Diversity Calculator Excel – BPMSG

The diversity calculator is an excel template that allows you to calculate alpha-, beta- and gamma diversity for a set samples (input data), and to analyze similarities between the samples based on partitioning diversity in alpha and beta diversity.

The template works under Windows OS and Excel 2010 (xlsx extension). No macros or links to external workbooks are necessary. The workbook consists of an input worksheet for a set of data samples, a calculation worksheet, where all necessary calculations are done, and a result worksheet “beta” displaying the results.


The template may be used to partition data distributions into alpha and beta diversity, it can be applied in many areas, for example

  • Bio diversity – local (alpha) and regional (beta) diversity
  • AHP group consensus – identify sub-goups of decision makers with similar priorities
  • Marketing – cluster analysis of similarities in markets
  • Business diversification over time periods
  • and many more.

Let me know your application! If you just need to calculate a set of diversity indices, you can use my online diversity calculator.

Calculations and results

Following data will be calculated and displayed:


  • Shannon Entropy H (natural logarithm) alpha-, beta- and gamma, and corresponding Hill numbers (true diversity of order one) for all samples
  • Homogeneity measure
    1. Mac Arthur homogeneity indicator M
    2. Relative homogeneity S
    3. AHP group consensus S* (for AHP priority distributions)


  • Table 1: Shannon alpha-entropy, Equitability, Simpson Dominance, Gini-Simpson index and Hill numbers for each data sample


  • Table 2: Top 24 pairs of most similar samples
  • Page 2: Matrix of pairs of data samples
  • Diagram 1: Gini-Simpson index and Shannon Equitability
  • Diagram 2: Average proportional distribution for all classes/categories
  • Diagram 3: Proportional distribution sorted from largest to smallest proportion (relative abundance)


  • Maximum number of classes/categories: 20
  • Maximum number of samples: 24

Description of the template:  BPMSG-Diversity-Calc-v14-09-08.pdf

Other posts explaining the concept of diversity


The template is free, but I appreciate any donation helping me to maintain the website. Thank you!

BPMSG Diversity Calculator Excel Template Version 2020-07-05 (zip)

The work is licensed under the Creative Commons Attribution-Noncommercial 3.0 Singapore License. For terms of use please see our user agreement and privacy policy.

As this version is the first release, please feedback any bugs or problems you might encounter.

Updated AHP Excel Template Version 08.02.13

An updated version of my AHP Excel template for multiple inputs is now available as version 08.02.13. Beside the extension from 8 to 10 criteria and from 7 to 20 participants some new features have been added. In the past it was sometimes difficult for participants to achieve a low consistency ratio. Now inconsistent comparisons in the input sheet will be highlighted, if the required consistency level is exceeded.  The level of consistency needed (“alpha” in the summary sheet) can also be changed from 0.1 (standard rule of thumb from Saaty) to higher values, for example 0.15 or 0.2. In addition another scale for the judgment can be chosen. For my projects I made good experience with the balanced scale.

A new feature is the consensus index. If you have more than 1 participant and do the group aggregation (select participant “0”), the consensus index is an indicator, how homogenous the judgment within the group was done. Zero percent means no consensus, all participants put their preference on different criteria;  100% means full consensus. Here the changes in detail:

Summary sheet

  • Number of criteria increased from 8 to 10
  • Number of participants increased from 7 to 20
  • Different scales added:
  1. Linear standard scale
  2. Log
  3. Sqrt
  4. InvLin
  5. Balanced
  6. Power
  7. Geom.
  • Alpha – allows to adjust consistency threshold (0.1 default)
  • Consensus indicator for group aggregation added
  • Geometric Consistency Index CGI added

Input sheets

  • Consistency ratio is calculated on each input sheet.
  • Priorities are calculated and shown based on RGMM (row geometric mean method)
  • Top three inconsistent pairwise comparisons highlighted (if CR>alpha)

Known Issues

Thanks to feedback from Rick, sometimes there seems to be a problem with the correct display of weights beside the criteria in the summary sheet. If you face this problem, unprotect sheet summary. Select weigths (O18:O27). Click “conditional formating”, “clear rules”,”clear rules from selected cells”. Then the values will be displayed correctly, and you can format them in the way you want. It is a strange effect; it only appears on one of my PCs, on the other it works fine. I uploaded a modified version, but not sure whether it works for everyone.

I appreciate any feedback! Please download the latest version from my AHP template download page.

Diversity Calculation in Excel – Diversity Indices and True Diversity

Diversity-IndicesIn my video “Diversity Index as Business KPI – The Concept of Diversity” I explain the mathematical concept of diversity introducing the Simpson Index λ and its complement (1-λ) as a measure of product diversification in markets.

Beside the Simpson Index there are many other indices used to describe diversity. I have developed a simple Diversity Excel template to calculate a couple of diversity indices for up to 20 categories. The following diversity indices are calculated:

  • Richness
  • Shannon entropy
  • Shannon equitability
  • Simpson dominance
  • Gini-Simpson Index
  • Berger-Parker Index
  • Hill numbers (“true diversity”) and Renyi entropy of order one to four

For a quick calculation of diversity indices you might also use my online calculator

For calculation of Shannon entropy and its partitioning into independent alpha and beta components  see here.

Any feedback is welcome!

Updated AHP Excel Template Version 11.12.12

AHP IconDue to feedback from several users, I revised the implementation of the power method for the calculation of the Eigenvector and Eigenvalue to improve the accuracy of my AHP excel template. The calculation sheet ‘8×8 in the workbook was completely reworked. My tests show a significant increase in accuracy. As an example see my updated post AHP template – numerical accuracy.

By default the number of iterations is now set to 12.  The check value in sheet ‘8×8 cell B33 shows the sum of all matrix elements solving the Eigenvalue equation (AI*λ) x = 0 with A the Decision matrix, λ = estimated principal Eigenvalue and x = estimated Eigenvector. The ideal check value is zero. With the example numbers given in the template the result is 5E-08.

Please let me know, if  you find any problems in the new version.

For the download of the latest version please go to the AHP template download page .

New AHP Excel template with multiple inputs

The AHP Excel template works under Office Libre and Excel version MS Excel 2013. The workbook consists of 20 input worksheets for pair-wise comparisons, a sheet for the consolidation of all judgments, a summary sheet to display the result, a sheet with reference tables (random index, limits for geometric consistency index GCI, judgment scales) and a sheet for solving the eigenvalue problem when using the eigenvector method (EVM). Latest version: 2022-07-08.

Alternative for complex AHP projects: AHP free online software.

Excel Template

  • Within the input worksheets (questionnaires) priorities are calculated using the row geometric mean method (RGMM).
  • Three consistency indices (the consistency ratio CR, the geometric consistency index GCI and overall dissonance Psi) are calculated. The level of consistency needed (α) is implemented as a variable input field in the summary sheet, and can be set between zero and one.
  • If CR exceeds α, the top 3 inconsistent pair-wise comparisons on the input sheets are highlighted, to allow the participants an adjustment of their judgments. The judgment resulting in lower inconsistency is proposed.
  • Final priorities are shown in a summary sheet; their calculation is based on the eigen vector method (EVM). For the solution of the eigenvalue problem the power method algorithm is applied with a fixed number of 20 iterations.
  • Different judgment scales are implemented.
  • Errors of the EVM and RGMM are show beside the calculated priorities.
  • Either individual participants, or an aggregation of individual judgments (AIJ) based on the weighted geometric mean of all participants’ judgments can be selected.


  • The template does not include the hierarchy of the decision problem and the final aggregation of weights, i.e. it is only suitable for finding the weights in each category or sub-category. For the definition of a hierarchy and evaluation of alternatives see here.
  • Sensitivity analysis of the final result is not included.

How to use the template?

A detailed description (pdf) is attached in the download file.


When you use the template for your research, please make a reference to the author’s paper.

Please cite:
Klaus D. Goepel, (2013). Implementing the Analytic Hierarchy
Process as a Standard Method for Multi-Criteria Decision Making In
Corporate Enterprises – A New AHP Excel Template with Multiple Inputs, Proceedings of the International Symposium on the Analytic Hierarchy Process, Kuala Lumpur 2013. DOI: https://doi.org/10.13033/isahp.y2013.047


Download AHP Excel Template Version 2022.07.08 (zip)

Please consider a donation, it will help me to maintain the website and program. An explanation of AHP (Analytic Hierarchy Process) is given in my video here. For terms of use please see our user agreement and privacy policy.

Your comments are always welcome!

BPMSG – One Year On-line

After being on-line with the website for 1 year, it’s time to change the entry page!

Here, on BPMSG.com you will find a couple of interesting articles related to business performance management, from a more practical than theoretical point of view.

Topics covered range from

A new topic was introduced just recently: “Value-driven leadership”. I started with a general article, and added a personality profiling tool (NEO-select). If interested, you might participate and send back the completed questionnaire to get a full report.

In the section other stuff  I post other interesting information, not fitting to the main topic of the site. For example a nice video of the olive-backed sunbird, a review of the Sennheiser Bluetooth Headset etc.

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.

Please also be so kind, if you use parts in your web-site or blog, to give credit and a link to my site. I hope you will find some useful information, let me know your feedback or contact me directly for any suggestions.

Klaus Goepel, Mar 2012

about the author

NEO-select leadership value profiling

NEO-select personality profiling is a tool to get a better insight in the different strengths of individuals. The inventory is developed based on the model of the big five dimensions of personality, and is conducted as a self-reporting assessment. Using a combination of selected facets in these dimensions, a ranking of leadership values is derived. It will give you a better insight in your behavior, and the driving values behind it.

You might download the questionnaire and the quick guide, how to fill below.

Fill out the questions, and you will get an immediate quick report of your levels and rankings in the broad five personality dimensions. The questions are available in English and German language. As a result you will get a quick and very simple summary.

To receive the full report – with much more detailed information – simply submit the completed questionnaire to the author.

Important note:

  1. Unzip the downloaded file into a working directory.
  2. Open Excel and load the xls file from there.
  3. The questionnaire is realized in Excel, and requires Macros to run for the control of the answering flow: enable macros.
  4. Once all questions are answered, the file will be stored under the exact same name in the same directory. (Don’t worry, your answers are saved)
  5. Submit the Excel file to the author and receive the full report.

If you don’t use a Microsoft environment, a simple spreadsheet version is available on request.