  We derive formulas for the leading mass, entropy, and long-range self-force
corrections to extremal black holes due to higher-derivative operators. These
formulas hold for black holes with arbitrary couplings to gauge fields and
moduli, provided that the leading-order solutions are static,
spherically-symmetric, extremal, and have nonzero horizon area. To use these
formulas, both the leading-order black hole solution and the higher-derivative
effective action must be known, but there is no need to solve the
derivative-corrected equations of motion. We demonstrate that the mass, entropy
and self-force corrections involve linearly-independent combinations of the
higher-derivative couplings at any given point in the moduli space, and comment
on their relations to various swampland conjectures.
