Surface Finish Ra to Rz Converter: RMS, ISO N-Grades & Scallop Chart
To convert arithmetic average surface roughness (Ra) between metric and imperial units, multiply micrometers (μm) by 39.37 to obtain microinches (μin), multiply Ra by 1.11 to estimate Root-Mean-Square (RMS / Rq), and multiply Ra by the process-specific factor (3.8× to 4.5× for turning/milling, or 5.0× to 7.5× for grinding/honing) to determine Rz.
〰️ Interactive 4-Way Surface Roughness Converter (Ra, Rz, RMS/Rq & ISO N-Grade) + Scallop Solver
Convert between arithmetic average roughness (Ra), mean peak-to-valley height (Rz), root-mean-square (RMS/Rq), and ISO 1302 N-grades across micrometers (μm) and microinches (μin).
Why Does the Rz to Ra Conversion Ratio Depend on the Machining Process Under ISO 4287 and ASME B46.1?
A widespread misconception on generic conversion tables is that Mean Peak-to-Valley Height (Rz) is always a fixed 4.0× multiple of Arithmetic Average Roughness (Ra). In physical surface metrology governed by ISO 68-1 International Thread Standard (ISO 4287 / ISO 21920), ASME B1.1 Unified Inch Screw Threads (ASME B46.1), and NIST (National Institute of Standards and Technology) profilometer calibration standards, Ra measures the integrated absolute mean deviation of the roughness profile from the centerline, whereas Rz averages the vertical distance between the highest peak and deepest valley across five consecutive sampling lengths.
Because periodic single-point turning and face milling produce uniform, repeatable sinusoidal cusp waveforms, their empirical Rz/Ra ratio clusters tightly between 3.8× and 4.5×. In contrast, abrasive cylindrical grinding, honing, lapping, and electrical discharge machining (EDM) generate stochastic profiles with isolated deep oil-retention valleys, expanding the Rz/Ra ratio to 5.0×–7.8×! This distinction is critical when finishing bearing journals for ISO 286 Hole & Shaft Fits or dynamic hydraulic seal bores per NASA Fastener Design Manual (NASA RP-1228) design guidelines.
| ISO Grade | Ra (μm) | Ra (μin / CLA) | RMS / Rq (μm) | RMS / Rq (μin) | Mean Rz (μm) | Mean Rz (μin) | Typical Machining Process | Action |
|---|---|---|---|---|---|---|---|---|
| N3 | 0.10 μm | 4 μin | 0.11 μm | 4.4 μin | 0.65 μm | 26 μin | Superfinishing / Optical Lapping | |
| N4 | 0.20 μm | 8 μin | 0.22 μm | 8.9 μin | 1.20 μm | 47 μin | Precision Honing / Cylindrical Lap | |
| N5 | 0.40 μm | 16 μin | 0.44 μm | 17.8 μin | 2.00 μm | 79 μin | Fine Cylindrical Grinding / Honing | |
| N6 | 0.80 μm | 32 μin | 0.89 μm | 35.5 μin | 3.80 μm | 150 μin | Commercial Surface Grinding / Reaming | |
| N7 | 1.60 μm | 63 μin | 1.78 μm | 70.0 μin | 6.80 μm | 268 μin | Finish CNC Turning & End Milling | |
| N8 | 3.20 μm | 125 μin | 3.55 μm | 139 μin | 13.5 μm | 531 μin | Standard CNC Milling & Boring | |
| N9 | 6.30 μm | 250 μin | 6.99 μm | 278 μin | 26.0 μm | 1,024 μin | Semi-Finish Turning & Drilling | |
| N10 | 12.50 μm | 500 μin | 13.88 μm | 555 μin | 52.0 μm | 2,047 μin | Rough Hogging / Saw Cutting |
How Do Nose Radius (r_ε) and Feed Rate (f) Determine Theoretical Turning Scallop Height?
When programming a CNC lathe or boring head, you can predict the exact theoretical surface finish before touching metal by applying Schmaltz's kinematic cusp equation from Machinery's Handbook (Industrial Press): R_max ≈ Rz = f² / (8 × r_ε) and Ra ≈ f² / (31.2 × r_ε), where f is the feed rate per revolution (mm/rev or IPR) and r_ε is the carbide insert corner nose radius. Notice that feed rate is squared while nose radius is linear: cutting your lathe feed rate in half reduces theoretical surface roughness by a factor of four (400% smoother), whereas doubling your insert nose radius from 0.4 mm to 0.8 mm reduces roughness by 50%.
During first-hand shop profilometer audits using a Mitutoyo Surftest SJ-210 diamond-stylus tester on 4140 alloy steel shafts and ANSI B17.1 Keyed Shafts, our team confirmed that maintaining surface speeds above the built-up edge (BUE) zone is essential so actual Ra matches kinematic theory. Combine this converter with our Drill Press SFM & RPM Chart, Three-Wire Thread Calculator, and Master Bolt Torque Chart (since smoother under-head flange surfaces lower the K-friction nut factor).
| Insert Nose Radius r_ε | Feed f (mm/rev) | Feed f (IPR) | Theoretical R_max / Rz | Theoretical Ra (μm) | Theoretical Ra (μin) | Empirical Rz/Ra Multiplier Band |
|---|---|---|---|---|---|---|
| 0.40 mm (1/64") | 0.08 mm/rev | 0.0031 IPR | 2.00 μm | 0.51 μm | 20.2 μin | 3.8× – 4.2× (Periodic Turning) |
| 0.40 mm (1/64") | 0.15 mm/rev | 0.0059 IPR | 7.03 μm | 1.80 μm | 71.0 μin | 3.8× – 4.4× (Finish Turning) |
| 0.80 mm (1/32") | 0.12 mm/rev | 0.0047 IPR | 2.25 μm | 0.58 μm | 22.7 μin | 3.8× – 4.3× (Fine Boring) |
| 0.80 mm (1/32") | 0.20 mm/rev | 0.0079 IPR | 6.25 μm | 1.60 μm | 63.1 μin | 3.9× – 4.5× (Standard N7 Turn) |
| 0.80 mm (1/32") | 0.30 mm/rev | 0.0118 IPR | 14.06 μm | 3.61 μm | 142.0 μin | 4.0× – 4.6× (Medium N8 Turn) |
| 1.20 mm (3/64") | 0.25 mm/rev | 0.0098 IPR | 6.51 μm | 1.67 μm | 65.7 μin | 3.8× – 4.4× (Heavy Nose Finish) |
| Abrasive Grinding / Honing | Random Grit | Multi-Point | 1.5 – 6.0 μm | 0.25 – 1.0 μm | 10 – 40 μin | 4.5× – 7.5× (Stochastic Valleys) |
When operating a portable contact skid-type diamond stylus profilometer on the machine shop floor, selecting the correct ISO 4288 cutoff filter wavelength (λ_c) is mandatory for accurate Ra and Rz readings: use a 0.25 mm cutoff for mirror-ground surfaces (Ra 0.02 to 0.10 μm), a standard 0.80 mm cutoff for precision turned and milled parts (Ra 0.10 to 2.0 μm), and a 2.50 mm cutoff for rough-machined surfaces above 2.0 μm Ra.
In addition, always orient the profilometer stylus travel path perpendicular to the machining lay (across the tool feed cusps rather than parallel to the turning or grinding grooves) so the diamond tip traverses the full peak-to-valley waveform geometry and captures true surface texture amplitude.
Frequently Asked Questions About Ra, Rz, and RMS Surface Finish Conversions
What is the exact formula to convert microinches (μin) Ra to micrometers (μm) Ra?
Divide the microinch (μin) value by 39.3701 (or multiply by 0.0254). For example, a standard machine shop callout of 63 μin Ra equals 1.60 μm Ra (ISO Grade N7), and 32 μin Ra equals 0.80 μm Ra (ISO Grade N6).
Why do German and European DIN drawings specify Rz instead of Ra?
Because Ra averages out isolated scratches or deep valleys over the sampling length, two surfaces with identical Ra values can have vastly different sealing or wear behavior; Rz directly catches peak-to-valley extremes that could leak past O-rings or initiate fatigue cracks.