Stagnant-lid planets (lack tectonic plates) are common in our solar system and likely among rocky exoplanets as well. Previous research on the interior of these planets has not accounted for the impact of the crust on mantle convection even though thick crusts do have an impact on their evolution. We derive new scaling laws for stagnant-lid interiors finding two end-member regimes the "thin" and "thick" crust limits that match the 2D convection models well.