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RMS vs Ra

A discussion started in 2001 and continuing through 2017 . . .


Q. What does the RMS means? How can we convert 3.2 - 6.3 RMS to Ra value? Please reply immediately.


Hitesh Panchal
- India



Term RMS refers to the mathematical Root Mean Square which is an average of peaks and valleys of a materials surface profile. Ra stands for roughness average.

Ra is a average of only peaks; therefore, to get an Ra, multiple your 3.2 to 6.3 by 2 to get 6.4 to 12.4 Ra.

tony kenton
AF Kenton
Nova Finishing Systems Inc.
Hatboro, Pennsylvania

Ed. note: This thread has continuing errors so it was very hard to follow. We went back and added this anachronistic running commentary based on clarifications by subsequent readers:
     RMS and Ra measure two different things, so there is no actual conversion factor. But for sine wave roughness the factor would be 1.11, and for many real world metal working processes the factor approximates 1.25. Later readers also noted that RMS is usually expressed in microinches whereas Ra is usually expressed in microns; but this is not universally true either, which adds to the confusion :-)


I thought I should point out an error in your RMS to Ra conversion. The ratio is not 2:1, but 1.11:1 This is a significant difference. An RMS of 60 µin would be an Ra of 54 µin, not 30 Ra. You may want to check/verify your source for the ratio as your response prompted me to double-check my own numbers. I am afraid you will find that I am correct.

Please let me know if I misunderstood your comments.

Still a nice website for information on finishing. Keep up the good work.

Michael Herron
ceramics - Golden, Colorado


I agree. RMS is generally accepted to be about 11% higher than Ra. Also note that outside of the US values are generally expressed in microns : 1 micron is equal to 40 micro-inch.


Michael Atkinson
electropolishing - London, England


Ra value means roughness average in microns whereas RMS means root mean square value in micro inches so if you know the conversion from mm to inches you have the answer with you..for e.g. 0.4 Ra value conversion is 16 rms.

- India

Anachronistic running commentary: This is apparently incorrect because Charuhas has omitted the 1.11 conversion factor, and the RMS should therefore be 17.8


Here is how I convert 0.1 µm Ra to RMS

1. step one: convert 0.1 µm to microinches
0.1 µm-.004 µin

2. step two: use the formula RMS=Ra/1.11
RMS=.004/1.11 which equals to: .0018 µin

3. step three: Write the result in standard engineering form:

.0018 µinRMS is usually written as: RMS 18

So here is completed plan on how to convert Ra to RMS (and back)
Good luck

Peter [last name deleted for privacy by Editor]
- Orange, California

Anachronistic running commentary: This is incorrect in step 1 because 0.1 um is not .004 µin; and in step 2a because the conversion factor is upside down; and in step 2b because of arithmetic error anyway. Correcting these errors: 0.1 µm = 4.0 µin; multiplying by 1.11 gives 4.4 µinRMS.


There is no formula to convert Ra values to RMS values or vice versa because the numbers are depending on the type of profile. The conversion factor 1.11 is valid only for sinusoidal profiles. The ratio for saw tooth profiles is closer to 1.17 and the ratio for random profiles can be as high as 1.2!

Fred Couweleers
- Trondheim, Norway

January 25, 2008

A brief response to the Peter from Orange California posting:

It appears there was a unit/conversion error at Step 1.

0.1 µm = 0.1 micrometer = 0.1 micron = 100 micro-millimeter (µ-mm)

Author appears to have divided 0.1 by 25.4 (to get 0.004), but that's the conversion from mm to in. Conversion from meters to inches would be to multiply by 39.37.

Step 2 also appears to have a division error: .004/1.11 = 0.0036 (not 0.0018)

It would seem simpler to convert 0.1 µm Ra to 0.11 µm RMS, then to 4.37 µin RMS.

Jon Johnson
- Los Angeles, California

Anachronistic running commentary: This answer and method appears to be correct, but in commenting upon the division error in step 2, Jon does not note that it should have been multiplication rather than division :-)

May 28, 2008

Actually, this entire thread seems to be riddled with errors.
Ra is in microns
RMS is in microinches

This is the best that I can figure:


However, 1.11 is just a theoretical relationship, and there really is no mathematical relationship, so the actual value varies by process. For most processes, 1.25 is the "best guess".

Sean Doll, P.E.
- Austin, Texas

Anachronistic running commentary: Thanks Sean, but let's underscore the word "entire" -- because your '.254' should be '.0254' :-)

July 25, 2008

Q. After reading all this, I am now completely confused. We have a part that calls for a 63 Ra finish on an English drawing and want to check it in RMS. Anyone know what the equivalent RMS value is?

ed gard
- south bend, Indiana

July 26, 2008

C'mon now, Ed. You can't read a dozen postings in a row, each pointing out the errors in the previous, while having larger errors themselves, without getting confused?  :-)

We've gone back and added a running commentary addressing the errors in the postings, so it should be clearer now. Your Ra is apparently in microinches, not microns. So the RMS you measure should probably be between about 1.11 and 1.25 times the Ra value that you quote.

Some subjects require studying in tutorial format. For example, you can't reasonably ask "How do you design a jetliner" or "How can I safely perform an appendectomy" in an internet posting; you need to take courses and read books. It's beginning to look like surface profile measurement may be a little too complicated for us to learn through buckshot pattern Q&A in an internet forum :-(


Ted Mooney,
Teds signature
Ted Mooney, P.E. RET
Pine Beach, New Jersey

October 20, 2008

Q. Hi gentlemen,

could you help me to calculate 300-400 RMS to be Ra?
Sorry but I don't full understand what you guys talking from beginning, I'm not so familiar with inch.

Soliqin Soliqin
Coating job - Karawang-Indonesia

November 16, 2008

1. Formula
RMS (Microinch)=(Ra/.0254)*1.11 (Micrometer)

2. 300 RMS=6.9 Micrometer
400 RMS=9.2 Micrometer

Kimj, Jaehak
- Daegu, South Korea

May 21, 2009 -- this entry appended to this thread by editor in lieu of spawning a duplicative thread

Q. What would a 250 Ra equal in RMS? Please respond. Need help NOW!

Thanks very much.

Richard Creed
Calibration Tech - Temple, TEXAS

May 22, 2009

Hi, Richard. We appended your inquiry to a letter that explains it all, including the fact that there is no exact conversion because they are measuring different things. Tall people will on average weigh more than short people, but you can't apply a conversion factor to determine a person's weight based on their height.

But for a sine wave profile, with RMS measured in microinch and Ra measured in micrometer, RMS = (Ra/.0254)*1.11, so an Ra of 250 micrometer would equal an RMS of 10,800 microinch. However ... this is so ludicrously rough that it is completely improbable. It seems far more likely that the 250 Ra you've given us is 250 microinches, not 250 micrometers -- equating to an RMS of 277.


Ted Mooney,
Teds signature
Ted Mooney, P.E. RET
Pine Beach, New Jersey

September 15, 2009 -- this entry appended to this thread by editor in lieu of spawning a duplicative thread

Q. I have to offer a part in aluminium oxide ceramics. The surface roughness indicated by the customer is "16 RMS". We indicate the surface roughness in Ra only. Can the RMS value be converted into Ra? If yes; what is 16 RMS in Ra? Appreciate any help.

Andrea Ropos
employee - Mannheim, Germany

October 2, 2009

Q. How to control Ra Value by programming the Feed and Tool Nose Radius calculation? Basically I want to know what is the formulae?

I want to understand the entire concept of Ra and RMS. I would also like to know if there are separate symbols for both. Also in some drawings the numbers are 16, 32, 64 etc whereas in some drawings they say 0.5, 1.2, etc. Can anyone help me to identify the differences?


Ebanezer Jacob
forging & turning of brass - Gujarat, India

January 19, 2010

Q. Is there any specification to use either Ra or Rz to any particular form of surface?
Kindly clarify on which type of surfaces Ra should be used and similarly Rz

arunan nattarayan
automotive - coimbatore, india

December 14, 2011

Q. Hi,
For what purpose Ra value should be calculated?
How to check the Ra value?

Kindly, guide me about this for tube surface finish in tube industry.


Mahesh S. Iyer
- Hyderabad, Andhrapradesh, India



December 14, 2011

Hi, Mahesh.

Ra is not to be calculated, it is to be measured with a profilometer =>

I am sorry but I do not really understand the question. Are you asking why "Ra" measurement specifically is important (as opposed to Rmax, Rz, and RMS)? Or are you asking why should tubes be of a uniform, predictable smoothness rather than of random roughness? Whether the tubing be plated, painted, machined, used as a bearing, or as a clutch or brake surface, or whatever, there are 101 reasons for needing a consistent finish. Even operations as simple as writing on the tubing with a marker, or sticking an adhesive label on it will have different results on a very rough surface than on a very smooth one. Good luck.

Ted Mooney,
Teds signature
Ted Mooney, P.E. RET
Pine Beach, New Jersey

January 19, 2012

Ra roughness average is the main height as calculated over the entire measured length or area. It is quoted in micrometers or micro-inches. For 2 dimensional computation:
Ra = 1/n * SUM(ABS[Zi-Zmean] from i = 1 to n

The root means square(RMS)average is precisely that: the square root of the average height deviations from the mean line/surface squared.

RMS = SQRT[ 1/n* SUM(Zi-Zmean)^2 ] from i=1 to n

These are for 2 dimensions

Ian Yee
- Austin, Texas USA

October 18, 2012

RMS= (RA/25.4)*1000


- singapore

October 19, 2012

Hi Solai. Thanks, but sorry, that's not correct. But it is a proper conversion from micrometers to microinches. So let's rewrite it to
Ra [µin.] = (Ra[µm]/25.4)*1000


Ted Mooney,
Teds signature
Ted Mooney, P.E. RET
Pine Beach, New Jersey

March 13, 2013

A. RMS and Ra are based on different methods of calculating the roughness. Both are done with a profilometer, but the profilometer calculates the roughness differently for Ra and RMS.

Ra is the arithmetic average of surface heights measured across a surface. Simply average the height across the microscopic peaks and valleys.

RMS is a Root Mean Squared calculation. That means you:
1) measure height across the microscopic peaks and valleys.
2) calculate the SQUARE of each measurement value
3) calculate the MEAN (or average) of those numbers (squared)
4) find the square ROOT of that number

The RMS is sensitive to the BIG peaks and valleys.
Ra is not.

Both numbers can be expressed in metric or inch.
RMS was more popular 40 years ago when I learned to measure surfaces. (most US industry still worked in inches.) Those old inch drawings specify RMS.

Ra is more commonly used today. (now most US industries work in metric) So they specify Ra in metric.

Both Ra and RMS can be expressed in metric or inch.
Inch/metric conversion guides are available on the web.
But there is no reliable way to convert between Ra and RMS.
It's only an estimate based on guessing what the shape of the microsurface looks like.

Read the user guide that came with your profilometer. Most of them can switch between RMS and Ra. Measure the part the way the drawing calls for.

Mark Anderson
- Watertown, Wisconsin, USA

January 2016

thumbs up sign"Measure the part the way the drawing calls for."

Bravo, Mark! You are absolutely correct.


Ted Mooney,
Teds signature
Ted Mooney, P.E. RET
Pine Beach, New Jersey

April 25, 2017

A. Hi People, I'm Tony from Taylor Hobson do Brasil.

RMS is the same as Rq, according to the Taylor Hobson definition:

Mathematically, Rq is the Square Root of the Mean of all the "Z" Values after they have been Squared.

Tony Pereira Ferreira
Taylor Hobson do Brasil - São Paulo, SP, Brazil

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