  We perform a calibration of the mixing length of convection in stellar
structure models against realistic 3D radiation-coupled hydrodynamics (RHD)
simulations of convection in stellar surface layers, determining the adiabat
deep in convective stellar envelopes.
  The mixing-length parameter $\alpha$ is calibrated by matching averages of
the 3D simulations to 1D stellar envelope models, ensuring identical atomic
physics in the two cases. This is done for a previously published grid of
solar-metallicity convection simulations, covering from 4200 K to 6900 K on the
main sequence, and 4300-5000 K for giants with logg=2.2.
  Our calibration results in an $\alpha$ varying from 1.6 for the warmest
dwarf, which is just cool enough to admit a convective envelope, and up to 2.05
for the coolest dwarfs in our grid. In between these is a triangular plateau of
$\alpha$ ~ 1.76. The Sun is located on this plateau and has seen little change
during its evolution so far. When stars ascend the giant branch, they largely
do so along tracks of constant $\alpha$, with $\alpha$ decreasing with
increasing mass.
