How to determine padding between copper pours on custom PCBs

Hi, I'm building a project which requires 15V, and a lot of current, for 4 motors. I'm trying to make a control board to contain the arduino and motor controllers all on the same board.

When working with these relatively higher voltages, I have to wonder, how much distance between two copper pours or opposite polarity will it take to make an arc? Is this something I should even worry about at 15V? I certainly don't want a short circuit with the kind of current I'm using.

I do not understand what you are asking.
At 15 V there is no chance of arcing at very low separation distance.
As far as current carrying capacity is concerned there ar many online calculators available.