topic 11675

# Convert resistivity units to conductivity units

A discussion started in 2001 but continuing through 2018

2001Q. Hi!

How do I convert resistivity measurements (in water samples) to conductivity units. For example, my readings were 18.4 Mohm-cm to _____ microS/cm?

Thanks,

Merlyn Lebron- Toa Alta, Puerto Rico

A. Hi, Merlyn. One is simply the inverse of the other. If the resistivity is 18.4 million ohm-cm, then the conductivity is 1/(18.4 million ohm-cm) = 1/(18.4 million) S/cm = 1/18.4 microS/cm.

Regards,

Ted Mooney, P.E.

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2004

Q. You explained how conductivity is the inverse of resistivity (surface), but is there any relation between conductivity and volume resistivity?

Brendan Phairstudent - New Hyde Park, New York

2004

A. I don't think the previous answer is restricted to surface resistivity vs. surface conductivity, Brendan. These terms are intended to be the inverse of each other regardless of the units or dimensions. But I feel your pain about obfuscatory terms like "volume resistivity" which seem to defeat the application of our everyday intuition :-)

I think the easiest way to keep it from going hopelessly abstract on us is to start with Ohm's Law, i.e., that current equals voltage divided by resistance. We know intuitively that if one wire is twice as long as another, it's resistance will be twice as great, which is to say that its conductance is half as great. If the diameter of one wire is twice the diameter of another, it's area is four times as great, so it's like having four wires in parallel, and the conductance is quadrupled, which is to say the resistance is quartered. If two wires are the same length and diameter, but one is made of a metal that carries electricity only half as well as the other, its resistivity is twice that of the other material, which is to say that its conductivity is half as great.

So, if we express resistivity in Ohm-inches, and length is expressed in inches, and area is expressed in square inches, then resistance is expressed in Ohms. Checking the logic of this by checking the units: to get the resistance in Ohms, we multiply the resistivity of the conductor in Ohm-inches by the length of the conductor in inches and divide by its area in inches^{2}, and all the units cancel out except the Ohms.

Ted Mooney, P.E.

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2006

Q. I am asking a question of water quality. I do not understand the relationship of resistivity to conductivity.

500 mmhos is how many megOhms?

Thanks,

manufacturing - California

2006

A. Again, conductivity is simply the inverse of resistivity, Paula. That is: Conductivity = 1 / Resistivity. Or Resistivity = 1/ Conductivity. In fact the term 'mho' is not the name of any scientist, but was invented just to be the mirror image or 'inverse' of Ohm. These days people tend to use Siemen rather than mho though.

But you can't get sloppy with 'the units' or you'll stay hopelessly confused forever... mhos is not a valid unit for conductivity and megOhms is not a valid unit for resistivity! Please start at the top of the page and study slowly. Also be careful with expressions like 'mmhos' because a leading m is usually an abbreviation for milli or 1/1000 when working in the metric system, whereas I think you are treating it as an abbreviation for micro or 1/1,000,000. Since we don't like our answers to be wrong by 3 orders of magnitude, I don't think you should take the chance of using that abbreviation :-)

Good luck.

Ted Mooney, P.E.

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August 27, 2009

A. Ted Mooney,

All of your answers are correct. The reason that resistivity or conductivity are volumetric is that the number represents a value given a medium of area unit and length unit, therefore volume.

Soil in a box 1 meter wide, 1 meter deep, and 1 meter long will measure OHM*meter. The value can then be converted to OHM*cm, or OHM*mm or OHM*inch. Resistivity of a sample of one cubic cm, or cubic mm, or cubic inch.

- Pittsburgh, Pennsylvania

October 13, 2009

*Q. "How do I convert resistivity measurements (in water samples) to conductivity units. For example, my readings were 18.4 Mohm-cm to _____ microS/cm?"*

Please clarify the answer to the above question, is the answer 0.054 microS/cm ?

- Elstree, Hertfordshire, UK

October 13, 2009

A. Hi, Chris. Conductivity is the opposite (or, more properly, the reciprocal) of Resistivity.

Years ago a Siemen/cm was called a "mho/cm"; something nice about that terminology was that it implied that a mho/cm is the reciprocal of an ohm-cm (which it is).

So, if you have

18,400,000 ohm-cm, then the reciprocal is

1 / (18,400,000 ohm-cm) or

1 Siemen / (18,400,000 cm)

.00000005.4 Siemen/cm or .054 microS/cm.

Regards,

Ted Mooney, P.E.

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November 25, 2009

A. If Conductivity = 0.054 µS

= 0.054 x 10-6 S

= 0.54 x 10-5 S

= 0.54 x 10-5 mho

Now Resistivity = 1 / Conductivity

= 1/ 0.54 x 10-5 mho

= 1.84 x 10-5 mho

= 18.4 Mmho

Sr. Manager - Mumbai, INDIA

June 15, 2010

Q. How can I convert soil thermal resistivity from (mK/W) to (ohm.m)

Meto HabElectrical Designer - Qatar

February 12, 2011

Q. The relation between a volume resistivity (VR) and surface resistivity (SR) can be defined as VR = SR * thickness if the material is fully conductive.

Can the relation hold good for conductive coatings on a substrate?

- Mumbai. Maharashtra, India

February 12, 2011

A. Hi Amol,

Please explain your situation that prompts you to ask. While resistivity is a meaningful physical quality, "SR" and "VR" are more in the nature of mathematical constructions than meaningful physical qualities, and the relationship between the two is a simple mathematical manipulation rather devoid of original physical insights, similar to converting length from meters to inches. Picture:

Take a short slice of a piece of wire; it's a cylinder. You can measure the electrical resistance of this cylinder in Ohms, or you calculate the resistance by dividing the voltage across it by the current that flows through it. If you look at the cylinder end-on, you see a circle, and that circle has some specific area or surface area or cross sectional area. If you multiply that surface area x the length of the slice of wire (or you could call it its thickness) you have the volume of the cylinder.

Resistivity, is a property of the wire and if you multiply the resistivity by the length and divide by the area you get the resistance.

If a coating on a substrate is more conductive than the substrate, it has lower resistivity than the substrate, and mathematical manipulations, like whether or not you include thickness in your units, doesn't change the fact.

Ted Mooney, P.E.

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June 10, 2011

Q. How do you convert microOhms per cm to Ohms per m? Thanks, Jag.

Jagan Jemployee - Chennai, TN, India

December 3, 2012

A. Hi Jag. This is not something you calculate so much as something you must take the time to implicitly comprehend. A microohm is a millionth of an ohm and a cm is 1/100 of a meter. So you take the value you were given and insert the conversion factors (1,000,000 microOhms)/ohm and (100 cm)/m.

Because these conversion factors are "equalities", always equal to 1, it doesn't matter whether you invert them. So you put them into your equation either as I have written them or 'upside down' as ohm/(1,000,000 microOhms) and m/(100 cm) depending on which way will let you cross out the microOhms term and cm terms you started with and leave you with the Ohms and m terms you want to end up with. You must learn to always "watch the units", and such conversions will come easily and always work right.

Example, with 5000 microOhms per cm

Try 5000 microOhms/cm x (1,000,000 microOhms)/ohm x (100 cm)/m ...

We have cm in the denominator of the first term and the numerator of the third term, so they can be crossed out, leaving ...

5000 microOhms x (1,000,000 microOhms)/ohm x 100/m, but this leaves us with microOhms in the numerators of the first and second terms. They can't be crossed out; but it is valid to invert the second term since it's an 'equality'...

5000 microOhms x ohm/(1,000,000 microOhms) x 100/m; now we can cross out microOhms since its in the numerator (of the first term) and denominator (of the second term), leaving ...

5000 x ohm/1,000,000 x 100/m = 0.5 Ohms/m.

Regards,

Ted Mooney, P.E.

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December 3, 2012

Q. Can I convert sheet resistance to conductance/conductivity without knowing the thickness of the thin film?

Azhar Pirzado- straqbourg, Alsace, France

December 3, 2012

A. Hi Azhar. Although the question is a bit abstract for me to follow, I'd say you can determine the conductance because it is the reciprocal of the resistance, but not the conductivity because you can't make the units match without additional terms like thickness.

Regards,

Ted Mooney, P.E.

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Hi Ted Mooney

Thanks for your answer!

- sSraqbourg, Alsace, France

December 7, 2012

Q. Hi All

I need to know how one can extract the value of resistance from IV graph in Origin. I just plotted V and I on x-axis and y-axis respectively. I wonder there is some easy way to extract the resistance?

Thanks is advance,

- Straqbourg, Alsace, France

May 14, 2013

A. Hi Azhar. Your question went unanswered a long time; perhaps other people had difficulty understanding it as well. Now that I very slowly re-read it, I see that you are asking how you can determine the resistance from a graph of current vs. voltage. Ohm's Law says V=IR, which can also be expressed as R=V/I. So you simply take any point on the line you graphed, and the resistance in Ohms is simply whatever the voltage (in Volts) is at that point divided by the current (in Amps) at that point.

Regards,

Ted Mooney, P.E.

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May 14, 2013

Q. My resistance reading is 0.0428 mohm/m how to calculate the conductivity.

AJAY S. LINGE- Pune, Maharashtra, India

May 14, 2013

A. Hi Ajay. You'll make best continuing progress on this if you carefully think it through, and then be very careful of your words and their precise meanings. The suffixes "-ance" and "-ivity" are very different and must not be confused. So your question cannot be answered because it is improperly asked; although a length of wire might exhibit a resistance of 0.04328 Ohms for each meter of its length, please carefully study the thread and figure out what is wrong with your question, and I think the answer will come to you. Thanks and good luck.

Regards,

Ted Mooney, P.E.

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August 28, 2013

Q. I'm trying to find an electrically equivalent material to a Silver filled Silicon, Ablebond 190-3. Original test method indicated Bond Joint Resistance: 0.03 ohm/0.5 in2. All available product's properties are now reported as Volume Resistivity, (i.e.: 0.01 ohm-cm). This bond forms an EMI seal, and I need to be able compare the properties. By definition Volume Resistivity (rho) = R*(A/L). If I know the bond area, can I convert the Bond Joint Resistance to Volume Resistivity?

- Sylmar, California, USA

September 3, 2013
A. George, Feather Hollow Eng. Stockton, California September 2013 A. Hi George. Sorry, I don't really know. My knowledge harks back only to definitions from school many years ago, and I have no actual experience with the term "bond joint resistance". But the units don't seem to work the way you would wish because the "bond joint resistance" seems to be independent of the thickness of the adhesive and to be controlled only by the surface area. It thus probably assumes a thin adhesive layer of under .010", with the exact thickness of the adhesive not being a critical factor in the resistance across the joint as long as it's in the accepted range. I strongly suspect that the other conductive filled adhesives you would like to use as a replacement are similar in application and properties, and I tend to doubt that "bond joint resistance" data is unavailable for them -- but it probably depends more on the material of the two surfaces to be joined than upon the volume resistivity of the thin layer of goop between them. Good luck. Regards, Ted Mooney, P.E. finishing.com Pine Beach, New Jersey Striving to live "Aloha" |

September 7, 2013

Thanks for your feedback. Understanding that Volume resistivity is Resistance/(Cross Sectional Area*Bond Line Thickness) the computation I made is at best, ambiguous. I don't have any of the original material for conducting a Volume Resistivity test. However, I do have a sample of the new material and the original manufacturer's test procedure used for "Bond Joint Resistance". Therefore, I will determine a "Bond Joint Resistance" for the new material and be able to compare it's electrical property. This seems to be the only way that I can get an answer that I can depend on. Also, the NSN for the original new material are the same, indicating that the Federal Government recognizes them to be suitable substitutions. I appreciate your comments and will post the conclusion when available.

George F. Tirone, PE

- Sylmar, California, USA

## Sourcing Electrical Resistivity to produce Electrical Conductivity Result

June 3, 2016Q. Hello,

I am attempting to produce a procedure for calibrating the electronics of a pH meter, not of the mV to pH, but the Conductivity module. I'm attempting to use a Fluke meter with appropriate wiring to the back of the conductivity module of the pH meter. I have determined and figured out the connections and wiring, but my question is how can I produce a conductivity result (in uS/cm or MOhm-cm) by sourcing the signal from the Fluke multimeter. My options for source signal are a voltage signal (V or mV), current signal (mA), or resistance (Ohm or KOhm). I have been wracking my mind on this for some time and appear to be missing something calculation-wise, etc.

Thank you,

- Grayslake, Illinois, USA

June 2016

A. Hi Adam. I'm not sure I understand, but this approach doesn't sound right from the get-go. It seems that you are trying to use a Fluke V-O-M as some sort of signal generator instead of using it as a meter; it wasn't designed to generate signals, and I don't know that it will generate a reliable and reproducible one. Although it generates a small voltage when in Resistance mode, there is no reason to even assume that the voltage is consistent for different scales.

I think what you need to do to calibrate a conductivity module is to connect it to a series of resistances or a resistor whose resistance can be varied, and make sure the module is reading the right resistance/conductance.

Regards,

Ted Mooney, P.E. RET

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June 5, 2016

Thank you Ted. That makes sense. I can simulate the mV signal and temperature signal just fine from the Fluke Documenting Processor, but it doesn't seem to work well with resistance. I can get a signal on the conductivity module, but it doesn't move no matter what I enter in the Fluke meter. I will try to locate a modifiable resistor to perform this task successfully. Thank you!

Adam Mivelaz- Grayslake, Illinois, USA

January 10, 2017

Q. I fail to understand why no one has yet just shown a graph with one axis in Ohms, KilOhms and MegOhms and the other axis in m Siemens, M Siemens, which for a simple man like me is easier to understand. I would do so myself but am no expert neither in the subject nor attaching graphs to this format.

Bernard Murphy- Wigan, Lancashire, UK

A. Hi Bernard. Good question, thanks. But a mho or Siemen is just the reciprocal/inverse of an Ohm.

1 Ohm is 1 Siemen, 2 Ohms is 1/2 Siemen, 1 million Ohms is 1/1,000,000 Siemen.

1 Siemen is 1 Ohm, 2 Siemens is 1/2 Ohm, 1 million Siemens is 1/1,000,000 Ohms.

Graphs of the reciprocal function (y=1/x) are easy enough to make for a mathematics lesson, but not useful for this because if you make a graph that goes to a million Ohms you won't even be able to see 1000 Ohms on it, let alone 100 Ohms or 2 Ohms. I think it's just easier to say that Ohms = 1/Siemens and Siemens = 1/Ohms.

Regards,

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January 11, 2017

Q. I had thought that if one axis is falling as the other rises, that the resultant would be a straight line, infinity conductance and zero Ohms sharing the "zero" point on both axes.

Bernard Murphy [returning]- Wigan Lancashire, UK

January 2017

A. Hi again. I suppose you could label the origin of the axis "infinite conductance" instead of "zero" is you wish, but it wouldn't be a straight line: "y= -x" would be a straight line, but that's not the relationship; it's "y= 1/x". It's a reciprocal function and asymptotic rather a straight line, so the graph won't be readable except over a very narrow and non-useful range. Thanks again.

Regards,

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May 31, 2017

Ted, you could make a log-log plot, slope = -1, as many orders of magnitude as you like.

Dan Niemeyer- Londonderry New Hampshire USA

June 2017

Good point, Dan, thanks for reminding me! Unfortunately, I did a google image search for "graph resistivity vs. conductivity" and scanned a hundred graphs without finding one, but if a patient reader finds such a graph, or makes one, we'll be happy to link to it.

To me the reciprocal function, which is exact, is so easy that a graph seems a bit silly ... but different people think differently; and I suppose that if no one had invented electronic calculators capable of instantly dividing 1 by another number I'd feel differently :-)

Regards,

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July 12, 2017

Q. Ted, My head is spinning! I have a salinity report using Ohms. How do I convert this to dS/m?

Diana Mayne- Johannesburg, South Africa

July 2017

A. Hi Diana. Your head will continue to spin, and there is nothing anyone else can do to help you, until you slow down and take it one small bite at a time and think about each bite.

Do you know what a "Siemens (S)" is? We told you above that is 1/Ohms; that is,

S = 1/Ω or Ω = 1/S. So 10 Ωs is 0.1 S, 2 Ωs is 0.5 S, 1 Ω is 1 S, 1/2 Ω is 2 S, and 1/10 Ω is 10 S. Start by learning and understanding that.

After you're sure of that, do you know what dS means? It means deciSiemens. A dS is one tenth of a Siemen, just as a decimeter is one tenth of a meter. So, building on what you learned above, 10 Ωs is 1 dS. 2 Ωs is 5 S, 1 Ω is 10 S, etc. You could say dS = 10/Ω or Ω = 10/dS.

Hopefully you now see how you can convert dS to Ωs and Ωs to dS ... but that you're not going to be able to convert Ohms to dS/m because, while dS is a measure of conductance (which is the inverse of resistance), but dS/m (dS per meter) has that extra unit of length in it. Your report which mentions Ohms, must also mention a unit of length (Ωs per inch, or Ωs per cm, or Ωs per meter, or something like that. Get back to us with that and it will be possible to carry on. Good luck.

Regards,

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July 12, 2017

Thank you so much Ted for your generous and very clear explanation. The report gives no mention of length at all but I now understand what I need.

Best wishes

Diana

- Johannesburg, South Africa

August 18, 2017

Q. Hi,

I am using Solinst TLC (Temperature, Level & Conductivity Meter) Model 107.

I am facing some problems while checking Conductivity in Wells. When I use this meter in room in drinking water, TLC meter shows EC in micro Siemens per centimeter but when I check EC in Wells in field, this meter shows EC in "M" unit.

What is this capital "M"???

and how can I get EC in micro Siemens per centimeter?

- Muscat, Oman

August 2017

A. Hi Syed. I have never done such measurements and never seen a Solinst TLC, but the instructions seem to indicate that "999.9M" means the conductivity is beyond what the instrument can measure.

Regards,

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October 22, 2018

Q. I have an application which is to measure the presence or absence of a layer of foam above a constant liquid level in a test chamber. The foam is aqueous (concentrated potassium chloride in water) and has a conductivity of about 1000 micromhos per cm2 (1000 micro siemens to you younger folks. I am thinking of doing this by either to 2 methods: place a conductivity probe at a fixed height above the liquid and when I get a step change in conductivity compared to wet air, I know I have foam. But that requires hardware and software to take the signal and change an analogue signal to an on / off.

The simpler approach is to buy a simple rod type point contact level switch which are available with .5 Ohm to 50 K Ohm resistance. Since the sample chamber is a small steel pot there is plenty of contact surface for the liquid and one side of the foam layer. The question is how do I calculate the diameter of the end of the level probe to ensure that when the foam touches it I get at least the 50 K Ohms resistance necessary to trip the level relay?

samuel Scott McNairLPS LLC - PELZER, South Carolina, USA

October 2018

A. Hi Samuel. You may know more about this than I do, but my understanding is that standard liquid level controls cannot be used to reliably measure/control foam. Googling 'foam level control' seems to explain that simple conductivity measurements will not work because dried foam fouls the electrode immediately.

Regards,

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