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APPLawD (Accurate Disk Potentials for Power Law Surface densities) determines the gravitational potential in the equatorial plane of a flat axially symmetric disk (inside and outside) with finite size and power law surface density profile. Potential values are computed on the basis of the density splitting method, where the residual Poisson kernel is expanded over the modulus of the complete elliptic integral of the first kind. In contrast with classical multipole expansions of potential theory, the residual series converges linearly inside sources, leading to very accurate potential values for low order truncations of the series. The code is easy to use, works under variable precision, and is written in Fortran 90 with no external dependencies.