  Recent years have seen a rapid reduction in the intrinsic loss of
nanomechanical resonators (i.e., chip-scale mechanical oscillators). As a
result, these devices become increasingly sensitive to the friction exerted by
smallest amounts of gas. Here, we present the pressure-dependency of a
nanomechanical trampoline resonator's quality factor $Q$ over ten decades, from
$10^{-7}$ to $10^{3}\,\mathrm{mbar}$. We find that the measured behavior is
well-described by a model combining analytical and numerical components for
molecular and viscous flow, respectively. This model relies exclusively on
design and typical material parameters, together with measured values of
intrinsic resonance frequency $f_\mathrm{in}$ and quality factor
$Q_\mathrm{in}$. Measuring $f_\mathrm{in}$ and $Q_\mathrm{in}$ at a pressure
$<\!10^{-7}\,\mathrm{mbar}$ self-calibrates our sensor over its entire
measurement range. For a trampoline's fundamental out-of-plane vibrational
mode, the resulting deviation between measured and simulated pressure
dependencies of the quality factor and resonance frequency is within $15\,\%$
and $4\,\%$, respectively. The resulting error for pressure values inferred
from quality factor and frequency measurements is $<10\,\%$, for pressures
between $\sim 10^{-6}$ and $\sim 10^{-1}\,\mathrm{mbar}$, and $<25\,\%$ for the
complete 10-decade measurement range. Exceptions are two outliers with
increased measurement errors, which might be related to the limited accuracy of
our commercial pressure gauge. Based on investigations with helium, we
demonstrate the potential for extending this sensing capability to other gases,
thereby highlighting the practical use of our sensor.
