The Planck mass is 2 x 10 -8 kilograms. In ordinary life, and even in nuclear physics, Planck units can be a real nuisance. But in the grand scheme of things, units are not very important. They are arbitrary human conventions. As long as you stick with some choice or other you will do okay.
Many constants involves units of length, time, mass, temperature, charge and so on.
The numerical value of these constants depend on the units we use. The numbers would change if we used different units. Thus, though they certainly tell us something about nature, to some extent they are human artifacts. Some of them are numbers like pi, e, and the golden ratio - purely mathematical constants, which anyone with a computer can calculate to as many decimal places as they want. These tell us facts about nature that are completely independent of our choices of units.