Shannon Diversity Index (H′)
Enter the number of individuals for each species (up to 40). Auto-updates as you type.
Controls
Species counts
Rows: 0/40
Actions
Results (auto-updating)
Log base: ln
Shannon index (H′)
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Evenness (E)
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Richness (k, species with n>0)
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Total individuals (N)
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Average per species (N/k)
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Classification
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Quick summary will appear here after you enter counts.
Step-by-step derivation
Provide at least one non-zero count to see the algebraic steps.
References
- Formula: H′ = −Σ (pᵢ · log_b(pᵢ)), where pᵢ = nᵢ / N, N = Σ nᵢ, b ∈ {e,10,2}.
- Evenness: E = H′ / log_b(k) for k ≥ 2; else E = 0.
- Shannon (1948) “A Mathematical Theory of Communication”.
- Ecology practice commonly uses ln, log₁₀, or log₂; base only rescales H′.