The quarter (lit. "one-fourth") is used as the name of several distinct English units based on ¼ sizes of some base unit.
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The "quarter of London" mentioned by the Magna Carta as the national standard measure for wine, ale, and grain was ¼ ton or tun. It continued to be used, e.g., to regulate the prices of bread. This quarter was a unit of 8 bushels of 8 gallons each, understood at the time as a measure of both weight and volume: the grain gallon or half-peck was composed of 76,800 (Tower) grains weight; the ale gallon was composed of the ale filling an equivalent container; and the wine gallon was composed of the wine weighing an equivalent amount to a full gallon of grain.
Length
In measures of length, the quarter (qr.) was ¼ of a yard, formerly an important measure in the cloth trade. 3 qr. was a Flemish ell, 4 quarters were a yard, 5 qr. was an (English) ell, and 6 qr. was an aune or French ell. Each quarter was made up of 4 nails. Its metric equivalent was formerly reckoned as about 0.228596 m, but the International Yard and Pound Agreement set it as 0.2286 exactly in 1959.
Weight
In measures of weight and mass at the time of the Magna Carta, the quarter was ¼ ton or (originally) 500 pounds. By the time of the Norman French copies of the c. 1300 Assize of Weights and Measures, this had changed to 512 lbs. These copies describe the "London quarter" as notionally derived from 8 "London bushels" of 8 wine gallons of 8 pounds of 15 ounces of 20 pence of 32 grains of wheat, taken whole from the middle of an ear; the published Latin edition omits the quarter and describes corn gallons instead.
The quarter (qr. av. or quartier) came to mean ¼ of a hundredweight: 2 stone or 28 avoirdupois pounds (about 12.7 kg).
Volume
In measures of dry volume, it was equivalent to the seam or 8 bushels of 8 grain gallons of 272 cubic inches.
In measures of liquid volume at the time of the Magna Carta, the quarter of wine was (originally) ¼ tun: 8 London bushels or 64 wine gallons. The tun was subsequently defined down 4 gallons to 252 and the quarter was effectively ¼ pipe or butt. The quarter of wine was a gallon larger than a hogshead. As 231 cubic inches were considered to make up a wine gallon, the measure was about 242¼ L.
The ale gallon was 282 cubic inches, meaning the quarter of ale was about 295¾ L.
Cardarelli also claims it can vary from 17–30 imperial gallons for liquor.