What is the Ra formula for turning?

The theoretical arithmetic roughness Ra = f²/(32×r), where f is feed per revolution in mm and r is the tool nose radius in mm. Result is in mm; multiply by 1000 for μm.

How does feed affect surface finish?

Surface roughness increases with the square of feed. Halving the feed reduces Ra by a factor of 4, making feed the dominant parameter for finish quality.

How does nose radius affect surface finish?

Larger nose radius produces better surface finish. Doubling the nose radius halves the Ra value. Typical radii range from 0.4 to 1.6 mm.

Why is actual Ra worse than theoretical?

Real Ra is typically 1.5–3× theoretical due to vibrations, tool wear, built-up edge, material properties, and machine rigidity. The formula gives the best achievable finish.

What is a good surface finish for turned parts?

Ra 1.6 μm is common for general machining. Ra 0.8 μm for precision fits. Ra 0.4 μm or better requires fine finishing or grinding.

Free Engineering Tool #212

Turning Surface Finish Calculator

Calculate theoretical surface roughness Ra for turning. Enter feed per revolution and tool nose radius.

Ra = f² / (32 × r)TurningAuto-Calc

Results

Theoretical Ra

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Rt (peak-to-valley)

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Estimated Actual Ra (×2)

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Theoretical Surface Roughness

Ra — arithmetic average roughness (μm)
Rt — peak-to-valley roughness (μm)
f — feed per revolution (mm/rev)
r — tool nose radius (mm)

Example — Standard turning

Given: f = 0.20 mm/rev, r = 0.8 mm

Ra = 0.20² / (32 × 0.8) = 0.04 / 25.6 = 0.00156 mm = 1.56 μm

Rt = 0.20² / (8 × 0.8) = 0.04 / 6.4 = 6.25 μm

Turning Surface Finish Calculator | Ra Formula | Vibromera

Published by Nikolai Shelkovenko on February 15, 2026 March 5, 2026

Results

Theoretical Surface Roughness