How does the cavity size in circumbinary discs depend on disc and binary properties? We investigate by simulating disc cavities carved by binary companions using smoothed particle hydrodynamics. We find that a cavity is quickly opened on the dynamical time, while the cavity size is set on the viscous time. In agreement with previous findings, we find long-term cavity sizes of 2-5 times the binary semimajor axis, increasing with eccentricity and decreasing with disc aspect ratio. When considering binaries inclined with respect to the disc, we find three regimes: (i) discs that evolve towards a coplanar orbit have a large cavity, slightly smaller than that of an initially coplanar disc; (ii) discs that evolve towards a polar orbit by breaking have a small cavity, equal in size to that of an initially polar disc; and (iii) discs that evolve towards a polar orbit via warping have an intermediate-sized cavity. We find typical gas depletions inside the cavity of ≳2 orders of magnitude in surface density.