Ra to Rz Conversion (and Rz to Ra)

Table of Contents

Converting Between R_a and R_z

You got a drawing with a callout for Rz. However, you are used to using Ra. Can you convert the R_z callout to R_a? The answer is not straightforward. Learn why, or head directly to the Ra-Rz converter calculator.

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What is the difference between R_a & R_z ?

R_a – The arithmetic average of the absolute values of the profile height deviations from the centerline.
R_z – the vertical distance from the highest peak to the lowest valley within the scanned profile.

You can learn more in our Surface Finish Units Dictionary.

How to Convert between R_a & R_z ?

A common question among machinists and engineers is, “How to convert from Ra to Rz?”. A precise conversion like one can make between Kw and HP is impossible since Ra and Rz are two different properties.

It is like asking, “how do I convert height to weight?”. You cannot convert. However, you can make a rough estimation based on statistics. A person with a height of 6 feet will weigh between 140 and 290 pounds (At a probability of 99%). We know he will not weigh 100 pounds, nor 400.

The same logic is applied when converting Ra to Rz (or Rz to Ra). Based on statistics, we can forecast the Rz range for a specific Ra with reasonable probability.

R_a / R_z Conversion formulas

Rz to Ra

\begin{array} \Large R_{a\,Min} = 0.03\,\times\,{R_z}^{1.3} &\\&\\ R_{a\,Max} = 0.24\,\times\,{R_z}^{1.06} &\\ \end{array}

Ra to Rz

\begin{array} \Large R_{z\,Min} = 3.8\,\times\,{R_a}^{0.95} &\\&\\ R_{z\,Max} = 14.5\,\times\,{R_a}^{0.75} &\\ \end{array}

Converting between Ra and Rz is not a good engineering practice. It is always recommended to Measure according to the method in which surface roughness is indicated on the drawing.

As you can see in the below graphs, the inaccuracy grows in higher R_a /R_z values.
The explanation is more clear when presented on the Log-Log graph.

R_a/ R_z Conversion Graph

R_a/ R_z Log-Log Conversion Graph

Ra-Rz Convertion Graph Logarithmic scale

R_a / R_z Convention Calculator

R_a / R_z Conversion Charts

R_a to R_z Metric

Ra [µm]	Rz Range [µm]
0.1	0.4 - 2.5
0.2	0.8 - 4
0.5	2 - 9
1	4 - 14
1.5	6 - 20
2	7 - 25
3	11 - 33
5	17 - 49
10	34 - 84
15	50 - 115
20	65 - 140

R_a to R_z Inch

Ra [µ Inch]	Rz Range [µ Inch]
4	16 - 100
8	32 - 160
20	80 - 360
40	160 - 560
60	240 - 800
80	280 - 1000
120	440 - 1320
200	680 - 1960
400	1360 - 3360
600	2000 - 4600
800	2600 - 5600

R_z to R_a Metric

Rz [µm]	Ra Range [µm]
1	0.03 - 0.2
5	0.3 - 1.3
10	0.6 - 3
20	1.5 - 6
50	5 - 15
100	13 - 32
150	21 - 49

R_z to R_a Inch

Rz [µ Inch]	Ra Range [µ Inch]
40	1 - 8
200	12 - 52
400	24 - 120
800	60 - 240
2000	200 - 600
4000	520 - 1280
6000	840 - 1960

Related Glossary Terms:

Surface Finish

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