knowing the width of your existing tire you can reach your hands behind the tires with front wheels turned lock to lock and you can guesstimate how much space is there. Any additional width you add to that is divided by 2 on the inside where it may rub. Tire rack has the widths listed for the tires they sell.
I had 285/75R16's on my 02 F150 that no one said would fit without a problem using this method and they are giant tires comparatively. On that truck the one spot to check is the driver side wiring bundle along the frame. Ford didn't tuck it in well which you can do yourself.