  We compute the QCD static force and potential using gradient flow at
next-to-leading order in the strong coupling. The static force is the spatial
derivative of the static potential: it encodes the QCD interaction at both
short and long distances. While on the one side the static force has the
advantage of being free of the $O(\Lambda_{\rm QCD})$ renormalon affecting the
static potential when computed in perturbation theory, on the other side its
direct lattice QCD computation suffers from poor convergence. The convergence
can be improved by using gradient flow, where the gauge fields in the operator
definition of a given quantity are replaced by flowed fields at flow time $t$,
which effectively smear the gauge fields over a distance of order $\sqrt{t}$,
while they reduce to the QCD fields in the limit $t \to 0$. Based on our
next-to-leading order calculation, we explore the properties of the static
force for arbitrary values of $t$, as well as in the $t \to 0$ limit, which may
be useful for lattice QCD studies.
