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Turning Surface Finish Calculator: Ra from Feed and Nose Radius

The finish a lathe leaves is mostly geometry: each revolution the insert corner draws a small arc, and the ridges between arcs set the roughness. This calculator turns feed and nose radius into theoretical Ra, and works backward to the feed that meets a drawing callout.

Your numbers

Feed per revolution

mm/rev

The finishing feed you plan to run.

Insert nose radius

Target Ra from drawing

Used to find the maximum feed that still meets the callout.

Your results

Theoretical Ra

1.5625

Micrometres, from Ra = f squared / (32 r).

Maximum feed for target Ra

0.2024

mm/rev. Real finishes are usually 1.5 to 3 times worse than theory.

Theoretical Ra in microinches

61.5158

Peak-to-valley height Rt

6.25

Micrometres, from Rt = f squared / (8 r).

Practical feed (60% of maximum)

0.1214

mm/rev, leaving margin for built-up edge and tool wear.

Theoretical geometric finish only. Actual Ra depends on material, speed, rigidity, coolant, edge condition and chatter.

Save results:

Theoretical Ra vs feed per revolution

Sweeps Feed per revolution from 0.05 to 0.5, holding your other inputs fixed.

Link finish targets to your routings

Optional: talk to us about carrying machining parameters and cycle times through your ERP routings.

Optional. The tool and every export work without this. No spam.

How to use the calculator

Enter the feed per revolution, pick the nose radius of your finishing insert, and read the theoretical Ra and Rt. If the drawing gives a target Ra, the maximum feed output tells you the fastest feed the geometry allows. Treat the practical feed as your starting point, since theory assumes a perfectly sharp, rigid, vibration-free cut. Use the chart to see how quickly roughness grows as feed climbs.

Feed is in mm per revolution, not per minute.
Nose radius is stamped on the insert box, for example CNMG 12 04 08 is 0.8 mm.
Ra results are in micrometres; the microinch line is for inch drawings.

The formula behind it

For a round nose tool with feed smaller than the nose radius, the ridge height is Rt = f squared / (8 r) and the arithmetic average is Ra = f squared / (32 r), where f is feed per revolution and r is nose radius. Because feed is squared, halving feed cuts Ra by four. Doubling the nose radius halves Ra. That is why a 1.2 mm radius insert can run noticeably faster than a 0.4 mm insert for the same finish.

Worked example

A shaft journal calls for Ra 1.6 um. With a 0.8 mm nose radius the maximum feed is the square root of 32 x 0.8 x 1.6 / 1000, which is about 0.20 mm/rev. In practice you would run closer to 0.12 mm/rev and verify with a profilometer or comparison plate. If cycle time matters, a wiper insert can often double feed at the same Ra, but check your supplier data because wiper geometry does not follow this simple formula.

Common mistakes

The most common error is using a feed larger than the nose radius, where the formula no longer applies and a flat contact patch forms. Another is expecting theory to match the part: built-up edge on soft steels and aluminium, worn edges, long overhangs and low speeds all raise Ra well above the figure. Too large a nose radius can also trigger chatter on slender parts, so confirm rigidity before chasing a finish with bigger radius.

Do not use this for threads, grooves or ground surfaces.
Check the tool has the radius you think it does after reshaping or wear.
Finishing depth of cut should be larger than the nose radius edge wear land to avoid rubbing.

Frequently Asked Questions

Is theoretical Ra the same as measured Ra?

No. Theoretical Ra is the geometric minimum for a perfect tool and machine. Measured values are commonly higher because of tool wear, vibration, built-up edge and material tearing. Use theory to set a safe starting feed and then confirm with a surface roughness tester.

What feed should I use for Ra 0.8 um?

With a 0.8 mm nose radius the geometric maximum is about 0.14 mm/rev. In practice start near 0.08 to 0.10 mm/rev, use sharp positive inserts at higher speed, and verify. A wiper insert may allow more feed.

Why does bigger nose radius give a better finish?

A larger radius makes shallower, wider scallops between passes, so ridge height falls for the same feed. The trade-off is higher radial cutting force, which can cause chatter on thin walls or long bars.

Does cutting speed affect Ra?

The formula ignores speed, but real finish improves at higher speed in steel because built-up edge disappears. Very low speed often leaves a torn, rough surface regardless of feed.

If speeds, feeds and finish targets live in drawings and routings, Netray can help pull them into your ERP routing data so planners see realistic cycle times.

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