26 x 1.5 is the approximate tire size, 36 is probably the number of spokes. The bead seat diameter is 559 (millimeters), but what you need to know is the ERD: (from Sheldon Brown)
Effective Rim Diameter. This is the rim diameter measured at the nipple seats in the spoke holes, plus the thickness of the two nipple heads. The E.R.D. is needed for calculating the correct spoke length.

The only way to find this on your rim is to measure it. Then you'll have to shop for a rim with the same ERD.