Quick answer
Simpson's index is D = 1 − Σ pᵢ², the probability that two items drawn at random belong to different categories. Counts of 3 and 1 give Σp² = 0.625 and D = 0.375.
Enter the counts. The calculator returns D and Σp².
Related tools: Shannon Diversity Index Calculator: Shannon–Wiener diversity index from species counts. Heat Index Calculator: Apparent temperature from air temperature and relative humidity (°F).
How to use the Simpson's Diversity Index Calculator
- Type counts per category, for example 30, 10, 5.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Counts per category | Text, such as 30, 10, 5 | — |
Formula and method
Formula
D = 1 − Σ pᵢ²
IEEE-754 double precision; shown to at most 6 decimal places.
Probability that two randomly chosen individuals belong to different categories (with replacement).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Counts per category = 3, 1.
| Result | Value |
|---|---|
| Simpson index D | 0.375 |
| Σp² | 0.625 |
Example 2
Inputs: Counts per category = 1 1.
| Result | Value |
|---|---|
| Simpson index D | 0.5 |
| Σp² | 0.5 |
The first line is the headline result (simpson index D). Below it the simpson's Diversity Index Calculator lists σp², which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Other versions
Some authors define Simpson's index with sampling without replacement, Σ n(n − 1) ÷ N(N − 1), which gives 1 − 6/12 = 0.5 for the same counts. This page uses the with-replacement form, 1 − Σp².
Reading values
D ranges from 0 (one category) towards 1 (many equally common). It emphasises the most common categories, unlike the Shannon index.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Counts per category: entering "5" shows "Enter at least 2 numbers." beside that field and no result.
Choosing between the Simpson's Diversity Index Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Shannon Diversity Index Calculator](/statistics/shannon-index/) | counts per category | Shannon index H′ |
| [Heat Index Calculator](/science/heat-index/) | air temperature and relative humidity | Heat index |
| [Ponderal Index Calculator](/health/ponderal-index/) | weight and height | Ponderal index |
| [Ape Index Calculator](/health/ape-index/) | arm span and height | Ape index |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
Assumptions and limitations
- At least two counts
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for counts per category to confirm this.
Frequently asked questions
Is higher always more diverse?
Yes, within a given definition.
What is the reciprocal index?
The inverse Simpson index is 1 ÷ Σp², which counts the effective number of categories.
What if I have one category?
Then D is 0, because every pair of draws comes from the same category.
What does the Simpson's Diversity Index Calculator calculate?
Simpson's index of diversity from counts. It returns Simpson index D and Σp².
What formula does the Simpson's Diversity Index Calculator use?
D = 1 − Σ pᵢ². Probability that two randomly chosen individuals belong to different categories (with replacement).
What do I need to enter in the simpson's Diversity Index Calculator?
You enter Counts per category.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. At least two counts.
What is an example of a simpson's Diversity Index result?
With counts per category 3, 1, the simpson index D is 0.375.
Where does the method come from?
The method follows: Simpson EH, Nature 163 (1949).
Related calculators
- Shannon Diversity Index Calculator — Shannon–Wiener diversity index from species counts.
- Heat Index Calculator — Apparent temperature from air temperature and relative humidity (°F).
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Sample Size Calculator — Sample size for estimating a mean or a proportion.
Sources
- Simpson EH, Nature 163 (1949)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.