Enter the serial dilutions

Original Inoculum Amount


Number of Tubes

(per dil. step)

Positive Tubes

(per dil. step)


Assumes microbial contamination is randomly distributed throughout the dilution.

Confidence limits are calculated using a normal approximation to log(MPN)

Confidence limits are calculated using a likelihood ratio approach

Recommend bias correction if total number of tubes is less than 15.

If Rarity Index < 1.00E-04, then outcome is improbable.

Calculate the original inoculum amounts (optional)

Note: Undiluted stock is 1g/mL, 10% is 0.1g/mL, etc.

Test Tube Size


Pipette Amount


Inoculum Amount


Inoculum Concen.



  1. Choose the number of dilution steps used in your experiment.
  2. Choose the confidence interval type and level desired.
  3. In the 'Calculator' tab, enter the amount of original inoculum in each test tube at each dilution step. These are analagous to the inoculum amounts shown in the BAM tables. The user may optionally calculate these amounts using test tube size, etc. in the 'Inoculum Amount' tab before manually entering the values in the 'Calculator' tab:
    1. Optional steps if using the 'Inoculum Amount' tab:

    2. Enter the inoculum concentration in the stock solution. Default is 1g/mL (undiluted). A 10% solution would be 0.1g/mL, etc.
    3. Enter the size of the test tubes used at each dilution step.
    4. Enter the amount of solution pipetted into each tube at each step.
    5. The amounts in the 'Inoculum Amount' column are the values that should be entered into the 'Calculator' tab if the entire tubes are incubated. The amounts in the 'Inoculum Concen.' columns should be entered into the 'Calculator' tab if only 1 mL of solution from each tube is incubated.
  1. Enter the number of tubes used at each dilution step.
  2. Enter the number of positive tubes found at each dilution step.


  • This app assumes the use of serial dilutions; however, a single dilution step (or no dilution step) may be used by changing 'Number of Dilution Steps' to 1.
  • The Asymptotic Lognormal confidence interval uses the approach described in Jarvis et al. (2010) with a slight modification for extreme cases (see CRAN package documentation). The Likelihood Ratio confidence interval uses the approach described in Ridout (1994) and Haas et al. (2014). Since the BAM tables use a different confidence interval approach, neither interval will match the BAM tables in general.
  • The method of Salama et al. (1978) was used for the bias-corrected point estimate of MPN. Also see Haas (1989) and Haas et al. (2014). "The relative difference in the bias-corrected estimate is substantial for five-tube experiments, averaging about -20% to -25%." (Haas, 1989)
  • The Rarity Index uses the technique described in Blodgett (2002, 2005, 2010) and Jarvis et al. (2010).


  1. Bacteriological Analytical Manual, 8th Edition, Appendix 2.
  2. Blodgett RJ (2002). "Measuring improbability of outcomes from a serial dilution test." Communications in Statistics: Theory and Methods, 31(12), 2209-2223.
  3. Blodgett RJ (2005). "Serial dilution with a confirmation step." Food Microbiology, 22(6), 547-552.
  4. Blodgett RJ (2010). "Does a serial dilution experiment's model agree with its outcome?" Model Assisted Statistics and Applications, 5(3), 209-215.
  5. Haas CN (1989). "Estimation of microbial densities from dilution count experiments." Applied and Environmental Microbiology, 55(8), 1934-1942.
  6. Haas CN, Rose JB, Gerba CP (2014). "Quantitative microbial risk assessment, Second Ed.," John Wiley & Sons, Inc. ISBN 978-1-118-14529-6.
  7. Jarvis B, Wilrich C, Wilrich P-T (2010). "Reconsideration of the derivation of Most Probable Numbers, their standard deviations, confidence bounds and rarity values." Journal of Applied Microbiology, 109, 1660-1667.
  8. Ridout MS (1994). "A comparison of confidence interval methods for dilution series experiments." Biometrics, 50(1), 289-296.
  9. Salama IA, Koch GG, Tolley DH (1978). "On the estimation of the most probable number in a serial dilution technique." Communications in Statistics - Theory and Methods, 7(13), 1267-1281.




Functional changes:

  1. The user now enters the amount of original inocula directly, similar to the BAM tables. The user has the option of calculating the inocula amount using test tube size, etc. as before if desired; however, the inocula calculations are now on a separate tab. The results must be manually transferred to the 'Calculator' tab.



Functional changes:

  1. User now enters the stock concentration, test tube size for each step and pipette amount for each step. Previously, the test tube size was assumed constant across all steps, the stock concentration was assumed full strength, and the user entered the dilution factor or chose an n-fold.

Aesthetic changes:

  1. In addition to the amount of inoculum in each test tube, the concentration of inoculum for each tube is also now calculated.
  2. A tab was added to show all the changes to the app after v1.0.0.