We describe a refinement of Ozsvath and Szabo's mapping cone formula for Hendricks and Manolescu's involutive Heegaard Floer homology. We will discuss our involutive mapping cone formula, focusing on several key algebraic properties which allow for efficient computations for knots in S^3. We will then discuss an application to the homology cobordism group. This work is joint with Kristen Hendricks, Jen Hom, and Matt Stoffregen.