How much battery capacity do I need for my Arduino tank?

What voltage are you running the motors at?

from the spec sheet:

At 3VDC we measured 150mA @ 120 RPM no-load, and 1.1 Amps when
stalled
 At 4.5VDC we measured 155mA @ 185 RPM no-load, and 1.2 Amps when
stalled
 At 6VDC we measured 160mA @ 250 RPM no-load, and 1.5 Amps when
stalled

Also, do you have an idea of how much the bot will weight and how fast you need it to move?

The motors will be running at an average of 4.4 volts. The battery voltage ranges from 8.4v to 6v and the L298n motor driver eats about 2.8v. So I used

 At 4.5VDC we measured 155mA @ 185 RPM no-load, and 1.2 Amps when
stalled

It will weight about 900 grams. The speed doesn't matter as long as it can move.

I see that. Likely a mistake but hopefully the OP also picked it up.

I think you misunderstood me. I used stall current because besides being the current a motor needs to start, it's also the maximum current a motor can draw when it's load is too heavy. Since I thought that the batteries had enough capacity to power the motors for long enough EVEN IF they were drawing stall current, is saw no need to calculate how much current the motors would realistically draw.

I don't agree with You. No DC motor will survive working at that current for maybe more then fractions of a minute. Don't run the motor at such conditions. It will burn.
Read the datasheet for maximum continuos load and stay below that. No need to calculate for much higher currents and end up with a much larger battery.

Ended up getting 2x1800 mAh batteries to be really really safe and they had way more capacity than I needed, as excepted.

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