As a complete novice, I had a similar revelation naively trying to derive one of Maxwell's mind-blowing insights connecting light to magnetism. It was well accepted that if you just divided the electric constant by the magnetic constant (in their respective inverse square force formulas), you end up calculating the speed of light. The units and numbers matched up nicely using old definitions and units. I wanted to see it soup to nuts in modern terms, but so much has changed not only in the definition of magnetism, but also new standardization of units, more accurate measurements of vacuum permeability... I just gave up. I'll take Maxwell's word for it.