Reduced Radius of Curvature in Hertz Contact

For two convex spherical surfaces along a corresponding principal direction, the reduced radius can be written as:

$$\frac{1}{R^*}=\frac{1}{R_1}+\frac{1}{R_2}.$$

• $R^*$ — reduced radius of curvature;
• $R_1$, $R_2$ — radii of curvature of the contacting surfaces.

Equivalently, for two convex surfaces:

$$R^*=\frac{R_1R_2}{R_1+R_2}.$$

For other combinations of curvature, the sign of an individual radius follows the adopted geometric convention. General three-dimensional contact requires the principal curvatures of both surfaces.

The calculator below corresponds to two convex surfaces with positive radii.