How is rainfall measured?

The measurement of flowing water is most commonly done in m^3/ min or litres per minute or in layman terms, volume per unit time.

Rainfall is evenly distributed over a given area. i.e. Directly beneath a cloud having an area of 3 square meters, the rainfall per square feet is the same for a square feet region anywhere within the silhouette cast by the cloud on the ground.Therefore, the level of increase of water in a jar/ test-tube or any other water collecting device, irrespective of the area of the device remains the same and this level measured for a particular span of time gives the mm per day information of the rainfall received.When they say rainfall reported for the day is 20 mm, they mean to say that if a huge pitcher is kept in the rainy area for the entire day, the vertical level of water collected in the pitcher would be 20 mm high. Later volume can be found by multiplying the mm of rainfall received with

area of the collector device. 

Au contraire to my intuition, the level of water rise in a small test-tube and the level of water rise in a beaker is the same in the rains. Intuitively I thought, test-tube would fill faster than the beaker but then I realized that also the number of drops falling in the test-tube is quite less compared to that of a beaker.

Generally a precipitation rate of 1-4 mm per hour is considered moderate rains, 4-16 mm per hour is considered heavy rains, 16-50 mm per hour is very heavy and over 50 mm per hour is extreme rains.