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).

Roughness Average (Ra)
[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 →