how are the units for physical constants determined?

Question

It seems like the units for the constants are determined just by cancelling units in the equation that aren’t wanted in the answer. This seems unscientific to me though so it feels like there must be a more thorough way

In: 5

Answer 1

Basically we have a couple(7 iirc) of fundamental measurements that, while arbitrary in magnitude, are based of things we currently assume constant, such as the speed of light. Examples are the second, the meter and the kilogram. All other measurements, while they might have their own units, are then combinations of these 7 arranged to be easily legible.

For instance, properly measuring power using fundamental measurements leads to an equation with kilos, squared meters and seconds to the power of -3. This is not intuitive at all, and the solution is then to define a unit of power and name it after a famous scientist, e.g. defining a watt as W=kg(m^2)(s^-3).

While you could call this arbitrary canceling, it is in reality a rearrangement of fundamental constants to make physics more understandable using purpose-made units instead of the fundamental ones.