Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios
${\rm \pi} /5\leqslant \varGamma \leqslant 4{\rm \pi}$, where
$\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number,
$10^3\leqslant Ra\leqslant 10^{11}$, and four orders of magnitude in the Prandtl number,
$10^{-2}\leqslant Pr\leqslant 10^2$. At large
$Ra$ where steady rolls are dynamically unstable, the computed rolls display
$Ra \rightarrow \infty$ asymptotic scaling. In this regime, the Nusselt number
$Nu$ that measures heat transport scales as
$Ra^{1/3}$ uniformly in
$Pr$. The prefactor of this scaling depends on
$\varGamma$ and is largest at
$\varGamma \approx 1.9$. The Reynolds number
$Re$ for large-
$Ra$ rolls scales as
$Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at
$\varGamma \approx 4.5$. All of these large-
$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (Phys. Fluids, vol. 21, 2009, 083603). Convergence of
$Nu$ and
$Re$ to their asymptotic scalings occurs more slowly when
$Pr$ is larger and when
$\varGamma$ is smaller.