How to use this calculator
- Choose what to solve. Pick "Find Ra/Rz" if you know the feed, or "Find max feed" if you have a target Ra.
- Enter the nose radius. Enter the tool nose (corner) radius of the insert.
- Enter the feed or target Ra. Enter the feed per revolution, or the Ra you need to hit.
- Read the finish. Read the theoretical Ra and Rz, and the feed used.
How it works
In turning, the round tool nose leaves a series of scallops between passes.
Their geometry sets the theoretical roughness from just the feed per revolution
f and the nose radius r:
Ra ≈ f² / (31.2 · r)
and the peak-to-valley height
Rz ≈ f² / (8 · r). Because the feed is squared, the finish improves
quickly as you slow the feed — halving the feed quarters the roughness — while a
larger nose radius spreads the scallop and lowers it linearly.
Running it the other way, the largest feed that still meets a target Ra is
f = √(Ra · 31.2 · r). This is the theoretical, perfect-tool
ideal: it assumes a true round nose and ignores built-up edge, tool wear,
vibration, deflection and the material — all of which push real roughness higher.
Worked example
Verified against the live calculator
Turning at a feed of f = 0.2 mm/rev with a 0.8 mm nose
radius: Ra = 0.2² / (31.2 × 0.8) = 0.04 / 24.96 ≈ 0.001603 mm = 1.60 µm
and Rz = 0.04 / (8 × 0.8) = 0.00625 mm = 6.25 µm. Switching to the
feed mode with a target Ra of 1.60 µm returns the same
f ≈ 0.2 mm/rev — the calculator is self-consistent. Remember the real
measured Ra will be somewhat higher.
Frequently asked questions
How do you calculate surface finish from feed and nose radius?
For turning, the theoretical roughness left by the round tool nose is Ra ≈ f²/(31.2·r) and Rz ≈ f²/(8·r), where f is the feed per revolution and r the nose radius (in the same units). For example f = 0.2 mm with a 0.8 mm nose radius gives Ra ≈ 1.6 µm and Rz ≈ 6.25 µm.
What is the difference between Ra and Rz?
Ra is the arithmetic-average roughness — the mean deviation from the centre line. Rz (here ≈ Rmax) is the peak-to-valley height of the scallop. For the ideal turned profile Rz is about four times Ra. Drawings may call out either, so the calculator shows both.
How do I get a finer finish?
Reduce the feed or increase the nose radius. Because roughness scales with f², halving the feed quarters the roughness; doubling the nose radius halves it. A larger nose radius is usually the cheaper lever, up to the point where it raises cutting forces and chatter.
Is the calculated Ra what I will actually measure?
No — this is the theoretical, perfect-tool ideal. Real Ra is always higher because of built-up edge, tool wear, vibration, deflection, an unstable setup and the workpiece material. Use the result as a best-case starting point and leave margin against the drawing callout.
What feed do I need for a target Ra?
Switch the mode to "Find max feed (for a target Ra)". The calculator rearranges the formula to f = √(Ra · 31.2 · r) and returns the largest feed that meets the target — then you back off for a safety margin.
Does this work for milling?
The f²/(8·r) and f²/(31.2·r) relations are the classic turning model (feed per revolution against the insert nose radius). Milling finish is governed by the scallop between passes and the feed per tooth, so use a milling-specific model there; for turning and single-point boring this is the standard estimate.
Method & assumptions
- Theoretical / ideal finish only — the geometric scallop of a perfect round nose. Real Ra is always higher.
- Ignores built-up edge, tool wear, vibration, deflection, an unstable setup and the workpiece material.
- Assumes a true round nose and a feed smaller than the straight portion of the insert edge; it is the standard model for turning and single-point boring.