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Overall Loop Accuracy
How to calculate the overall loop accuracy

I request the experts of this forum to kindly answer my question:

If there are five elements in a loop (Say an Orifice, a DP sensor, DP transmitter, Sq. root extractor & a 4-20mA Reader) each with an individual accuracy of x, y, z, p, q percent of the full scale. Then what should be the effective overall accuracy of the loop?

thanks and regards

RMS = root mean square

See the last paragraph of this article on "Understanding Flowmeter Specs" for an example (mag, not DP, but principle is identical)


By Michael Batchelor on 14 March, 2009 - 6:30 pm

Most plants use the square root of the sum of the squares.

When you figure it out, don't forget that you want to convert the individual instrument tolerance back to real numbers, not the percent. I.e., a quarter percent instrument ( 0.25%) is really 0.0025.

A one percent instrument (1%) is really 0.001.

So, square the tolerance of each instrument in the loop (remember the numbers are smaller, not bigger), add the 5 results together, then take the square root of the sum.

Basically, what Carl said.


Michael Batchelor
Industrial Informatics, Inc.
3281 Associate Dr.
N. Charleston, SC 29418

The textbook answer, if all errors are independent, is:

SQRT (x^2 + y^2 + z^2 + p^2 + q^2)


By Alan Balcombe on 14 March, 2009 - 11:11 pm

Begging Carl's pardon, I think he meant a Root Sum Square (RSS) calculation, but I couldn't reach the link he mentioned.

Wikipedia mentions RSS under the heading "Tolerance stacks".

Purists might tell you to just take the worst case - the sum of each element in the group's maximum specified uncertainty.

But those more sympathetic will accept that elements' uncertainties may be random and therefore the different polarities added together may improve the overall uncertainty.

If you have individually calibrated the dp transmitter, square root extractor and meter then for a given dp you can sum these elements' uncertainties. Your flow primary element supplier and/or the flow engineering standard will give you a (random) error for the primary element depending on the installation.

Note that flow primaries such as orifice plates uncertainties increase with flow turndown, so you'll get better accuracy at higher flow rates. The same may apply to your dp transmitter and square root extractor.

If you havent purchased or calibrated the equipment yet, then you could do the RSS calculation. Take each element's % uncertainty, square it, sum them all, the take the square root of the total. It'll give you a more probable and typical system accuracy for that value of flow/dp but which is less than the sum of each element's worst case.

I hope this helps a bit.
Alan Balcombe
Weidmuller Inc.
(alan.balcombe @

For any serious study of this issue, I strongly recommend Ron Dieck's book on measurement uncertainty, which can be obtained from ISA Press.

Walt Boyes
Editor in Chief
Control and
Read my blog SoundOFF!! At

By Carl Ellis on 15 March, 2009 - 8:36 pm

previous URL had excess <br>

correct URL:

or search for "understanding flowmeter specifications" at


Thank you.



Suppose we want to calibrate a Flow measurement device to have an acceptable accuracy,for example we say +/-0.2% accuracy is acceptable,could you guide me about the points that have to be considered to achieve the required accuracy in calibration?Even for the calibrator that is used for.


I'm not Alan, but let me take a turn with this.

First, what kind of flow meter? Flow meters are not all created equal. Unless we know what the meter is, we can't even begin to guess what kind of installed accuracy you will get.

Second, what fluid?

What pipe size and material?

What flow rates? Min. Max. and Average?

An installed accuracy of +/- 0.2% of what? Full Scale? Indicated reading?

You ought to know this: an installed accuracy of that magnitude is probably impossible.

Besides, you'd have to have a prover of known accuracy that is better than an order of magnitude better than the accuracy you are trying to calibrate to in order to do it.

There is no electronic calibration means available.

Walt Boyes
837 Suncrest Drive
Aurora IL 60506

Thank you for your reply.

Our application is Oil & Gas. About the flowmeter, I mean an orifice element which is connected to a flow computer, in addition to the dp, Pressure, Temperature and density are connected to flow computer, too.

First I want to know about the points that have to be considere for test equipments that we ned to use for calibration. I would greatly appreciate if you could advise me.

Best regards,

You will be lucky if you have an installed accuracy of the system of better than +/- 10% of reading...and you could have an installed accuracy of +/- 50% of reading easily.

You need to consider the inaccuracies caused by piping, flow perturbation through the orifice, wear on the orifice, the installed accuracy of the differential pressure transducer, the installed accuracy of the temperature transmitter, the installed accuracy of the density transmitter, and the contribution to inaccuracy of the flow computer itself. Each of these can be significant.

It is not possible to use electronic means to calibrate this system. You can check the pressure transmitter, temperature transmitter and density transmitter, as well as the flow computer, by simulating the inputs from the orifice, from the RTD, from the density sensor, to the transmitters-- and the signal from the transmitters to the flow computer.

However, this is not calibration. You cannot assume it is calibration, nor can you use such a "calibration" in most locales as proof of custody transfer accuracy.

In order to calibrate a flow system as you have described, you must compare it to a known reading system with a known accuracy at least ONE ORDER OF MAGNITUDE better than the accuracy of the system you are trying to calibrate.

Walt Boyes
Editor in Chief
Control and
Read my blog SoundOFF!! At

Mr. Boyes,

Thank you for your reply.
As you have stated in your reply "in order to calibrate a flow system as you have described, you must compare it to a known reading system with a known accuracy at least ONE ORDER OF MAGNITUDE better than the accuracy of the system you are trying to calibrate."
So if we could use a test equipment which generates a signal such as the signals connected to flow computer (for example to use a Temperature simulator to simulate temperature) with the order of the accuracy mentioned above, then could we call it calibration the device?
Second about the order of the accuracy you mentioned for the device using to apply test signal, is there any standard to explain about it in detailed?

Best regards,

"Calibration" refers to comparing the device reading to a physical standard. Simply using an electronic simulator to emulate a temperature value checks the performance of the transmitter but is not "calibrating the system."

This is nearly always impossible under normal conditions, so there has arisen the use of electronic simulators and calibration checkers. Many people are confused about the difference between checking the operation of a transmitter and calibrating the system. Vendors often deliberately assist this confusion.

I know that's probably not what you wanted to hear, and some people, especially vendors, may take issue with me on this.


Walt Boyes
Editor in Chief
Control and
Read my blog SoundOFF!! At

By Rohit Chandak on 13 May, 2009 - 6:47 am

Dear Vahid,

There is a instrument calibration & then there is a system calibration wherein entire flow metering system is being calibrated. The instrument calibration as suggested by Mr. Walt has to be tested against proven & highly accurate system. The appropriate system is selected based on meter on test & the accuracy required. Few of the calibration methods could be gravimetric, against master meter (Accuracy of +/-0.15% of reading), prover system etc. Master Meter is a common device to calibrate orifice plates. The other instruments can also be calibrated as per their standard practice & integrated to find out the system inaccuracy.

In field calibration can be done using prover system wherein the complete system can be loop tested against prover system. There are various other methods to do it.

For Orifice I would highly recommend it to be laboratoy tested against master meter or against prover system.

By Alan Balcombe on 19 March, 2009 - 8:34 pm

Thanks for taking this over Walt. They are better answers than I would have given!
Alan Balcombe

By Carl Ellis on 18 March, 2009 - 8:36 pm

I would suggest that you register (no cost)and spend several hours reading the various material on flow measurement and its uncertainties at

This is all non-vendor specific academic research.

Good stuff.

Carl Ellis

Thank you all for the replies. I wish to further ask if errors x & y are in percentage of full scale. z & p are in terms of percentage of readings and q is percentage of reading plus or minus, say, 2 counts. In such a mixed description of errors how can determine the overall accuracy.

thanks and regards

By W.L. Mostia on 16 May, 2009 - 11:57 pm

Back in 1996, I wrote a 3-part article on instrument/system accuracy for Control Magazine. I believe that the articles would explain the basics of instrument accuracy for those of you who are interested. There are also references given. Unfortunately when I checked the Control Magazine archives, they do not appear to go back that far. If anyone is interested in the articles, I would be happy to e-mail them to you in PDF form.

William(Bill) L. Mostia, Jr. PE
Sr. Consultant
SIS-Tech Solutions

Yes please email me your articles... thanks for that..

jamesbosch [at] yahoo [dot] com

By Bob Pawley on 17 May, 2009 - 12:10 pm

rjpawley [at] shaw [dot] ca


Could you please send me the pdf file at

ritika.ritika.ritika.ritika [at] gmail [dot] com

Thanks and Regards

By Sushant Chanana on 17 May, 2009 - 11:47 pm


sushant.chanana [at] sedl [dot] in

sushant Chanana