Quick answer
The Shannon index is H′ = −Σ pᵢ ln pᵢ, and evenness is H′ ÷ ln S. Counts of 3 and 1 have proportions 0.75 and 0.25, so H′ = 0.5623 and evenness = 0.8113.
Enter the counts for each category. The calculator returns the diversity index and evenness.
Related tools: Simpson's Diversity Index Calculator: Simpson's index of diversity from counts. Heat Index Calculator: Apparent temperature from air temperature and relative humidity (°F).
How to use the Shannon 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
H′ = −Σ pᵢ ln pᵢ; evenness = H′ ÷ ln S
IEEE-754 double precision; shown to at most 6 decimal places.
Zero counts are ignored.
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 |
|---|---|
| Shannon index H′ | 0.562335 |
| Evenness | 0.811278 |
Example 2
Inputs: Counts per category = 1 1.
| Result | Value |
|---|---|
| Shannon index H′ | 0.693147 |
| Evenness | 1 |
The first line is the headline result (shannon index H′). Below it the shannon Diversity Index Calculator lists evenness, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
What the number means
H′ rises with the number of categories and with how evenly the counts are spread. It is 0 when only one category is present, and equals ln S for S equally common categories.
Sample caveats
The index describes the sample you counted. A small sample underestimates diversity, because rare categories are missed.
Diversity and evenness
Counts of 3 and 1 give proportions 0.75 and 0.25 and H′ = −(0.75 ln 0.75 + 0.25 ln 0.25) ≈ 0.5623. Evenness is H′ ÷ ln S = 0.5623 ÷ 0.6931 ≈ 0.8113.
The index uses natural logarithms here. Tools using base 2 or base 10 give different numbers, so compare only values calculated the same way.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Counts per category: entering "0 0" shows "At least one count must be positive." beside that field and no result.
Choosing between the Shannon 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 |
|---|---|---|
| [Simpson's Diversity Index Calculator](/statistics/simpsons-diversity-index/) | counts per category | Simpson index D |
| [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
Which logarithm is used?
The natural logarithm.
What is evenness?
H′ divided by its maximum, ln S.
How does it compare with Simpson's?
Shannon weights rare categories more.
Why do different tools give different Shannon values?
They may use a different logarithm base. This page uses natural logs.
What does the Shannon Diversity Index Calculator calculate?
Shannon–Wiener diversity index from species counts. It returns Shannon index H′ and Evenness.
What formula does the Shannon Diversity Index Calculator use?
H′ = −Σ pᵢ ln pᵢ; evenness = H′ ÷ ln S. Zero counts are ignored.
What do I need to enter in the shannon 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 shannon Diversity Index result?
With counts per category 3, 1, the shannon index H′ is 0.562335.
Where does the method come from?
The method follows: Shannon CE (1948), A Mathematical Theory of Communication, Bell System Technical Journal 27: 379-423 and 623-656 (the entropy formula H = −Σ pᵢ ln pᵢ).
Related calculators
- Simpson's Diversity Index Calculator — Simpson's index of diversity from 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
- Shannon CE (1948), A Mathematical Theory of Communication, Bell System Technical Journal 27: 379-423 and 623-656 (the entropy formula H = −Σ pᵢ ln pᵢ)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.