Practical guide

What theoretical cusp height does—and does not—predict

Apply the planar spherical-profile equation correctly and avoid confusing geometric cusp with measured surface finish.

The circle equation predicts the geometric remainder between two adjacent planar passes of a spherical profile. It is useful for comparing nominal stepover and cusp height under the same idealized assumptions.

It does not directly produce Ra, Rz or another measured finish metric. Real surfaces also depend on slope, path projection, tool orientation, runout, deflection, wear, material response, holder/spindle condition and machine motion. Non-spherical tools require their own geometry. Label outputs theoretical, retain enough precision for calculation, and validate demanding finish requirements with an appropriate process and measurement plan.