth part" (13c.), from Latin quarta (pars), fem. of quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

Compare Latin quartarius "fourth part," also the name of a small liquid measure (the fourth part of a sextarius), which was about the same as an English pint.

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bushel (n.)
early 14c., measure of capacity containing four pecks or eight gallons, from Old French boissel "bushel" (13c., Modern French boisseau), probably from boisse, a grain measure based on Gallo-Roman *bostia "handful," from Gaulish *bosta "palm of the hand" (compare Irish bass, Breton boz "the hollow of the hand").

The exact measure varied from place to place and according to commodity, and though in 19c. in Britain it acquired a precise legal definition, it varied in U.S. from state to state. Used since late 14c. loosely to mean "a large quantity or number." From late 14c. as "a bushel basket." To hide (one's) light under a bushel is from Matthew v.15.
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