Surface Finish Stepover Calculator
When using a ball end mill for 3D surface contouring, each tool pass leaves a small cusp or scallop between adjacent passes. The height of this scallop determines the surface roughness before any polishing. This calculator computes scallop height from ball end mill radius and stepover distance, and also solves the inverse: given a target scallop height, what stepover should you use? This is the standard formula from Machinery's Handbook for surface finishing operations.
Scallop height formula
Scallop height h = R - sqrt(R^2 - (s/2)^2)
Approximate (small stepover): h = s^2 / (8R)
Where R = ball end mill radius (mm) and s = stepover distance (mm). The exact formula uses the Pythagorean theorem. The approximate formula is accurate within 5% when s is less than R (stepover less than ball radius).
Stepover guidelines for different finish requirements
- Rough contouring pass: stepover 30 to 50% of ball diameter. Scallop 0.1 to 0.5 mm acceptable.
- Semi-finish pass: stepover 10 to 20% of ball diameter. Target scallop 0.02 to 0.05 mm.
- Finish pass for polishing: stepover 5 to 10% of ball diameter. Target scallop 0.005 to 0.02 mm.
- Die and mold finishing: stepover 2 to 5% of ball diameter. Scallop below 0.005 mm, then hand-polish.
- Larger ball mills (8 to 12 mm dia) are preferred for large surfaces as they achieve the same scallop with larger stepover and faster cycle time.
Surface finish stepover calculator: frequently asked questions
What is scallop height in CNC machining?
Scallop height (also called cusp height) is the small peak left between adjacent cutting passes when 3D contouring with a ball end mill. Smaller scallop height means a smoother surface but requires more closely spaced passes and longer machining time.
What scallop height should I target?
For raw machined finishes: 0.01 to 0.05 mm (10 to 50 microns) is typical for industrial parts. For molds and dies requiring polishing: 0.005 mm or less. For rough 3D surfacing passes: 0.1 to 0.5 mm is acceptable.
How does ball mill radius affect scallop height?
Larger ball mills produce lower scallop heights at the same stepover because the curvature is more gentle. Scallop height scales inversely with ball radius, so doubling the radius halves the scallop height at the same stepover.
What is the relationship between stepover and scallop height?
Scallop height scales approximately with stepover squared divided by 8 times ball radius (for small stepover values). Halving the stepover reduces scallop height by a factor of four, at the cost of doubling the number of passes and roughly doubling cycle time.
Does this formula apply to flat end mills?
No. This formula is for ball (spherical) end mills in 3D surface contouring. Flat end mills leave no scallop in the Z direction during 2.5D operations but do leave a step between each Z level. For flat end mills, the surface roughness depends on feed marks and Z step height.
Official sources
- Industrial Press: Machinery's Handbook (scallop height and surface finish formulas).
- NIST: Manufacturing Systems Integration Division.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.