Mushtaq is correct in saying that  you cannot convert your CFUs to MPNs but it is possible to use a statistical approach that will give you an approximation.  First you should recognize that although a colony count is more precise than an MPN value the result you obtain is not an absolute value.

I assume that your calculated count of 100 CFU/g is based on counting 10 colonies on a 1 in 10 dilution of your matrix. Assuming Poisson, then the count of 10 colonies in 1 ml of a 1 in 10 dilution will give with have a standard deviation of ±√10 = ±3.16. So it would be possible that, on 95% of occasions, the ‘true’ colony count could lie between (10 ± 2 x 3.16) = 3.7 to 16.3 CFU/ml of the 1 in 10 dilution.

If, for your matrix with 100 CFU /g, you had inoculated multiple tubes (e.g. 5 tubes) at each of several dilutions (e.g. 1 in 10, 1 in 100, 1 in 1000) then the probability for a positive result in 1ml of each of the 1 in 10 dilutions would be 1 (i.e. you would expect all tubes to be positive – using the Poisson equation, the probability for a negative result would be p = 0.000045).  For 1 ml of the 1 in 100 dilution, the probability of a positive result would be 0.63 (i.e. 3 tubes out of 5 would be positive) and for 1 ml of a 1 in 1000 dilution, the probability for a positive result would be about 0.1).  So if you then use a MPN table for a [5,5,5] test combination with positive results of 5, 3, 1 you would get an MPN of 11 /ml of the 1 in 10 dilution or 110 /g of the original matrix, but for 5,3,0 the MPN would be 7.9 /ml or 79 /g of your matrix . 

For more help see: Jarvis, Wilrich and Wilrich (2010) J appl. Microbiology 109, 1060 – 1067; Jarvis  (2016) ‘Statistical Aspects of the Microbiological Examination of Foods’ 3rd edn, Academic Press, Chapter 8.

There is no way to convert CFU to MPN and vice versa. CFU's are the Colony Forming Units in a given sample volume as in, these ARE the colony forming units in 100mLs of a sample. CFU's are definitive. MPN's are the Most Probable Number of cfu's in a given sample volume as in, there are PROBABLY this many cfu's in 100 mLs of a sample. MPN is an estimate of probability. (answered by Wiki)

Mushtaq is correct in saying that  you cannot convert your CFUs to MPNs but it is possible to use a statistical approach that will give you an approximation.  First you should recognize that although a colony count is more precise than an MPN value the result you obtain is not an absolute value.

I assume that your calculated count of 100 CFU/g is based on counting 10 colonies on a 1 in 10 dilution of your matrix. Assuming Poisson, then the count of 10 colonies in 1 ml of a 1 in 10 dilution will give with have a standard deviation of ±√10 = ±3.16. So it would be possible that, on 95% of occasions, the ‘true’ colony count could lie between (10 ± 2 x 3.16) = 3.7 to 16.3 CFU/ml of the 1 in 10 dilution.

If, for your matrix with 100 CFU /g, you had inoculated multiple tubes (e.g. 5 tubes) at each of several dilutions (e.g. 1 in 10, 1 in 100, 1 in 1000) then the probability for a positive result in 1ml of each of the 1 in 10 dilutions would be 1 (i.e. you would expect all tubes to be positive – using the Poisson equation, the probability for a negative result would be p = 0.000045).  For 1 ml of the 1 in 100 dilution, the probability of a positive result would be 0.63 (i.e. 3 tubes out of 5 would be positive) and for 1 ml of a 1 in 1000 dilution, the probability for a positive result would be about 0.1).  So if you then use a MPN table for a [5,5,5] test combination with positive results of 5, 3, 1 you would get an MPN of 11 /ml of the 1 in 10 dilution or 110 /g of the original matrix, but for 5,3,0 the MPN would be 7.9 /ml or 79 /g of your matrix . 

For more help see: Jarvis, Wilrich and Wilrich (2010) J appl. Microbiology 109, 1060 – 1067; Jarvis  (2016) ‘Statistical Aspects of the Microbiological Examination of Foods’ 3rd edn, Academic Press, Chapter 8.

Thank you Mushtaq Ahmad for your clarification as I was having the same idea.

Dear Basil,

Thank you very much for enlightened me on this matter. That was a comprehensive explanation. Hope to use that to solve my issue. Thanks once again

Hello,I have the same question,

I conducted MPN test for total and fecal coli form determination from polluted ground and surface water , and get the maximum result in the MPN table (1100) and is any method available for converting it in to a specific number?I heard there is some logarithmic method available, please help...

Hello Joice

From your cited value I suspect that you have tested 3 replicates of each of 3 dilutions starting with a 1 in 10 dilution of your test sample and that all the tests gave positive results.  If that is so, then the result merely shows that the levels of test organisms in your water sample is >1100/ml and strictly you should refer to  it as 'infinity' because it is not possible to calculate an MPN result.   Unfortunately you cannot adjust the value using log or other transformations,  The only answer is to repeat the work testing a greater number of dilutions (e.g. 10-4, -5 or -6) to ensure that at one or more dilutions you obtain at least 1 negative result.   Alternately, you could estimate the level of organisms using plate count methods.  

Sorry, but there is no quick way out of this situation!

i work on powder infant food , i take 1g then i put it in 70ml liquid media in flask and incubate it for 24h , then i take 1ml and diluted it three times in 9ml of water 

after that i take 0.2ml from tube 2 (1:100) then i spread it on solid media in petri dish , incubate for 24h and the count of colonies was 80, i calculate cfu and the result         80×100 CFU/ml   is that correct?  i need cfu/g because the orginal sample powder food .??? can you help me >>>>>>>>>>>??

Interesting!

How would i relate a test of sample (e.g. tomato) which is conducted in mpn and as well as cfu for E. Coli ?