  We apply the critical geometry approach for bounded critical phenomena [1] to
$3d$ percolation. The functional shape of the order parameter profile $\phi$ is
related via the fractional Yamabe equation to its scaling dimension
$\Delta_{\phi}$. We obtain $\Delta_{\phi}= 0.4785(7)$ from which the anomalous
dimension $\eta$ is found to be $\eta=-0.0431(14)$, a value compatible with,
and more precise than, its previous direct measurements. A test of hyperscaling
is also performed.
