The observed baryon asymmetry of the Universe provides a fundamental probe of high-scale physics and the thermal history of the electroweak plasma. Within the Standard Model, sphaleron processes partially convert a primordial $B-L$ asymmetry into baryon number, and the corresponding sphaleron conversion factor is a key ingredient in quantitative predictions of baryogenesis scenarios.

In this talk, after first reviewing the classic derivation by Khlebnikov and Shaposhnikov, I will go beyond equilibrium treatment and solve a Boltzmann equation for baryon number evolution through the electroweak crossover. By including higher-order corrections to the grand canonical partition function as well as the temperature dependence of the Higgs expectation value and the sphaleron rate, I present a precision value for the sphaleron conversion factor.