A Latin term (Gr. noummion) originally meaning “coin.”
In 307, Constantine introduced a reduced size and weight silver plated follis (nummis). Constantine also introduced a new diademed portrait. Over the fourth and fifth centuries the nummis was continually reduced and also debased until the silver plating disappeared. Different denominations were issued but we often do not know what they were called by the Romans and often different size coins were the same denomination, just again reduced. We don't know with certainty the ancient names or values of many of the late Roman bronze coins and refer to them with designations based on size.
AE1 = c. 26 mm - 30 mm. Sometimes called the maiorina, sometimes a double-centenionalis.
AE2 = c. 20 mm - 26 mm. Sometimes called a centenionalis. At first it was a coin about 22 mm - 26 mm and weighing 4.9 - 6.1 grams, but later--the "reduced centenionalis" was 20 - 22 mm and about 3.0 to 4.7 grams.
AE3 = c. 17 mm - 21 mm. Early examples are sometimes called a Nummus, later ones sometimes called a half-centenionalis, they are about 18 - 22 mm and until about 325 C.E. weighed about 3.0 - 3.5 grams. From about 326 - 336 it weighed only 2.5 - 3.0 grams. After Constantine divided the Empire between his sons and half-nephews, 337, the coin was further reduced to what we call AE3/4 or AE4.
AE3/4 = c. 15 mm - 18 mm. Also sometimes called a nummus These are 15 - 18 mm and weigh about 1.4 - 2.0 grams.
AE4 = less than 17 mm. Properly called nummus minimus, but also called a nummus, a small coin, heavily leaded, and devoid of silver. Initially these coins were 13-16 mm and 1.3 - 1.7 grams but declined in the late 4th and 5th centuries to where they are only 9.5 - 12 mm and 0.7 - 1.0 grams.
The designation or denomination of these coins is based on the usual size for the type. The coins were handmade and the same type can vary significantly in size. Some individual coins that are larger or smaller than usual for their type will be outside the parameters above.