Statistics How To

Simpson’s Diversity Index: Definition, Formula, Calculation

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What is Simpson’s Diversity Index?

Simpson’s diversity index (SDI) measures community diversity. Although it’s commonly used to measure biodiversity, it can also be used to gauge diversity differences in populations in schools, communities and other locations.

The range is from 0 to 1, where:

  • High scores (close to 1) indicate high diversity.
  • Low scores (close to 0) indicate low diversity.

One of more the useful aspects of the index is to compare two sets of data to see which is more diverse. For example, if one has an SDI of 0.5 and another has an SDI of 0.35, then the set with the SDI of 0.5 is more diverse.



  • n = number of individuals of each species
  • N = total number of individuals of all species

The following solution steps explain how to solve the problem by hand. I actually used Open Office Math to solve this problem. You can download the ODS worksheet, with the formulas, here.

Sample question: What is Simpson’s Diversity Index for the following table of 5 species?

Step 1: Insert the total number in the set (89) into the formula N (N – 1) and solve:
N (N – 1) = 89 (81 -1) = 7832
Put this number aside for a moment.

Step 2: Calculate n(n – 1).

  1. Subtract 1 from each individual count (see the third column in the table below).
  2. Take each answer from (1) and multiply by each n (see the fourth column).

Step 3: Calculate D:

  1. Divide your answer from Step 2 by your answer from Step 1,
  2. Subtract your answer from 1.

D = 1 – (6488 / 7832) = 0.17.

The diversity index for this particular set is 0.17.

Simpson’s diversity index cannot be negative. If it is, check your calculations for arithmetic errors.


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Simpson’s Diversity Index: Definition, Formula, Calculation was last modified: October 12th, 2017 by Stephanie