Okay...according to the label on my machine it says "12v (and a symbol that is a line with three dashes under it) 6.67 A
That is probably the maximum draw your machine would achieve with maximum treating pressure and heated humidifier. Your needs are probably much less.
Here is how I would attach your problem. I find it easiest to think in watts when we are moving back and forth between 12v, 120v and other voltages. To help get you in the ballpark I'll give an example from my CPAP. I rarely use the heated humidifier (never for camping because of the amperage draw) and my treatment pressure is 11 cm. My CPAP takes power from a transformer rated 19v. I've also seem them at 24v. Based on my particulars I've worked out that my CPAP draws on average about .53 amp at 19 volts. Here is where I convert to watts. When voltage changes, amperage changes but watts stay the same, so:
19v x .53 amp = 10 watts (at 19 volts)
since watts stay the same I can calculate,
10 watts / 12 volts = .83 amps (at 12 volts)
or
10 watts / 120 volts = .08 amps (at 120 volts)
Watts are an instantaneous measure of how much electricity is flowing at any given moment.
----
The only way to tell how many watts your machine draws at your treating pressure is to measure. There is a little device that costs about $25 called a "Kill-a-watt." You can google it and can probably find one in your home town. You plug it into a wall outlet and then plug your CPAP into the Kill-a-watt. After one night you can look at the reading on the Kill-a-watt but it might be better to let it run for a week and divide by 7 to get your daily usage. The Kill-a-watt provides a readout in kilowatt-hours (KWH) which is the amount of electricity consumed by using 1000 watts for 1 hour. In my case after 1 week it would probably say something like .42 KWH. Multiply this number by 1000 to get watt-hours (420 watt-hours) and divide by 7 days to get 60 watt-hours per night. You're almost there . . .
To get your daily requirment in Amp-hours for a 12v system then you just divide the 60 watt-hours by 12 and you get 5 amp hours per night. Multiply the daily amp-hour requirement by the number of days you want to supply power for and you know your need. Let's say you want four nights of power for your CPAP. 5 amp-hour per night x 4 days = 20 amp hours.
Now you're really almost there . . .
If you are going to use a lead-acid battery (car battery, deep cycle marine, golf-cart or jump starter) people generally recommend that you not plan to regularly draw the battery below 50% which means you should double your estimated need when sizing the battery, so in my example I would need a battery rated at about 40 amp-hours or greater.
I know that sounds complicated so if you follow this 1 week testing process and simplify all of the calculations you get:
Battery Needed (in amp-hours) = Reading from Kill-a-watt (in KWH) x 24 x number of camping nights desired
which, for my example with a 7 night test would be
.42 KWH x 24 x 4 days camping = 40 amp-hour battery needed.
Remember that if you run through an inverter you lose some efficiency so, to be save bump the estimate up by 10 to 20%. In my case at least a 50 amp hour battery is what I would be targeting. Also, it seems to me that at altitude, my CPAP works a little harder so a little extra is not a bad idea, not to mention that it's nice to have a little extra power on hand to charge a camera battery or cell phone.
All that seems overly complicated and I'm almost embarassed to post this but, at a minimum, beg, borrow or buy a Kill-a-watt, run it a week and post the result here. Any number of people can walk you forward from there.
Hope this helps. For years I only camped in state parks in the "water and electric" section so I could run an extension cord to my CPAP. Last year I bought a little tent camper and put together a battery system. Now I can camp for up to about a week anyplace I choose. Good luck.
