# Simpson’s Diversity Index Calculator

Created by Purnima Singh, PhD
Reviewed by Wojciech Sas, PhD and Steven Wooding
Last updated: Jun 05, 2023

Omni's Simpson's diversity index calculator allows you to measure the diversity of species in a given community. Just enter the population of different species, and our calculator will compute Simpson's index for your data.

If you are more interested in estimating the variance of a population, our population variance calculator might come in handy. We also recommend checking out the standard deviation calculator to brush up on your statistics.

Read on to learn the definition and formula for Simpson's diversity index. You will also find an example of Simpson's diversity index calculation.

## What is Simpson's index?

Simpson's indices are a way of quantifying the biodiversity of communities. The value of Simpson's index reflects how many different types of species are in a community and how evenly distributed the population of each species is.

The Simpson's index $D$ () is the probability that any two individuals randomly selected from an infinitely large community will belong to the same species, i.e.,

$\scriptsize D = \sum p_i^2$

where $p_i$ is the proportion of individuals in the i-th species.

If you have a finite-size community, the formula for calculating Simpson's index ($D$) is:

$\scriptsize D = \frac{ \sum n_i(n_i -1)}{N (N-1)}$

where:

• $n_i$ — Number of individuals in the i-th species; and

• $N$ — Total number of individuals in the community.

Simpson's index is one of the most popular and robust ways to measure diversity in a community; as $D$ increases, diversity decreases. Although originally proposed to measure diversity in ecological communities, nowadays, we use it widely in quantifying diversity in other areas as well — for example, gender or ethnicity diversity at organizations.

The Shannon diversity index is another approach for quantifying species diversity. You can read more about it in our Shannon diversity index calculator

## Simpson's diversity index formula

According to the original formula proposed by Simpson, a higher $D$ value suggested a community with low biodiversity. This sounds a bit counterintuitive, as typically, a high diversity index should imply a more diverse community. Hence, we usually express Simpson's diversity index as $1-D$, which is also known as the Gini-Simpson index, i.e.,

$\scriptsize \begin{split} \text{Gini-Simpson index} &=(1-D) \\ &= 1 - \left ( \frac{\sum n_i(n_i -1)}{N (N-1)} \right ) \end{split}$

The Gini-Simpson index (or Simpson's index of diversity) measures the probability that two randomly selected individuals belong to different species.

Another popular index for measuring diversity is the inverse Simpson index:

$\scriptsize \text{Inverse Simpson index} =\frac{1}{D}$

## How to use Simpson's diversity index calculator?

Let us see how to calculate Simpson's diversity index for the following data set:

Species label

Population

A

300

B

335

C

365

1. Enter the species population, i.e., 300, 335, and 365, in the first, second, and third-row, respectively. You can enter data for up to 50 species.
2. The calculator will display the Simpson's Index ($D = 0.33$), Simpson's diversity index ($1 - D = 0.67$), and Simpson's reciprocal index ($1 / D = 2.99$) in the result section.

## Example of Simpson's diversity index calculation

Lets us calculate the diversity indices for the same data set as above:

1. Sum the population of individual species to get the total number of observations, $N$.

$N = 300 + 335 + 365 = 1000$.

2. Evaluate $N (N - 1)$:

$N(N - 1) = 1000 \times 999 = 999,000$.

3. Determine $n_i(n_i-1)$, for each species:

$300 \times 299 = 89,700$; $335 \times 334 = 111,890$; and $365 \times 364 = 132,860$.

4. Add the values in step 3 to get $\sum n_i(n_i-1)$:

$89,700 + 111,890 + 132,860 = 334,450$.

5. The Simpson's Index ($D$) is:

$D = \frac{\sum n_i(n_i-1)}{N(N - 1)}$
$D = 334,450 / 999,000$
$D = 0.33$.

6. The Simpson's diversity index (or Gini-Simpson index, $1 - D$) is:

$1- \frac{\sum n_i(n_i-1)}{N(N - 1)} = 0.67$.

7. Simpson's reciprocal index ($1 / D$) is:

$1 / D = 2.99$.

As you can see, calculating the diversity indices for large data sets is quite cumbersome and not everyone's cup of tea. That is why we recommend using Simpson's index calculator so that you can easily estimate Simpson's indices.

## Simpson's diversity index interpretation

The Gini-Simpson index score varies between 0 and 1. A high score indicates high diversity, and a low score indicates low diversity. When the diversity index is zero, the community contains only one species (i.e., no diversity). As the number of different species increases and the population distribution of species becomes more even, the diversity index increases and approaches one.

## FAQ

### How do I calculate Simpson's diversity index?

To calculate Simpson's diversity index for any community, follow the instructions:

1. Add the individual species populations to get N.

2. Determine N × (N - 1).

3. Work out n × (n - 1) for each species, where n is the number of individuals in each species.

4. Sum all the values in step 3.

5. Divide the sum obtained in step 4 by the value obtained in step 2. As a result, you will get Simpson's index D.

6. Evaluate Simpson's diversity index as 1 - D.

### How do I use Simpson's diversity index?

Simpson's diversity index gives a measure of community diversity. We can use it to get an idea about how diverse any specific institution/community is. We can also use it to compare two different communities to see which is more diverse.

### What does a high Simpson's index of diversity indicate?

The higher the value of the index, the greater the diversity of the community. A diversity index close to 1 means that there are several species in the community, and the population proportion of species is even.

### What does a low Simpson's diversity index mean?

A low Simpson's diversity index means that the community is not very diverse. For example, if there are only one species in the community, Simpson's diversity index is 0.

Purnima Singh, PhD
Input population data for each species
Species 1
Species 2
You can add data for up to 50 species; fields will appear as you need them.
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