According to the RAK itself, it's currently using 166.2 mA.

This is way higher than what I've seen people post about online who were using an external power meter. (They're ssying around 6 mA)

If it were to use 166.3 mA for 6 hours, it'd use about 1Ah, which would mean a 3Ah battery would not even last a full day. So I'm not sure where it's getting that number, but I'm highly skeptical.

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I wonder if that's because of the difference between being a router versus being just a standard client.

I would say monitor your power usage for a while and take the highest one you see and make a battery set that will last something like 72 hours with the highest draw you see so that you get a good buffer zone.

so 170ma*72hrs = 12,240mah (12.2A) or 5v*12.24a = 61.2wh

Any suggestions for a meter that can take measurents over time?

I only have an DVOA meter that gives me the current measurements.

I don't have any suggestions, no. Sorry about that.