The quarter (lit. "one-fourth") was used as the name of several distinct English units based on ¼ sizes of some base unit.
The "quarter of London" (Latin: quarterium Londoniense) mentioned by 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. 3qr. was a Flemish ell, 4 quarters were a yard, 5qr. was an (English) ell, and 6qr. was an aune or French ell. Each quarter was made up of 4 nails. Its metric equivalent was formerly reckoned as about 0.228596m, but the International Yard and Pound Agreement set it as 0.2286 exactly in 1959.
Weight
Tool chest with nett weight 2qrs3lbs (about 27kg).
The modern statutory definition of Imperial units, the Weights and Measures Act 1985 as amended by The Units of Measurement Regulations 1994, defines the quarter as a unit of mass equal to 28 pounds.
The quarter (qr.av. or quartier) came to mean 1⁄4 of a hundredweight: 2 stone or 28 avoirdupoispounds (about 12.7kg): this is its (only) statutory definition since 1993.
It is still used to indicate the weight of bells, whose weight are usually given in the form "cwt-qrs-lbs". cwt indicates a hundredweight (112 lb), so a 'quarter' is 28 lb.
Colloquial usage
In Britain and Ireland, "quarter" was also a common shortening of "quarter-pound," (113grams) when selling food by weight, such as sweets.
Volume
The Weights and Measures Act 1824 (5 Geo. 4. c. 74) declared that, for measures of liquids and unheaped dry volume, a 'quarter' equals eight bushels (64 imperial gallons (290.95L), where a gallon is defined as a volume of water weight ten troy pounds). The term pail is also used for this unit of dry volume. The 1824 Act delegitimised all previous definitions.
The Weights and Measures Act 1985 (as amended) no longer shows the quarter as a unit of volume: an 1825 quarter of wheat would weigh about 494lb (224kg), substantially more than the 1985 definition.
In measures of liquid volume at the time of Magna Carta, the quarter of wine was (originally) ¼ tun: 8 London bushels or 64 wine gallons (242.27L) . The tun was subsequently redefined as 252 gallons, and the quarter was effectively ¼ pipe or butt. The quarter of wine was a gallon larger than a hogshead: since the wine gallon was considered to be 231 cubic inches, the measure was 242.27 litres.
The ale gallon was 282 cubic inches, meaning the quarter of ale was 295.75 litres.
↑Ruffhead, Owen, ed. (1763a), The Statutes at Large, vol. I: From Magna Charta to the End of the Reign of King Henry the Sixth. To which is prefixed, A Table of the Titles of all the Publick and Private Statutes during that Time, London: Mark Basket for the Crown, pp.148–149. (in English)& (in Latin)& (in Norman)
↑"An Act for ascertaining and establishing Uniformity of Weights and Measures (17 June 1824)"(PDF). legislation.gov.uk. 17 June 1824. p.639,640. Retrieved 19 January 2020. Two such Gallons shall be a Peck, and Eight such Gallons shall be a Bushel, and Eight such Bushels a Quarter of Corn or other dry Goods, not measured by Heaped Measure.. (The date of coming into effect was 1 May 1825).
Cardarelli, François (2003), Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins, London: Springer, ISBN978-1-4471-1122-1.
Rutter, Henry (1866), "Measures of Length: III.—Cloth Measure converted into Metric", The Metric System of Weights and Measures compared with British Standard Weights and Measures in a Complete Set of Comparative Tables; also, Tables of Equivalent Prices under the Two Systems; and of Chinese and Indian Weights compared with Metric Weights, etc., London: Royal Exchange. (in English)& (in French)
Stockton, A.M. (1823) [Reprinted 1839], "Cloth Measure", The Western Calculator, or a New and Compendious System of Practical Arithmetic; containing the Elementary Principals and Rules of Calculation in Whole, Mixed, and Decimal Numbers Arranged, Defined, and Illustrated, in a Plain and Natural Order; Adapted to the Use of Schools, throughout the Western Country and Present Commerce of the United States, 4thed., Pittsburgh: J. Howe for Johnston & Stockton.
Wormell, Richard (1868), "87. Cloth Measure", Murby's Graduated Arithmetic, Specially Adapted to the Requirements of the Revised Code, London: Thomas Murby, p.68.