I just bought the inverter from West and the directions were to "calculate" the fuse size but didn't say how. Maine sail's answer is the most logically put and understandable. When I do household wiring I base it on the wattage (amps X Volts). The calculation for the battery fuse was new to me. This was not 1 where the fuse size was given adn a call to West Marine resulted in "no information available"
Mike
If you use 2 GA UL 1426 105-C wire it has a 210 amp rating outside an engine compartment and a 178 amp rating inside an engine compartment but this is really to small for an inverter with an 1800 continuous rating as surge or intermittent use can be much higher.
At 1800 watts you are on the border of 2 GA and 1 or 1/0 wire however if this is a Xantrex XM 1800 it requires 2/0 wire and a run of less than 5'.
If you're total run is 8' or less, round trip, 2 GA will be marginal for loads nearing 1800 watts. If the pos & neg combined lengths are more than 11 feet you'll want to use 1/0 wire. This is for 1800 watts ONLY. Most inverters can surge to nearly double the constant rating thus manufacturers suggest larger wire such as 2/0 as Xantrex does on many of their 1800 +/- units.
1800 Watts at 10.5 volts = 171 amps of potential draw and the wire, and it's length, round trip, should ideally be sized to handle the full load (perhaps 3600 watts) even if you never plan to do that. What you are trying to do is sizing the inverter to the bare minimum, not the max rated, as ideally should be done.
I used 10.5 volts based on your battery, a Xantrex XM 1800 cut out of 10.5 volts, and how fast a single group 31 would sink to about 10.5 volts if supplying anywhere near 1800 watts.
Just six minutes of run time with a 1000 watt microwave (your may be smaller) will burn 8.3 amps. If you have a single group 31 deep cycle battery this is a fairly large portion of your usable Ah's. Most group 31's are about 110 Ah's. For good battery life you don't want to discharge a battery below 50% of capacity. So your usable capacity is now just 55 amp hours not 110 amp hours.
To further compound the issue, when out cruising, you will rarely if ever be able to recharge your bank beyond 80-85% of capacity without some very, very long engine run times. So now you have 85% of 110 Ah's which is 93.5 usable Ah's. 93.5 minus 55 (to a 50% depth of discharge) leaves you with 38.5 actual usable Ah's from a 110 Ah battery.
Six minutes of a 1000 watt microwave @8.3 Ah's is nearly 22% of your real usable battery capacity when you take in (SOC) state of charge and (DOD) depth of discharge.
Perhaps you have two group 31's as a house bank? If so just double the numbers above. Coffee makers run significantly longer and I have not calculated inverter inefficiencies into the equation..
Just food for fodder...
As I have mentioned before the best money you can spend is $200.00 on a good battery monitor like the Victron BMV-600. It will really help you understand your system and how it is working..
The bottom line is that you want to protect the wire, as close as possible of within 7" of the battery. This fuse should not exceed the ampacity of the wire while at the same time not blowing fuses.