I will describe a new procedure for coarse-graining over the gravitational degrees of freedom inside a surface in the context of AdS/CFT. I will prove that in general dimensions, this coarse-graining gives an explanation of an infinite family of gravitational area laws. In three bulk dimensions, it is also straightforward to derive the precise dual of these area laws as strong subadditivity of the von Neuman entropy in the dual CFT. I will discuss a number of implications of this, which include an explanation for the geometric bulk phenomenon of extremal surface barriers