Why is power density of RF waves measured in m2 or cm (Area) and not in cm3 or m3 (volume) ?

I mean aren't those waves travelling (radiating) in 3D space?

I am new to this topic so please pardon if there are any problems in the question.


This is sometimes called intensity, to avoid confusion with the power density of devices such as batteries and capacitors, where it is indeed measured in $W/m^3$. Radiation intensity on the other hand measures how much energy hits (or passes through) a unit of area per unit of time. This is the same as the energy volume density times the radiation's speed, so it is measured in:

$$J/m^3 \cdot m/s = J/m^2/s = W/m^2$$

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