[en] Recent observations of protoplanetary disk have reported spiral structures that are potential signatures of embedded planets, and modeling efforts have shown that a single planet can excite multiple spiral arms, in contrast to conventional disk–planet interaction theory. Using two and three-dimensional hydrodynamics simulations to perform a systematic parameter survey, we confirm the existence of multiple spiral arms in disks with a single planet, and discover a scaling relation between the azimuthal separation of the primary and secondary arm, ${\mathrm{\varphi <!--\; ??\; -->}}_{\mathrm{s}\mathrm{e}\mathrm{p}},$ and the planet-to-star mass ratio q: ${\mathrm{\varphi <!--\; ??\; -->}}_{\mathrm{s}\mathrm{e}\mathrm{p}}={102}^{\circ <!--\; ???\; -->}{(q/0.001)}^{0.2}$ for companions between Neptune mass and 16 Jupiter masses around a 1 solar mass star, and ${\mathrm{\varphi <!--\; ??\; -->}}_{\mathrm{s}\mathrm{e}\mathrm{p}}={180}^{\circ <!--\; ???\; -->}$ for brown dwarf mass companions. This relation is independent of the disk’s temperature, and can be used to infer a planet’s mass to within an accuracy of about 30% given only the morphology of a face-on disk. Combining hydrodynamics and Monte-Carlo radiative transfer calculations, we verify that our numerical measurements of ${\mathrm{\varphi <!--\; ??\; -->}}_{\mathrm{s}\mathrm{e}\mathrm{p}}$ are accurate representations of what would be measured in near-infrared scattered light images, such as those expected to be taken by Gemini/GPI, Very Large Telescope/SPHERE, or Subaru/SCExAO in the future. Finally, we are able to infer, using our scaling relation, that the planet responsible for the spiral structure in SAO 206462 has a mass of about 6 Jupiter masses.