Operation
Insert nose radius (ISO insert code)
mm
mm/rev
µm
mm
mm
Drawing finish (sets target Ra)
Theoretical Ra and Rz from feed and nose radius in turning, the feed you need for a target finish, ball-nose cusp height in milling, and Ra ↔ Rz ↔ N-grade ↔ microinch conversion with typical values for each process.
| Feed | Ra | Rz (Rt) | N grade |
|---|
| N grade | Ra µm | Ra µin | Typical process |
|---|
A round-nosed tool leaves a row of circular arcs on the surface, one arc per revolution. Their height is the theoretical peak-to-valley roughness; the arithmetic mean of that profile is Ra.
These are geometric (theoretical) values. Real surfaces come out rougher: built-up edge, vibration, tool wear and soft gummy materials typically add 1.5–3 × at low cutting speed and 1.2–1.5 × at good conditions. Wiper inserts roughly halve Ra at the same feed. Rz from a profilometer is usually 4–7 × Ra on turned surfaces.
This calculator predicts the surface finish a turning or ball-nose milling operation can reach, before you cut. From the feed per revolution and the insert nose radius it gives the theoretical Ra and peak-to-valley height, and it works backwards from a drawing callout such as Ra 0.8 µm (32 µin) to the feed you need. Machinists, CNC programmers and process engineers use it to pick an insert and feed that meet the finish without slowing the job down more than necessary.
To hold Ra 0.8 µm with an R0.8 insert, run about 0.11–0.14 mm/rev, or keep 0.20 mm/rev with a wiper insert. Halving the feed cuts Ra to a quarter, because Ra grows with the square of the feed.
For turning with a round-nosed insert, the theoretical peak-to-valley height is Rt = f² / (8 · r) and the arithmetic mean roughness is Ra ≈ f² / (31.2 · r), with feed f in mm/rev and nose radius r in mm (multiply by 1000 for µm). Example: 0.2 mm/rev with a 0.8 mm radius gives Rt = 6.25 µm and Ra = 1.6 µm. Real finishes are usually 1.2–2 × the theoretical value because of tool wear, vibration and built-up edge.
Rearrange the formula: f = √(31.2 · r · Ra) with Ra in mm. With a 0.8 mm nose radius, Ra 1.6 µm needs about 0.20 mm/rev and Ra 0.8 µm about 0.14 mm/rev. With a 0.4 mm radius the same finishes need 0.14 and 0.10 mm/rev. Then reduce by 15–25 % to cover real-world effects, or use a wiper insert, which allows roughly double the feed for the same Ra.
Ra is the arithmetic average deviation of the profile from its mean line, so one deep scratch barely changes it. Rz is the average of the five largest peak-to-valley heights over the evaluation length, so it reacts to the extremes. On turned surfaces Rz is typically 4 to 7 times Ra. Drawings in Europe often specify Rz, while US drawings mostly use Ra in microinches. Convert with care, because the ratio depends on the process.
N grades are roughness classes from the older ISO 1302 scheme. Each step doubles the Ra value: N5 = 0.4 µm, N6 = 0.8 µm (32 µin), N7 = 1.6 µm (63 µin), N8 = 3.2 µm (125 µin) and N9 = 6.3 µm (250 µin). N6 to N7 is a typical finish-turned or ground bearing seat, N8 is a normal machined surface, and N9 to N10 is roughing.
Multiply by 39.37: 1 µm = 39.37 µin. Common pairs are Ra 0.4 µm = 16 µin, 0.8 µm = 32 µin, 1.6 µm = 63 µin, 3.2 µm = 125 µin and 6.3 µm = 250 µin. Drawings usually round to these preferred values rather than the exact conversion.
The cusp left between two parallel passes is h = R − √(R² − (s/2)²), where R is the ball radius and s the stepover. A 10 mm ball (R = 5 mm) at 0.5 mm stepover leaves h = 0.00625 mm, about 6.3 µm, roughly Ra 1.6 µm. Halving the stepover cuts the cusp to about a quarter. Tilting the tool 10–15° also helps, because the centre of the ball has zero cutting speed and rubs instead of cutting.