High-resolution imagery and digital elevation models (DEMs) were used to measure the planimetric shapes of well-preserved impact craters. These measurements were used to characterize the size-dependent scaling of the departure from circular symmetry, which provides useful insights into the processes of crater growth and modification. For example, we characterized the dependence of the standard deviation of radius (σR) on crater diameter (D) as σR ∼ Dm. For complex craters on the Moon and Mars, m ranges from 0.9 to 1.2 among strong and weak target materials. For the martian simple craters in our data set, m varies from 0.5 to 0.8. The value of m tends toward larger values in weak materials and modified craters, and toward smaller values in relatively unmodified craters as well as craters in high-strength targets, such as young lava plains. We hypothesize that m ≈ 1 for planforms shaped by modification processes (slumping and collapse), whereas m tends toward ∼ 1/2 for planforms shaped by an excavation flow that was influenced by strength anisotropies.Additional morphometric parameters were computed to characterize the following planform properties: the planform aspect ratio or ellipticity, the deviation from a fitted ellipse, and the deviation from a convex shape. We also measured the distribution of crater shapes using Fourier decomposition of the planform, finding a similar distribution for simple and complex craters. By comparing the strength of small and large circular harmonics, we confirmed that lunar and martian complex craters are more polygonal at small sizes. Finally, we have used physical and geometrical principles to motivate scaling arguments and simple Monte Carlo models for generating synthetic planforms, which depend on a characteristic length scale of target strength defects. One of these models can be used to generate populations of synthetic planforms which are very similar to the measured population of well-preserved simple craters on Mars.