1 Cup [US] = 0.25 (1/4) Quart [Fluid, US]
1 Cup [US] = 0.21484175 Quart [Dry, US]
1 Cup [Metric] = 0.22 Quart [UK]
There is a quarter (1/4 or 0.25) fluid quart in a cup, because from the smallest to the largest units between cup to quart, cup is a half (1/2) of a pint and pint is half (1/2) of a quart, that makes 1/2 * 1/2 = 1/4 quarts in a cup.
For example, to calculate how many quarts there are in 12 cups, multiply the cup value by the conversion factor, 12 cups * 1/4 (qt in 1 cup) = 3 quarts in 12 cups.
Cup is a metric and US customary volume unit. The imperial and Canadian cups are replaced by metric cups. 1 metric cup is 250 ml (1/4 litre), 1 US cup is 236.58 ml, 1 imperial cup is 284.13 ml and the Canadian cup is 227.3 ml.
Quart is an imperial and US customary unit. 1 US fl. quart approximately equals to a liter (1 L is 1000 ml and 1 US fl. quart is 946.3 ml). US dry quart is 1101.2 ml. Imperial (UK) quart is the largest and equals to 1136.5 ml. 1 Imperial quart is 1.2 US fluid quarts. The abbreviation is "qt".