There is no one correct form of dimensional analysis. For instance is vertical distance the same kind of thing as horizontal distance? It depends on your application. For interior design, no, since placing an item of furniture on its side violates the rules of furniture arranging. In the cgs system, unlike the SI system, capacitance has the dimension of length; the unit of capacitance is the centimeter. That's because the cgs unit of capacitance is the capacitance of an isolated sphere with a radius of 1 centimeter. In SI, capacitance is ampere-seconds per volt, which makes a nice symmetry with inductance, which is volt- seconds per ampere. Multiply a capacitance by an inductance and you get seconds squared. Take the reciprocal of its square root, and you get a frequency, which is indeed the resonant frequency of the resulting circuit. (Just remember that that frequency is in radians per second, not hertz.) There was a major change in the foundations of SI last year. It didn't (intentionally) change the size of any unit, but it did subtly change what they were units *of*, and which physics equations were conjectures and which were true by definition. Consider the dimensionless fine structure constant, alpha. The speed of light in a vacuum switched from a measured value to a defined value (exactly 299792458 meters per second) in 1982. When I learned that the charge of the electron and the Planck constant were to also change from measured values to defined values, I complained to David Newell <https://www.nist.gov/people/david-b-newell> that this would implicitly make alpha a defined value too, and that that was cheating, since it's dimensionless. He patiently explained that in SI, unlike in cgs, alpha also depends on the permeability of free space, aka the magnetic constant, mu-nought. And that its value, then defined, would become a measured value with the 2019 change. (In cgs, mu-nought doesn't exist, i.e. it's a dimensionless unity.) That means that if alpha turns out not to be constant after all, but to vary over time or location, we're constrained to regard that as a change in mu-nought, rather than in the speed of light, the Planck constant, or the charge of the electron. But it's really all rather arbitrary. George Hart pointed out that torque and energy have the same dimensions, but aren't the same thing. The usual explanation is that the former is a vector and the latter is a scalar. Another way to look at it is that one newton-meter of torque means applying one newton of force at right angles to the center of rotation which is one meter away, while one newton-meter of energy means applying one newton of force over a distance of one meter in the *direction* of that one meter rather than at right angles to it. Torque and energy having the same dimensions implies that so do angular momentum and action. Angular momentum and action are unusual in that both are quantized. The same Planck constant applies to both.