Engineering Tools

Ball End Mill Cusp Height Calculator

Scallop height and approximate surface roughness left between adjacent ball-nose finishing passes.

Enter the ball end mill radius and the stepover between passes to get the geometric cusp height and its approximate Ra.

Why parallel ball-nose passes leave a scallop

A ball end mill cuts with a curved tip. When two adjacent finishing passes are offset by a fixed stepover, the curved tip does not fully overlap the material it removed on the previous pass — a small ridge, or cusp, is left standing between the two passes. The cusp height is the peak-to-valley size of that ridge, measured perpendicular to the nominal surface.

For a tool radius r and a stepover s, the cusp height follows directly from circle geometry: the tip traces a circular arc of radius r, and two adjacent arcs intersect at a point offset r − √(r² − (s/2)²) below the tips. That expression is exactly what this calculator evaluates — no empirical correction or lookup table is involved.

Surface roughness is reported as an approximation, Ra ≈ cusp height ÷ 4, scaled from millimeters to micrometers. This is a standard geometric estimate for a scalloped profile, not a measured value — it assumes the tool tip is a perfect sphere with no runout and ignores machine vibration, deflection, and material behavior, all of which tend to make the measured finish coarser than this number.

When to Use This

  • Picking a stepover for a 3D finishing toolpath before committing to a cycle-time estimate.
  • Checking, before running the program, whether a chosen stepover can plausibly hit a target Ra.
  • Comparing two candidate ball radii to see which gives a lower cusp height at the same stepover.

Common Mistakes

  • Treating the calculated Ra as the guaranteed finished surface roughness — it is a geometric ceiling assuming ideal tool contact, and actual measured roughness is commonly higher.
  • Entering a stepover larger than the tool diameter — beyond a stepover of 2 × tool radius the two passes no longer overlap and the scallop model no longer describes what is cut.
  • Reusing one stepover value across a whole 3-axis surface regardless of local slope — this calculator assumes the tool axis is normal to the surface, which only holds on some regions of a curved part.

FAQ

What does a smaller stepover actually buy you?

Cusp height falls roughly with the square of stepover, so halving the stepover cuts the theoretical cusp to about a quarter — but it also roughly doubles the number of passes and the machining time, since h scales with s² while pass count scales with 1/s.

Why does the calculator reject a stepover larger than twice the tool radius?

The underlying formula takes the square root of r² − (stepover/2)². Once stepover/2 exceeds the tool radius, that term goes negative and has no real square root — physically, the passes have stopped overlapping at all, so there is no scallop to measure. This calculator rejects that input rather than return a meaningless result.

Is the reported Ra the number I should put on a drawing?

No — it is a theoretical lower bound from geometry alone. Real finishing passes add roughness from tool runout, spindle vibration, and workpiece deflection, so the measured Ra on the part is typically higher than this calculation. Use it to compare stepover or tooling choices relative to each other, not as a guaranteed spec.