Surface Roughness Calculator Formula

Understand the math behind the surface roughness calculator. Each variable explained with a worked example.

Formulas Used

Ten-Point Roughness (Rz)

rz_value = ra_value * rz_factor

Ra in micro-inches

ra_inches = ra_value * 39.37

ISO Grade (N)

n_class = (ra_value <= 0.025) ? 1 : ((ra_value <= 0.05) ? 2 : ((ra_value <= 0.1) ? 3 : ((ra_value <= 0.2) ? 4 : ((ra_value <= 0.4) ? 5 : ((ra_value <= 0.8) ? 6 : ((ra_value <= 1.6) ? 7 : ((ra_value <= 3.2) ? 8 : ((ra_value <= 6.3) ? 9 : 10))))))))

Variables

VariableDescriptionDefault
ra_valueArithmetic Mean Roughness (Ra)(micrometres)1.6
rz_factorRz/Ra Ratio (typical 4-7)5

How It Works

Surface Roughness Parameters

Surface roughness describes the fine irregularities on a machined surface.

Key Parameters

Ra (arithmetic average roughness) is the most common measure - the average deviation from the mean line.

Rz (ten-point height) is the average difference between the 5 highest peaks and 5 deepest valleys. Rz is typically 4-7 times Ra depending on the machining process.

ISO Roughness Grades

N1 (Ra 0.025) through N12 (Ra 50), each step doubling the roughness.

Worked Example

A machined surface with Ra = 1.6 micrometres.

ra_value = 1.6rz_factor = 5
  1. 01Rz = 1.6 x 5 = 8.0 micrometres
  2. 02Ra in micro-inches = 1.6 x 39.37 = 63 micro-in
  3. 03ISO grade: Ra 1.6 corresponds to N7

Frequently Asked Questions

What Ra values do common processes achieve?

Grinding: 0.1-1.6 Ra. Turning: 0.8-6.3 Ra. Milling: 0.8-6.3 Ra. Lapping: 0.012-0.1 Ra. Polishing: 0.006-0.05 Ra. Sand casting: 12-25 Ra.

Why specify surface roughness?

Roughness affects friction, wear, fatigue life, sealing ability, appearance, and coating adhesion. Tighter roughness requirements increase machining cost and time, so specify only what the function requires.

How is surface roughness measured?

The most common method uses a stylus profilometer that drags a diamond tip across the surface and records height variations. Non-contact methods include optical interferometry and confocal microscopy.

Ready to run the numbers?

Open Surface Roughness Calculator