Advancements in manufacturing technology provide users with new opportunities for the design of gears. Special gearings with customized non-involute tooth profile geometries offer a promising alternative to conventional involute gears, addressing limitations, such as undercutting and small radii of curvature near the tooth root. However, the absence of standardized design procedures for non-involute gears, such as ISO 6336 for involute gears, often necessitates reliance on numerical simulations and methodologies using approximations. Analytical methods for determining key parameters—such as the topological load distribution and contact pressures—are currently specialized for involute gears and can hardly be directly applied to special gears. This paper proposes a generalization of the analytical static load distribution calculation for non-involute tooth profiles. A relationship between the applied torque and the transmission error at every meshing position is derived. This approach is validated using the calculation software RIKOR with two exemplary involute gearings, demonstrating consistency with the established method. Additionally, the proposed framework is applied to an exemplary cycloid gear and an eccentric cycloid gear to demonstrate the capability to analyze arbitrary tooth profile geometries. The results highlight the potential for the reliable and efficient design of non-involute gears through analytical methods.