We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in $$\mathcal{N}$$ = 2, D = 4 gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in AdS ₄ which have an AdS ₂ × M ₂ near horizon geometry, where M ₂ is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in D = 5 supergravity which have an AdS ₃ × M ₂ near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual $$\mathcal{N}$$ = (0, 2), d = 2 SCFT.