  We study the equation of state of pure SU($2$) gauge theory using Monte Carlo
simulations. The scale-setting of lattice parameters has been carried by using
the gradient flow. We propose a reference scale $t_0$ for the SU($2$) gauge
theory satisfying $t^2 \langle E \rangle|_{t=t_0} =0.1$, which is fixed by a
natural scaling-down of the standard $t_0$-scale for the SU($3$) case based on
perturbative analyses. We also show the thermodynamic quantities as a function
of $T/T_c$, which are derived by the energy-momentum tensor using the small
flow-time expansion of the gradient flow.
