  Within the $\Lambda$CDM cosmological model, the absolute value of Einstein's
cosmological constant $\Lambda$, sometimes expressed as the gravitating
mass-energy density $\rho_\Lambda$ of the physical vacuum, is a fundamental
constant of nature, whose accurate measurement plays a central role in testing
some proposed theories of quantum gravity. Several combinations of currently
public cosmological data and an assumed flat $\Lambda$CDM cosmological model
are used here to make a joint Bayesian inference on the combination of
conventional parameters $\Omega_\Lambda h^2$ that corresponds to the absolute
physical density $\rho_\Lambda$. In physical units, we obtain $\rho_\Lambda =
\left(60.3\pm{1.3}\right)\times 10^{-31}{\rm g/cm^3}$, the most accurate
constraint to date, with an absolute calibration of cosmological measurements
based on CMB temperature. Significantly different values are obtained with
calibrations that use a local distance scale, mainly connected to systematic
differences in the value of the Hubble constant. It is suggested that future
comprehensive cosmological parameter studies assuming the $\Lambda$CDM model
include constraints on the vacuum density.
