Shannon Diversity Index Calculator
Enter the count of individuals in each group or species, separated by commas or spaces, to get the Shannon index H in nats, Pielou's evenness, and the effective number of species.
Example: with Counts per group (comma or space separated) 40, 30, 20, 10 → Shannon index H: 1.2799 nats.
- Pielou evenness0.9232
- Effective species (e^H)3.60 effective species
- Sample4 groups, N = 100
Computed by the calculator below using its default values. Change any input to see your own numbers.
Shannon H = -Σ p·ln(p), in nats. Evenness rescales it to 0-1; e^H is the effective species count.
Entropy borrowed from information theory
The Shannon index measures how hard it is to predict the group of a randomly chosen individual. If one group dominates, prediction is easy and H is low; if many groups are equally common, every pick is a surprise and H is high. The formula H = -Σ p·ln(p) sums each group's proportion times its log, and the minus sign makes the total positive. It rewards both richness, meaning more groups, and evenness, meaning similar abundances.
Evenness and effective species
H by itself has no ceiling, which makes raw values hard to compare. Pielou's evenness fixes the scale by dividing H by its maximum, ln(S), where S is the number of groups; the result runs from 0 to 1, with 1 meaning perfectly even. Exponentiating H gives the effective number of species, e^H, the count of equally common groups that would yield the same H. It is often the most intuitive way to report diversity.
How it’s calculated
Shannon index H = -Σ p_i · ln(p_i), where p_i = n_i / N is each group's proportion (natural log, units of nats). Pielou's evenness = H / ln(S) with S the number of groups, ranging 0 to 1. Effective number of species = e^H. To convert H to bits (log base 2), multiply by 1.4427; to base 10, multiply by 0.4343.
Uses natural logarithms, so H is in nats; make sure any values you compare use the same log base. Counts should come from one sampled community.
Typical Shannon H (natural log)
| H (nats) | Community read |
|---|---|
| 0 | One group only; no diversity |
| 0.5 - 1.5 | Low to moderate diversity |
| 1.5 - 2.5 | Fairly diverse |
| 2.5 - 3.5 | Highly diverse |
| Above 3.5 | Very high diversity; many even groups |
H has no fixed maximum; it rises with richness and evenness. Multiply H in nats by 1.4427 to convert to bits.
Common mistakes
- Mixing log bases. Natural log gives nats, log base 2 gives bits, log base 10 gives decits, all valid but not comparable without converting.
- Reporting H without evenness or richness. The same H can come from a few even groups or many uneven ones.
- Including zero counts. Groups with zero individuals are simply absent and contribute nothing; only positive counts enter the sum.
Frequently asked questions
What is the Shannon diversity index formula?
H = -Σ p·ln(p), where p is each group's proportion of the total. This tool uses natural logarithms, so H is expressed in nats. Higher H means greater diversity.
What is a good Shannon index value?
Most ecological studies land between about 1.5 and 3.5. There is no fixed maximum, since H rises with both the number of groups and how evenly individuals are spread, so compare values only within the same log base.
What is Shannon evenness?
Pielou's evenness is H divided by ln(S), where S is the number of groups. It rescales H to a 0-to-1 range where 1 means all groups are equally abundant, separating evenness from richness.
What is the effective number of species?
It is e^H, the number of equally common groups that would produce your H. Reporting this true diversity is often clearer than the raw index because it is a plain count.
How does Shannon differ from Simpson's index?
Both summarize diversity, but Shannon (entropy-based) is more sensitive to rare groups, while Simpson's is driven more by the common, dominant ones. Reporting both gives a fuller picture.