> because so many people get this wrong.
All these terms are just so unintuitive for a mere mortal like me.
Energy? Power? The difference between those two words has as much importance to the common person as the difference between "empathy" vs "compassion", or "theory" vs "hypothesis", or "less" vs "fewer".
kW being a "stuff over time", but kWh being "amount of stuff"? I don't doubt the math checks out if you expand all units, but I'm as dumb as a wet rock so it took me a while to get this.
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If people wanted me to understand this way sooner, they should have started asking me to think in terms of "kcal" (kilocalories).
At least I know that kcal is an "amount of stuff" because it's something you hear if you talk about food. And there's no mention of "hour" anywhere in the name (like with "kWh"), so the name doesn't have anything misleading.
Then just tell me that "860.421kcal/h = 1kW" (the numbers don't really matter), and ask me to solve for kcal.
When I move the "h" from the left to the right, and the equation becomes "860.421kcal = 1kW * h", everything will click.
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Food has kcal, so kcal is something that can be stored. When the equation has "kcal" on the left, it has "kW * h" on the right, so that means batteries store "kW * h".
When I think of "kW" alone, I will remember that the "* h" moved to the left side and became "/h".
I might forget stuff, but I know what food is, and I know that there exists an equation, at one side there's "kcal", at the other side there's "kW", and there's an "h" somewhere in there.
And "kcal * h" will look wrong af, so I will remember that if the "h" at the left side, it will be "kcal/h".
Result: Now I have an intuition for this.
(EDIT: Escaping, and add some separators to hopefully make the comment easier to read.)