what is the largest tire i can put on my 2010 wrangler unlimted without putting on a lift kit

not really so maybe a 31 or 32 inch but you could also do a body lift like a 2inch body lift and then you can go alot bigger you could get 32s or a little higher

33" s are my best guess but it all comes down to your gear ratios and intended usage

31's on a JK, you don't want a 2" body lift as stated above, basically you'll be left with a heightened COG (center of gravity) and unusable lift. Body lifts are only to allow you to get extra clearance for tires. 31x10.5/(rim size) will fit and tuck well on your JK with stock suspension. If you flat/tube fender the front and load corner guards on the rear, bit of trimming you can fit up to 35's on 2" or less. The Lower Forty Jeep was modified with no lift whatsoever and is running 40's but you'd have to be capable of a lot of custom fab type work. If you just want the biggest tires possible on stock suspension without tweaking the exterior appearance or trimming etc. go with 31's. The factory wheel backspacing will be more than enough so that the tires won't rub, though that slightly varies depending on the type of tire. I had 31x10.5 on my TJ when it was stock and I didn't rub even at full lock. Am currently running 2.5" OME on the suspension with 35x10.5 Super swampers. By keeping it low you're able to creep up steeper inclines, versus bouncing on heightened degree incline climbs like you would with 4+" of suspension lift.

with my 2inch body lift and 2 inch suspension lift it hasnt efected my center of gravity one bit i go rock crawlin all the time up roush creek in pa ive been up inclines to where ive only had 3 wheels on the ground and ive had my jeep on more then a 45 degree angle so just doin a 2inch body lift doesnt effect your center of gravity