CNC / machinist calculator
Surface Finish Calculator (Ra and Ball-Nose Scallop)
Predict the finish before you cut it. For turning, enter the feed per revolution and the insert nose radius to get the theoretical roughness Ra and Rmax. For 3D milling, enter a ball-nose radius and a stepover to get the scallop height left between passes, or work backward from a target scallop to the stepover you can get away with. These are the geometric floor; real finish is rougher, but the geometry is what you control with feed and stepover.
Turning finish (feed marks)
- Theoretical Ra
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- Theoretical Rmax
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Ball-nose scallop (3D milling)
- Scallop height
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- Stepover for target
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How it works
Theoretical surface finish in turning comes from the feed marks the tool nose leaves. With a feed per revolution and a tool nose radius, the peak-to-valley roughness Rmax is about the feed squared divided by eight times the radius, and the average roughness Ra is the feed squared over thirty-two times the radius. Halving the feed quarters the roughness, and a bigger nose radius smooths the marks for the same feed.
In 3D milling with a ball-nose tool, the finish on a surface comes from the scallops left between parallel passes. The cusp height is the ball radius minus the square root of the radius squared minus half the stepover squared. Inverting that gives the stepover for a target cusp, which is what you actually set in CAM. A stepover of five to ten percent of the tool diameter gives a fine finish; ten to twenty percent is general work.
Both numbers are theoretical minimums. Real roughness is worse because of tool deflection, runout, built-up edge and vibration, often by a factor of one and a half to three, so treat the result as the best case the geometry allows and leave margin.
Worked example
Turning at 0.008 in/rev with a 1/32 in nose radius gives a theoretical Ra of about 64 micro-inches. Cut the feed in half and the roughness drops to a quarter.
Frequently asked questions
How do I calculate surface finish in turning?
Theoretical roughness comes from the feed and the tool nose radius. Rmax is about the feed per revolution squared divided by eight times the nose radius, and Ra is the feed squared over thirty-two times the radius.
How do I get a better finish when turning?
Reduce the feed per revolution or fit an insert with a larger nose radius, since roughness scales with feed squared and inversely with radius. A wiper insert improves finish further by flattening the feed marks at a given feed.
What is scallop or cusp height in ball-nose milling?
It is the small ridge of material left between adjacent tool passes on a 3D surface. The cusp height is the ball radius minus the square root of the radius squared minus half the stepover squared, so a smaller stepover leaves a smaller cusp.
What stepover gives a good ball-nose finish?
A stepover of five to ten percent of the ball diameter gives a fine finish suitable for visible surfaces, while ten to twenty percent is normal for general work. Use the target-cusp mode to set the exact stepover for a roughness you need.
Why is my real surface rougher than the calculator says?
These formulas give the geometric minimum. Tool deflection, spindle and holder runout, built-up edge and vibration all add roughness on top, commonly one and a half to three times the theoretical value, so leave margin against the spec.
Related calculators
Sources
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.