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CNC Turning Surface Roughness and Feed Calculator

On a lathe, the surface finish at a given feed is set by the insert's nose radius. This calculator gives the theoretical roughness and the largest feed that still meets your Ra, along with the turning time.

Your numbers

Feed per revolution

mm/rev

Insert nose radius

Target Ra on the drawing

Workpiece diameter

Length of cut

Cutting speed

m/min

Depth of cut

Your results

Theoretical Ra at this feed

0.8789

Micrometres, geometric minimum.

Maximum feed for the target Ra

0.2024

mm/rev.

Theoretical peak-to-valley Rt

3.5156

Micrometres.

Spindle speed

1,273

Cutting time at this feed

0.5236

Minutes for one pass.

Material removal rate

cm3 per minute.

These are geometric, theoretical values. Real Ra is usually higher because of built-up edge, tool wear, vibration, machine condition and material. Treat the result as a lower bound and verify with a surface roughness tester.

Save results:

Theoretical Ra (um) vs feed per revolution

Sweeps Feed per revolution from 0.05 to 0.4, holding your other inputs fixed.

Link finish requirements to routing times

Optional: a short review of how to store process parameters with ERP routings.

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

How to use it

Select the nose radius of the insert, enter the feed per revolution you plan to run and the Ra on the drawing. The calculator shows the theoretical Ra and Rt and the maximum feed that would still hit the target. Fill in diameter, length and cutting speed to see the spindle speed, the time of a pass and the removal rate. Use the chart to see how fast Ra grows as you raise the feed.

The formulas

For a tool with nose radius r and feed f, the theoretical peak-to-valley height is Rt = f^2 / (8 x r). The arithmetic average is Ra = f^2 / (32 x r), both in the same length unit, converted here to micrometres. Rearranged, the feed for a target Ra is f = sqrt(32 x r x Ra). With a 0.8 mm radius and a 1.6 um Ra requirement, the maximum feed is about 0.20 mm/rev. Doubling the nose radius allows a feed about 41 percent higher for the same Ra.

Ra grows with the square of the feed.
Ra falls in proportion to nose radius.
A larger radius also increases radial force and the risk of chatter.

Practical limits

The geometric formula holds only when the depth of cut is larger than the nose radius's contribution and the feed is less than the nose radius. At very low feeds, built-up edge and rubbing prevent Ra from improving, so there is a feed below which finish gets worse. Wiper inserts break the rule: their flat land lets you run roughly twice the feed for the same Ra. Treat the figure as a planning aid and verify on the first part.

Common mistakes

People often pick a nose radius that is too big for a thin or long part, and then see chatter that ruins the finish, which is worse than a slightly lower feed. Another mistake is confusing Ra with Rz, which differ by about a factor of four or more. If your drawing uses RMS or Rz, convert before you use the target here.

Frequently Asked Questions

Is the calculated Ra what I will measure?

Usually the measured value is higher. The formula assumes a perfectly sharp, rigid tool with no vibration and no material side flow. Real parts often come out 20 to 100 percent above the geometric figure, so leave margin.

What nose radius should I choose?

For finishing, the largest radius the part's rigidity allows. A common choice is 0.8 mm for general work, 0.4 mm for finishing small parts or thin walls, and 1.2 mm or more for roughing and heavy cuts.

Does depth of cut matter for the finish?

Not in the geometric formula as long as the depth of cut is at least about the nose radius. If the depth is smaller than the radius, the effective radius is smaller and the roughness is higher.

How do wiper inserts change this?

A wiper insert has a flat on the trailing edge that smooths the ridge. It allows a feed of around twice the normal feed at similar Ra. Use the manufacturer's data because the formula here does not model wipers.

If you manage lathe jobs in an ERP and want routings to reflect real cycle times, we can discuss how. This calculator stands alone.

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