SYZ ENGINEERING PRELIMINARY DESIGN TOOL · REFERENCE-BASED ESTIMATE
Surface Roughness Converter (Ra ↔ RMS ↔ N-Grade)
Convert arithmetic average roughness (Ra) to RMS (Rq) and the nearest ISO 1302 roughness grade number (N1–N12).
SURFACE FINISH · Ra / RMS / ISO GRADE NUMBER
Surface Roughness Converter
Converts arithmetic average roughness (Ra) to RMS (Rq) and the nearest ISO 1302 roughness grade number (N1–N12).
[Micrometers, μm]
1 μm = 39.4 μin. Common machined-surface callout example: 1.6 μm Ra ≈ 63 μin Ra.
Equivalent RMS (Rq)
1.776 μm
≈ 69.9 μin Ra · Nearest ISO grade: N7
✔
Ratio assumes a sinusoidal-like profile — real Ra:RMS ratio varies 1.0–1.3× by process.
Engineering Model (sinusoidal-profile approximation)
Standard Reference
ISO 1302 defines the N1–N12 roughness grade numbers as a fixed geometric progression. The Ra:RMS ratio of ≈1.11 is the exact value for a pure sinusoidal surface profile — a common textbook approximation, not a universal conversion for every real surface texture.
Calculation Method
RMS ≈ 1.11 × Ra
Assumptions & Limitations
- The 1.11× ratio is exact only for an idealized sine-wave profile — ground, turned and milled surfaces each have different real Ra:RMS ratios, typically in the 1.0–1.3× range.
- N-grade is reported as the single nearest standard value, not an interpolated in-between figure.
- Does not account for waviness or lay direction, both of which affect functional surface performance independent of Ra/RMS.
STATIC REFERENCE DATA
Reference: Full ISO 1302 Roughness Grade Table
Precomputed values from the exact formula used above — useful as a quick lookup without re-entering inputs.
| Grade | Ra (μm) | Ra (μin) | Typical Process |
|---|---|---|---|
| N4 | 0.2 | 7.9 | Lapping, honing, superfinishing |
| N5 | 0.4 | 15.7 | Grinding, honing |
| N6 | 0.8 | 31.5 | Grinding |
| N7 (calculator default) | 1.6 | 63.0 | Precision turning, grinding |
| N8 | 3.2 | 126.0 | Turning, milling |
| N9 | 6.3 | 248.0 | Rough turning, milling |
| N10 | 12.5 | 492.0 | Rough machining, sawing |
Process associations are typical/approximate ranges commonly cited in machining references — actual Ra achieved depends heavily on tooling, feed rate and material.
WORKED EXAMPLE
Reading a 1.6 μm Ra Drawing Callout
A rod end bore drawing calls out 1.6 μm Ra on the bearing seat. What does that mean in RMS and ISO grade terms, and is it achievable by standard turning?
- RMS ≈ 1.11 × 1.6 = 1.776 μm (sinusoidal-profile approximation).
- 1.6 μm Ra ≈ 63 μin Ra — matches the commonly seen “63 RMS” callout on US-drawing legacy prints (loosely; many older prints label Ra as “RMS” even though they’re numerically close but not the same quantity).
- Nearest ISO grade: N7, typically associated with precision turning or grinding.
- Standard turning alone often lands in the N7–N9 range depending on feed and tooling — 1.6 μm Ra is achievable but toward the finer end; verify with your machinist’s actual process capability.
Related reading: Metallurgy & Quality Control →