How do you calculate Ra from feed and nose radius?

Theoretical Ra (µm) ≈ f² ÷ (32 × rε) × 1000 with f in mm/rev and rε in mm. 0.2 mm/rev on a 0.8 mm nose radius gives about 1.6 µm.

What feed do I need for Ra 0.8?

f = √(32 × rε × Ra ÷ 1000). On a 0.8 mm nose radius that is about 0.14 mm/rev in theory — nearer 0.11 with a realistic margin.

Why is my measured Ra worse than calculated?

The formula only models the geometric cusps; built-up edge, vibration, wear and material tearing add on top. Real surfaces typically measure 1.2–2× theoretical.

Can turning reach Ra 0.4?

Not dependably — the required feed sits at the minimum-chip-thickness limit where finish degrades again. Turn to ~Ra 1.6 and finish by another route; we electropolish 316L and titanium to Ra ≤0.4 µm.

Free Engineering Tool

Turned Surface Finish Calculator — Ra from Feed & Nose Radius

The question asked at every lathe: what feed do I need for the Ra on the drawing? This works the classic relationship both ways — feed and insert nose radius → theoretical Ra, or target Ra → the maximum feed that can achieve it — with an honest note on how far reality sits above the theory.

Feed (mm/rev)

Insert nose radius rε (mm)

Reference tool. This is the theoretical (geometric) finish — the cusps the nose radius leaves at a given feed. Real turned surfaces typically measure 1.2–2× the theoretical Ra once built-up edge, vibration, tool wear and material behaviour join in, and below roughly 0.05 mm/rev the theory collapses entirely (minimum chip thickness). Treat the result as the floor, not a promise. Figures are provided in good faith for early design guidance and are not a substitute for the published standard or your own engineering judgement. Always verify against the controlled standard and your drawing before manufacture. If a feature is critical, tell us at quotation stage and we'll confirm it explicitly.

Feed, nose radius and the finish you actually get

A turned surface is a very fine screw thread: each revolution the insert moves along by the feed, and the nose radius leaves a scallop between passes. Geometry alone fixes that scallop, and the standard approximation is Ra ≈ f² ÷ (32 × rε) — feed in mm, radius in mm, then ×1000 into µm. Because feed enters squared, halving the feed quarters the theoretical roughness, while doubling the nose radius only halves it. That is why finish problems are usually solved at the feed, and why the reverse mode of this tool — drawing Ra in, maximum feed out — is the direction that earns its keep.

The classic worked example: f = 0.2 mm/rev on an rε 0.8 insert gives 0.04 ÷ 25.6 = 1.56 µm — which is why “0.2 on an 0.8 nose gives you about Ra 1.6” is folklore on every shop floor. It is also self-consistent with the N grades: to hold N6 (Ra 0.8) on the same insert you must come down to about 0.14 mm/rev, and N5 (0.4) wants under 0.10 — at which point cycle time doubles and it is usually cheaper to machine at N7 and electropolish, which is exactly what we do on 316L and titanium medical work.

Reality sits above the theory, not below it: built-up edge in gummy materials, vibration from slender parts, worn edges and coolant condition all add roughness the formula cannot see. A well-behaved setup lands 1.2–1.5× theoretical; a marginal one 2× or worse. And below roughly 0.05 mm/rev the model fails in the other direction — the edge starts ploughing rather than cutting once feed approaches the edge radius, and the finish gets worse as you slow down. If the number this tool gives you is a feed under 0.05, the honest answer is a finer-finishing process, not a slower turn.

Questions engineers actually ask

Turned finish — FAQ

How do you calculate surface finish from feed rate?

Theoretical Ra (µm) ≈ f² / (32 × rε) × 1000, with feed f in mm/rev and insert nose radius rε in mm. A 0.2 mm/rev feed on a 0.8 mm nose radius gives about 1.6 µm Ra.

What feed rate do I need for Ra 1.6 or Ra 0.8?

Rearrange to f = √(32 × rε × Ra / 1000). On a 0.8 mm nose radius: Ra 1.6 needs about 0.20 mm/rev; Ra 0.8 needs about 0.14 mm/rev; Ra 0.4 about 0.10 mm/rev — before the real-world margin.

Why is my actual Ra worse than the calculation?

The formula only models the geometric cusps. Built-up edge, vibration, tool wear, insufficient coolant and material tearing all add roughness on top — typically 1.2 to 2 times the theoretical value. Use the calculation as the floor.

Does a bigger nose radius always improve finish?

Geometrically yes — Ra falls in proportion to radius — but a larger nose increases radial cutting force, which invites chatter on slender parts and can worsen the real finish. It also changes corner geometry. Balance, do not maximise.

Can turning achieve Ra 0.4?

Rarely straight off the tool, and not reliably — the required feeds sit at or below the minimum-chip-thickness limit. The dependable route is to turn at Ra 1.6 or so and finish by another process; we provide electropolishing to Ra 0.4 or better on 316L and titanium.

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