  We use large-scale lattice simulations to compute the rate of baryon number
violating processes (the sphaleron rate), the Higgs field expectation value,
and the critical temperature in the Standard Model across the electroweak phase
transition temperature. While there is no true phase transition between the
high-temperature symmetric phase and the low-temperature broken phase, the
cross-over is sharply defined at $T_c = (159\pm 1)$\,GeV. The sphaleron rate in
the symmetric phase ($T> T_c$) is $\Gamma/T^4 = (18\pm 3)\alpha_W^5$, and in
the broken phase in the physically interesting temperature range
$130\mbox{\,GeV} < T < T_c$ it can be parametrized as $\log(\Gamma/T^4) =
(0.83\pm 0.01)T/{\rm GeV} - (147.7\pm 1.9)$. The freeze-out temperature in the
early Universe, where the Hubble rate wins over the baryon number violation
rate, is $T_* = (131.7\pm 2.3)$\,GeV. These values, beyond being intrinsic
properties of the Standard Model, are relevant for e.g. low-scale leptogenesis
scenarios.
