Estimate the theoretical surface finish a cut will leave. Turning finish comes from the feed and the tool nose radius; ball-nose milling finish comes from the stepover and the ball radius. Real finish is always a little rougher, but these set the target.
Turning finish
Ball-nose milling finish
Theoretical values. Tool wear, runout, vibration, and built-up edge all make the real finish rougher.
How it works
For turning, theoretical roughness average is Ra = feed squared / (32 × nose radius), and peak-to-valley is feed squared / (8 × nose radius). A bigger nose radius and a lighter feed both smooth the finish. For ball-nose milling, the leftover scallop height between passes is radius minus the square root of (radius squared minus half-stepover squared).
Improving the number
To smooth a turned surface, reduce the feed per rev or fit a larger nose radius. To smooth a ball-nose finish, reduce the stepover — it cuts the scallop quickly but adds machining time.
FAQ
Why is my real finish worse? The formulas give the best-case geometry; in practice tool wear, runout, chatter, and built-up edge add roughness on top.
Compare against the Surface Finish Chart and read How to Improve Surface Finish.