Ball End Mill Scallop Height and Stepover Calculator
In 3D finishing, the ridges left between passes are called scallops or cusps. Their height controls how much polishing you need, so choosing the right stepover is the main lever on surface quality and cycle time.
Your numbers
The tallest cusp you will accept on the surface.
Your results
The formula is exact for a flat surface under a ball end mill with no run-out or deflection. On slopes and curved surfaces, the true scallop is larger in the direction of the slope. Real finish also depends on tool wear and run-out.
Scallop height (um) vs stepover (mm)
Sweeps Stepover from 0.1 to 3, holding your other inputs fixed.
Cost finishing time against polishing hours
Optional: a short review of how to cost machining versus hand finishing in your ERP.
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How to use it
Enter the ball diameter and the stepover you are considering to see the scallop height in micrometres. Or enter the target scallop height and read the stepover that achieves it. Fill in the surface width, pass length and feed rate to see the number of passes and the time at the target stepover. The chart shows how quickly the scallop grows with stepover, which makes it easy to see why small changes at fine stepovers cost a lot of time.
The geometry
Two adjacent passes of a ball of radius R, spaced s apart, intersect at a point below the tool top. The cusp height is h = R - sqrt(R^2 - (s/2)^2). Turning it around, s = 2 x sqrt(2 x R x h - h^2). For a 10 mm ball with 0.5 mm stepover, h is about 6.3 um. Because h grows with the square of s for small stepovers, halving the stepover cuts the scallop to about a quarter but doubles the number of passes and the time.
- Scallop varies roughly with s squared divided by 8R.
- Larger balls leave smaller scallop at the same stepover.
- Surface slope increases the effective stepover seen on the surface.
Choosing a target
Typical targets: 10 to 20 um for light polish moulds, 2 to 5 um when the surface will be only lightly hand-finished, and larger values for functional surfaces that are not cosmetic. The scallop height is a peak-to-valley number, so the roughness Ra is smaller, often a quarter or less of the cusp height. Balance the finishing time against the polishing hours saved, and compare the result with your hourly machine rate to see the cost trade-off.
Common mistakes
People often set the stepover as a percentage of the tool diameter and forget that scallop depends on the radius and not on the percentage. Another is ignoring that the effective cutting diameter shrinks when only the tip of a ball cuts at shallow depths on flat areas, where surface speed at the very tip is close to zero. Tilt the tool or use a bull-nose cutter in flat regions.
Frequently Asked Questions
How is scallop height related to Ra?
Scallop height is the peak-to-valley height of the ridges. For a regular cusp profile the Ra is much smaller, commonly around one quarter or less of the height. Use scallop for toolpath planning and a profilometer to verify Ra.
Does this work on sloped surfaces?
Not exactly. The stepover is measured in the plane of the toolpath, but on a slope the distance between passes on the surface is larger, so the real scallop is bigger. Many CAM systems have a constant-scallop strategy that corrects for this.
Should I use a bigger ball or smaller stepover?
A bigger ball gives smaller scallop at the same stepover, but it cannot reach tight corners and needs more power. A small stepover with a small ball is slow. The best answer is often a large ball for open areas and a small ball for details.
What about a bull-nose or barrel cutter?
The same geometry applies with the effective radius of the cutting arc. Barrel and lens-shaped tools have a very large effective radius, which allows far larger stepovers for the same scallop. Use the arc radius in place of the ball radius.
If you track mould and die jobs in an ERP, we can help connect machining times to job costing. This calculator works on its own.
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