Your 550D has a resolution of 5184 x 3456
That means that your max 360x180 resolution is around 11000x5500.
You can easy find out what your max resolution is if you know the FOV.
Lets look at a10mm fisheye like the Tokina 10-17mm at 10mm.
At
http://www.frankvanderpol.nl/fov_pan_calc.htm
You can see that a 10 mm fisheye on a Canon APS (1.5) gives you 87 degrees horisontal FOV in Portrait.
Your max resolution is now 360/87 = 4.13 x 3456 pixels = 14.300 pixels
Hans