Watt Hours are a unit of watts multiplied by hours. Watts *per* hour would be a unit of watts *divided* by hours, which would obviously produce a very different result.
We are more familiar with the phrase “per hour” because we commonly use it to measure speed in miles or kilometers per hour. But you might have heard a comparable unit to Watt Hours used in a business setting when people talk about man hours. The idea being if ten people worked on a task for a 40 hour businesses week, then the task was completed in 40 hours but took 400 total man hours to complete (i.e. it would theoretically take 400 hours of work for one person).
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