Blau Index Calculator

How to measure diversity? use our Blau Index Calculator that can helps you do just that. For calculation, just enter the number of categories and their proportions to find the Blau Index.

Blau Index Calculator

Blau Index Calculator

Enter any 2 values to calculate the missing variable

blue index calculator tool

What is the Blau Index?

The Blau Index is a measure of diversity within a population. It shows how evenly distributed different categories are. Higher values indicate greater diversity.

How to Use the Calculator

To use the Blau Index Calculator is simple. Follow these steps:

  1. Enter the number of categories: Enter the total number of distinct categories in your population.
  2. Enter the proportions: Enter the proportions of each category, separated by commas.
  3. Calculate: Click the 'Calculate' button to find the Blau Index.


  • Number of categories: 3
  • Proportions: 0.5, 0.3, 0.2

How to Calculate the Blau Index

To calculate the Blau Index, use the formula:

BI=1(pi2)BI = 1 - \sum (p_i^2)


Variable Description
BI Blau Index of diversity
pip_ Proportion of each category in the population


1. Identify categories and proportions:

Let's say you have three categories with proportions 0.5, 0.3, and 0.2.

2. Square each proportion:

    • 0.52=0.250.5^2 = 0.25


    • 0.32=0.090.3^2 = 0.09


    • 0.22=0.040.2^2 = 0.04


3. Sum the squared proportions:

    • 0.25+0.09+0.04=0.380.25 + 0.09 + 0.04 = 0.38


4. Subtract from 1:

    • 10.38=0.621 - 0.38 = 0.62


5. Result:

The Blau Index is 0.62.

Calculator Inputs Example

1. Basic Example

Input Values Blau Index Calculation
Number of Categories: 3 1(0.25+0.09+0.04)=0.621 - (0.25 + 0.09 + 0.04) = 0.62


Proportions: 0.5, 0.3, 0.2  

2. Advanced Example

Input Values Blau Index Calculation
Number of Categories: 3 1(0.16+0.1225+0.0625)=0.6551 - (0.16 + 0.1225 + 0.0625) = 0.655


Proportions: 0.4, 0.35, 0.25  


What does a high Blau Index indicate?

A high Blau Index shows a high level of diversity in the population.

Can the Blau Index be negative?

No, it ranges from 0 (no diversity) to 1 (maximum diversity).

What if my proportions don't add up to 1?

Make sure the sum of your proportions equals 1 for accurate calculation.

Final Thought

Please share your feedback and let us know how you used the tool. How was your experience with the Blau Index Calculator? I hope it was helpful. Your insights can help us improve it.

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