The size of shot glasses varies greatly but the average shot is 1.5 ounces; and there are 8 ounces in a cup. Thus, you'll need about 5 shot glasses to fill a cup.
You can also buy "short shot" glasses or "pony shots" which are 1 ounce. Pony shots are commonly used with martinis, Manhattans, and Rob Roys.
In the news, South Koreans drink 13.7 shots of liquor per week on average, which is the most in the world. Find out how other countries hold their liquor at Quartz.