Ball-End Mill Scallop (Cusp) Height Calculator
Height of the ridges a ball-nose cutter leaves between passes on a 3D surface, and the largest stepover that keeps them under the finish you want.
Results
The dashed line marks the value you entered.
What this tool does
Finishing a curved surface with a ball-end mill leaves small ridges between neighbouring passes, because the round tip dips back between them. Their height is h = R − √(R² − (s/2)²), so it grows with the square of the stepover and shrinks with the cutter radius: a stepover of 10 % of the diameter leaves a cusp only about 0.25 % of the diameter high — 0.025 mm with a 10 mm ball. That is why finishing passes can be wide and still look smooth, as the chart shows. The formula is for the cusp measured at right angles to the surface; the finish also depends on feed, runout and tool deflection.
Formula
h = R − √(R² − (s ÷ 2)²) · s = 2 √(h (D − h)) (R = cutter radius, s = stepover, h = cusp height)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dc | Diameter of the ball-end cutter | mm |
st | Stepover between passes | mm |
hs | Cusp height you can accept | mm |
H | Cusp (scallop) height left between passes | mm |
SS | Largest stepover for that cusp height | mm |
SP | …as a share of the cutter diameter | % |
Worked example
- Diameter of the ball-end cutter10 mm
- Stepover between passes1 mm
- Cusp height you can accept0.005 mm
- Cusp (scallop) height left between passes0.0251 mm
- Largest stepover for that cusp height0.447 mm
- …as a share of the cutter diameter4.5 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.