Calculation method
Calculation
Ra ≈ f² ÷ (32 × Nose Radius)Rt, approx. ≈ f² ÷ (8 × Nose Radius)Feed ≈ √(Target Ra × 32 × Nose Radius)Use values in the units shown by the calculator. Inputs must be positive and physically meaningful.
Average roughness (Ra) formula
For an ideal turned surface produced by a round tool nose, the common geometric approximation is Ra ≈ f²/(32r). Feed f and nose radius r must use the same base length unit. The calculator reports the result in both µm and µin.
Surface roughness conversion calculator
The result is shown in both major Ra unit conventions. 1 µm = 39.3701 µin, so a 6.3 µm Ra specification is about 248 µin Ra and a 3.2 µm Ra specification is about 126 µin Ra.
| Ra µm | Ra µin (approx.) |
|---|---|
| 0.4 | 16 |
| 0.8 | 32 |
| 1.6 | 63 |
| 3.2 | 126 |
| 6.3 | 248 |
| 12.5 | 492 |
How surface roughness is measured
Ra is the arithmetic average of profile deviations over the evaluated length. Real inspection uses a profilometer and defined filtering/cutoff settings. A formula based on tool geometry predicts an ideal best-case profile; it does not replace measurement when a drawing requires a verified finish.
Ra and Rz conversions: why there is no universal exact ratio
Ra and Rz describe different properties of a surface profile. A fixed multiplier can be a rough rule of thumb for a particular process, but it is not an exact conversion that applies to every manufactured surface. MachiningCalc therefore keeps the theoretical peak-to-valley geometry labeled separately instead of presenting it as a guaranteed measured Rz.
Cutting conditions from a target Ra
Switch the calculator to Max theoretical feed from target Ra to rearrange the formula and calculate the feed that corresponds to a target finish for a known nose radius. Treat that feed as a geometric upper bound before process margin, vibration, wear and material effects are considered.
Factors that affect actual surface finish
- tool wear, edge preparation and built-up edge;
- machine and workholding rigidity;
- chatter, runout and vibration;
- material microstructure and spring-back;
- nose-radius choice and cutting forces;
- measurement method, cutoff and filtering.
Additional technical reference
Methodology, standards and validation
MachiningCalc separates deterministic math from cutting-data recommendations. The calculator performs the geometry and unit relationships; the correct starting cutting data still depends on the tool, work material, coating, machine and setup.