Transport & Manufacturing
CNC Lathe Surface Finish Roughness ($Ra$) from Nose Radius & Feed
Calculate cnc lathe surface finish roughness ($ra$) from nose radius & feed using the stated engineering or scientific relationship and adjustable field inputs.
Preparing your result…
What this calculator does
Calculates CNC Lathe Surface Finish Roughness ($Ra$) from Nose Radius & Feed using the formula verified against the cited source.
What your result means
An estimate from the inputs you enter, within the scope stated below — not advice.
Formula
Ra ≈ f² ÷ (32 × nose radius)
The step-by-step working for your own numbers appears with the result above and in the PDF report.
Frequently asked questions
Symbols and assumptions
- Inputs
- The values entered in the fields above
- • Ideal turning geometric roughness Ra≈feed_per_rev²/(32×tool nose radius), in the same length unit as feed and radius; multiply mm result by1000 for micrometres.
Sources and review
Reviewed 2026-10-18 · Next review 2027-04-18
- • This is a small-feed geometric approximation for a rounded conventional cutting edge, not a measured Ra guarantee. Surface roughness also depends on vibration, built-up edge, material, wear and wiper geometry. Distinguish Ra from maximum peak/valley height and use feed per revolution, not per minute.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Quick reference
| Scenario | Feed per revolution (mm) | Tool nose radius (mm) | Theoretical Ra |
|---|---|---|---|
| Worked example | 0.15 | 0.8 | 0.8789 µm |
| Half the amounts | 0.08 | 0.4 | 0.5 µm |
| Double the amounts | 0.3 | 1.6 | 1.7578 µm |
Need the full picture? Get the detailed PDF report with charts, tables, formulas and working steps.
Reviewed 2026-10-18 · Next review 2027-04-18
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