Why are Watt Hours not Watts per Hour? Are they the same thing?
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Watt hours is multiplying power and time to give an energy: it’s energy divided by time (power) times time, to give energy.
When we say “<something> per <something else>”, it means the first thing divided by the second. So watts per hour would have units of energy divided by time *squared* and would be something like how fast some power is changing. It’s basically going the opposite direction of watt-hours.
A nice analogy that might help is thinking about energy as being like distance. In that analogy, power is like distance per time, or speed. To get total distance from some speed, you need to multiply the speed (power) by how long you have been going that speed (time) to give total distance. Watt-hours as a unit would be kind of like mph-hours or something. It sounds weird, but it’s just a distance. Speed per time is an *acceleration* in this analogy and tells us how fast our speed is changing. Acceleration has units of distance per time squared, just like watts per hour would have units of energy per time squared and would tell us how fast some power is changing.
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