We present results for levels in 36 K (the mirror of nucleus 36 Ar) that are used in rp reaction rate calculations. The levels are also determined from the Isobaric Mass Multiplet Equation and the binding energies of the T=1 analog states as a check on the assignment of spins and parity. Where the analog states are not known the levels are calculated with two-body interactions that use the sd-shell interactions USDA and USDB as the charge-independent parts, with a Coulomb, chargedependent and charge-asymmetric Hamitonian added. The gamma-decay lifetimes and 35 Al to 36 K spectroscopic factors are calculated with the same interactions, and together with experimental information on the levels of excited states, are used to determine the 35 Ar(p,γ) 36 K reaction rates.