The article presents formulas for determining the dimensions of involute-bevel gearwheels and the gears composed of them. It examines the most general cases of gears formation, consisting of two involute-bevel gearwheels with crossing axes (hyperboloid gears), with intersecting axes (bevel gears), and with parallel axes (cylindrical gears). Gears composed of involute-bevel gearwheels have design, technological, and operational advantages compared to gears composed of conventional cylindrical and bevel gearwheels. The use of involute-bevel gearwheels with crossing axes allows for achieving the required contact character of the teeth from localized contact to linear contact, reducing sensitivity to manufacturing and assembly errors, and increasing the load capacity of the gear compared to helical gear from cylindrical gearwheels. Bevel gears with involute-bevel gearwheels allow for the creation of gears with any desired small shaft angles, which is difficult to achieve with conventional bevel gearwheels. The use of internal meshing bevel gears with modified tooth profiles in planetary reducers allows for gears comparable to harmonic gears in terms of power and kinematic characteristics, but with a higher operational life. The use of involute-bevel gearwheels in cylindrical gears improves the smoothness of the mechanism and allows for adjusting the center distance and backlash in the meshing, making them suitable for backlash-free drives. By combining the taper angles of the gearwheels and the inclination of the teeth, it is possible to create a one-way rotation mechanism—a freewheel mechanism. Modern CAD systems do not take into account the geometry features of gears with involute-bevel gearwheels, which limits their application in technology. The article proposes an algorithm for calculating the main geometric parameters of gears with involute-bevel gearwheels with arbitrary axis placement in space. Examples of geometric calculations of various types of gears based on the proposed algorithm are provided.