How flat is the Universe?

In order to answer this question, we combine ten independent astrophysical constraints in the space of the density parameters $\Omega_m$ of gravitating matter and $\Omega_{\Lambda}$ of vacuum energy. We find that $\Omega_m=0.31\pm 0.07$, $\Omega_{\Lambda}=0.63\pm 0.21$, and thus $\Omega_m + \Omega_{\Lambda}=0.94\pm 0.22$. The total $\chi^2$ is 4.1 for 8 degrees of freedom, testifying that the various systematic errors included are generous. We also determine $\Omega_m$ in the exactly flat case. Five supplementary flat-case constraints can then be included in our fit, with the result $\Omega_m=1-\Omega_{\Lambda}= 0.337\pm0.031$. It follows that the age of the Universe is $t_0 = 13.5\pm 1.3$ (0.68/h) Gyr.