I come here as "a new kid" to soak up knowledge from people who gained that knowledge from their own blood, sweat and tears. That leaves me in a position with very little to give back. When the opportunity comes up, usually off topic, although in this case it is kinda related...
You should stop there. It "could" be, however small air compressors tend to get rated a lot the same as vacuum cleaners. The shop vac type in particular. I've got a 6 horsepower one in my basement that plugs into a 15 amp outlet and gives no trouble. That does NOT compute. Even pushing limits, that does not compute. A 6 horse motor, with no belt, no load, not even a pulley on it to slow it down, that won't start on a residential outlet. The 20 amp breaker will trip the instant the switch closes. What they've "actually" done is let the advertising department cherry pick the technical details to make up good sounding things. So it's rated the "peak" horsepower. That is, they took the inrush current, which is essentially a dead short circuit, while the motor is "stalled" and before it gets enough rotation to start working properly... And converted that "short circuit current" into horsepower, and called it that. The actual motor weighs less than four pounds and could not, on it's best day, run at one horsepower, let alone six. But it's fine for a vacuum.
Compressors are bad, but not that bad, but their horsepower rating is not a "fair" one unless you bought a loose motor to put on it, that came with it's own rating. DO NOT use that as a reference. If anything, use the Full Load Amps (FLA) from the data tag, and reverse engineer a proper horsepower rating for it if you want "some" kind of comparison. But they're overrated. Shot in the dark, from what I've seen, I'd guess your compressor's amps put it closer to one horse. Maybe three quarters, but probably one. (And that's all you needed.... Don't let that darken your day of you do go look at the nameplate, the compressor is fine, it's plenty to run a small compressor, it just leaves you with a skewed impression of the rest of the world. Even if they're overrated, small compressors almost ALWAYS come with enough motor to burn up the pump. It's not the weak link.
I do like your approach however. When the math and ratings get overwhelming, comparing to "known good", while NOT a stamp of approval (because issues like this come up all the time), it is a very good "reality check" to let you know when you're calculations or assumptions have gonee off the rails. When you explore new things, sometimes stuff does go off the rails. I can vouch for that.
