Forget the Hz - it has no impact on "power". (It's merely the frequency AC equipment operates at. Stateside uses 60Hz because they're stuck in older imperial units whereas most of the civilised use 50Hz being metric (full wave rectified is 100Hz, hence a hekto-Hertz or deci-kilo-Hertz) - but ignore everything in these parenthises - I'm just stirring and it will just confuse the innocent.)
Yep - 120V @ 1A means about 10A @ 12V (both are 120W).
I say about because you can probably add ~20% inefficiency - the inverter may need 12A input.
(Inverter input should be less for higher input voltage. IE - if your car is charging at 14V, then 10A is 140W which might be enough for a 120W AC load. If running off the battery only and it supplies 12V, 140W/12V means 11.7A compared to 10A@14V. That's the fun of
constant power loads.)
And the pump's 120W figure is useful. It means you want at least a 120W output inverter.
But a pump is a motor and that probably has a high inrush current.
Some 120W inverters will handle 120W motors. Some bigger inverters won't.
[Then again - maybe the 1A is a PEAK current - it may only be typically 0.5A = 60W.
And I'm ignoring "power factor". I'm assuming 120V @ 1A is 120W. It's really 120VA (literally 120 volts x 1 amps = 120 volt-amps = 120VA) which may mean 100W or less. The above are fun things called "power factor" (pf = W/VA) and rating plates. Stick to DC - you still have rating plate issues (and dangers interrupting high currents), but no power factor issues, and no under-informed stating "pf is cosΦ"....]
My method would be:
- consider a 12V pump (if the AC pump is the only "big" AC load you have)
- consider a portable battery pump. I have one that cost ~$45 and it probably pumps for ~30 minutes. I use it for an inflatable 3m (3 person) boat. Handy for inflating mattresses in the middle of the night because all inflatable mattresses deflate (if camping).
- for a 120W AC pump, a 150W inverter may suffice. Normally I double the expected load - hence a 240W = 300W inverter.
A 300W inverter isn't bad. They are fairly common and cheap these days. (My last inverter was a 600W for $89.)
And most inverters have double their rating for surges (ie, my 600W has 1200W surge) though those figures can be vague and are arguably
inherent in the design -a bit like 300W RMS audio power means a
guaranteed 600W "music" power).
That might handle motor inrush currents. Might.
I'd suggest a 300W inverter for your 120W pump. But maybe a good 150W will do.
As to efficiencies, there probably isn't that much difference between the sizes. There use to be, but not now with modern techniques etc.
Most inverters seem to have (say) a 0.6 to 1.5A idling current (on but no load; this includes 2kW inverters).
And although supplies (inverters, fuses etc) are often
designed for operation or best efficiencies at 70%-90%, the low utilisation efficiency isn't that bad (maybe 60% or 70% efficiency at 10% load compared to 80-90% nearer full load) Besides, often larger inverter have larger components and cabling hence less resistive losses than a smaller inverter for the same load..... Poo like that drives many implementors nuts! And my readers.
Now, if you could bring the pump to test the inverter... (A few times - there is a difference between switching on a motor near an AC zero crossing as opposed to the AC peak voltage... And switch off too - the reactive "off" spike can blow inverter outputs.)
By the way, if anyone assures you that "their" inverter will power "whatever" load, then they shouldn't object to a few trials with "whatever"... (Private sellers ok, but not retailers...)