Prius inverter?

To get 375 watts out at 110v you have to put 375 watts in at 12 v (plus a little for losses). Right?

The 12 volt DC input circuit must be able to handle the amps produced on the output 110 AC voltage. So in this case the inverter would be connected to a 12 volt power supply with a 5 amp fuse. Because the output of the inverter is only at 3.4 amps.

Tester

Wattage into the inverter must equal wattage out of the inverter (ignoring losses for the moment).

Going into the inverter: 31 amps @ 12v = 375 watts.
Going out of the inverter: 3.4 amps @ 110v = 375 watts.

The input amperage to the inverter will actually be around 35 amps, because those devices have an efficiency around 85%.

This same thing (equal watts means higher amps at lower voltage) is why you don’t have to change out the wiring when converting a 6v car to 12v. The wiring is already bigger than it needs to be to handle the lower amps of a 12v system.

I have run my mobile office with a 400 watt inverter. It ran a printer and a laptop. I now have 1000 watt inverter. Its wired to a power point thats strait off the battery. I have powered a 20" TV and a DVD player or my DTV receiver off it. As for Drill battery chargers some work some don’t. You will have to run the car. So in your case a small gen-set is what you will need to build with.

As cool as it might be to want 110v from your Prius, after all what is it but an expensive rolling genset, I would strongly advise against hacking the car’s electrical system.
You will certainly void the warranty, the reason Toyota won’t do it. Even if the DC/DC converter is rated 100a I doubt it is designed for sustained 100a loads, about what you can expect from a 1000w inverter. Even if it is designed for that load connecting directly to the battery might bypass some of the safety features. Like the cooling fans for the solid state controls. I suspect the Prius accessory outlets are deliberately designed to be off when the car isn’t running for just that reason. Inverters are inefficient. You are converting 288DC to 12DC to 110AC then back to something between 7 and 20 DC. Better IMO to divide and conquer. For your driving needs look into adding a second 12V accessory outlet. The Toyota dealer might even give you the OK. If you want to be creative look to the barn. Set up a 12v system there. Buy small generator to charge one or more deep cycle batteries or build one from a salvaged alternator, or try a solar charger. You can get 12v chargers for most cordless tools and run some lights and a sound system.

The basic relationship between power, volts and current for DC and single phase resistive loads is given by the formula P=IE or Watts = amps x volts

Trying to power up an all-electric camp site with your Prius’s starting battery is insane. You will have power for about 10 minutes before the battery voltage drops to below 11 volts and the inverter kicks out…The 12 volt power supply system in the Prius will not take kindly to continuous heavy loads for which it was not designed…It might give you 250 extra watts (20 amps) to play with but you are on thin ice after that…

If you are going to go ahead with this, then install a group 27 deep-cycle battery (100 amp hour) in the trunk using an R/V battery isolator to connect it to the existing starting battery…

Here’s what you need (lots of different brands):

Those things are quiet, light, and put out 1000 - 2000 watts, depending on the model.

A thousand watts for a couple of computers?How much does a IPad use?,you can get high capacity batteries for a lot of laptops and you can get some pretty impressive run time on some of this modern cordless power equipment.Dont monkey around with the electronics on that Prius-Kevin

Why not get a 12V DC adapter for your daughters laptop to charge as needed? Same is true for all those devices you mention. It is rare you would charge all at once.