Power is traditionally expressed as Watt(s) (W) but you can of course convert into any other unit of power.
If my A/C unit is rated at 3000 Watts (meaning it can consume 3000 Watts under full capacity) it can also be expressed as being rated at 3 kW (kilo Watts).
Horsepower is just another unit of power (1 horsepower = 746 Watts).
That means that a 3000 Watt A/C unit has around 4 horsepower.
I think everyone else has covered how to convert horsepower to other types of measurement. I can tell you the why part. It’s a marketing trick. They want people to think it’s a powerful machine so they use horsepower because people connect the idea with powerful cars or heavy equipment. It sounds better because it makes people think about how much power it’s going to put out. If you were to use watts people would instead think of the power being used and associate it with paying the electric bill. Emotional context is a big part of getting people to buy one brand over the other. They may be the exact same machine with a different label, but one machine has 4 horsepower and the other uses 3000 watts. Even though it means basically the same thing and the machines are identical people are going to buy the one that makes them feel better about the purchase.
The manufacturer can’t make any promises about how much air their device will deliver, or how cold that air will be, because that depends a lot on the current temperature of your room, the humidity, altitude, position of the unit, and a bunch of other factors that they cannot possibly know. All they can do is say, “when you plug it into the wall, it uses this much power.” The primary working component of your A/C is basically just an electric motor, and motor power is typically advertised in horsepower.
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