  Studies of planetary atmospheric composition, variability, and evolution
require appropriate theoretical and numerical tools to estimate key atmospheric
parameters, among which the mass-loss rate is often the most important. In
evolutionary studies, it is common to use the energy-limited formula, which is
attractive for its simplicity but ignores important physical effects and can be
inaccurate in many cases. To overcome this problem, we consider a recently
developed grid of about 7000 one-dimensional upper-atmosphere hydrodynamic
models computed for a wide range of planets with hydrogen-dominated atmospheres
from which we extract the mass-loss rates. The grid boundaries are [1:39]
MEARTH in planetary mass, [1:10] REARTH in planetary radius, [300:2000] K in
equilibrium temperature, [0.4:1.3] MSUN in host star's mass, [0.002:1.3] au in
orbital separation, and about [10^{26}:5*10^{30}] erg/s in stellar X-ray and
extreme ultraviolet luminosity. We then derive an analytical expression for the
atmospheric mass-loss rates based on a fit to the values obtained from the
grid. The expression provides the mass-loss rates as a function of planetary
mass, planetary radius, orbital separation, and incident stellar high-energy
flux. We show that this expression is a significant improvement to the
energy-limited approximation for a wide range of planets. The analytical
expression presented here enables significantly more accurate planetary
evolution computations without increasing computing time.
