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Surface Finish Standards: Ra vs Rz

Why "Smooth" isn't a specification. Decoding Ra, Rz, and the math behind surface texture.

The Language of Roughness

In CNC machining, surface finish is critical for sealing surfaces, bearing fits, and aesthetics. The two most common metrics are Ra and Rz.

Ra (Average Roughness)

The arithmetic average of the absolute values of the profile height deviations from the mean line.

Best for: General indication of surface texture. Most common in US/ISO.
Weakness: Hides singular defects (scratches).

Rz (Mean Roughness Depth)

The average of the maximum peak-to-valley heights of 5 consecutive sampling lengths.

Best for: Sealing surfaces and sliding fits. Common in DIN (German) standards.
Strength: More sensitive to extreme peaks/valleys.

Conversion Chart (Approximate)

While there is no exact mathematical conversion (because they measure different things), this chart provides the industry-accepted equivalence.

GradeRa (µm)Ra (µin)Rz (µm)Process
N12502000200Flame Cut / Saw
N96.325025Rough Milling/Turning
N71.6636.3Finish Milling
N60.8323.2Grinding / Fine Turn
N40.280.8Lapping / Polishing

How to Calculate Theoretical Finish

In turning, theoretical surface finish is determined by Feed Rate and Tool Nose Radius.

Ra = (f²) / (32 × r)
Where:
f = Feed per revolution (mm/rev or ipr)
r = Tool nose radius (mm or inch)

Takeaway: To improve finish, decrease feed rate or increase nose radius.

Need a Number?

Calculate the theoretical Ra for your turning operation based on feed and insert radius.

Open Calculator

Reality Check

Theoretical finish is just geometry. Real world factors like vibration, tool wear, and built-up edge (BUE) will always make the actual finish roughly 2x worse than the theoretical calculation.