  We present the numerical equivalence between the Wilson flow and stout-link
smearing, both of which are known to be a relatively new technique for
smoothing the gauge fields on the lattice. Although the conceptional
correspondence between two methods was first pointed out by L\"uscher in his
original paper [J. High Energy Phys.~08 (2010) 071], we provide a direct
analytical proof of the equivalence between the two methods at finite lattice
spacing $a$ in the zero limit of the stout-smearing parameter $\rho$. The
leading order corrections start at ${\cal O}(\rho)$, which would induce ${\cal
O}(a^2)$ corrections. It is, therefore, not obvious that they remain equivalent
even with finite parameters ($a\neq 0$ and $\rho\neq0$) within some numerical
precision. In this paper, we demonstrate the equivalence of both methods by
directly comparing the expectation value of the action density, which is
measured in actual numerical simulations.
