Shannon-Wiener Diversity Index (H′), Pielou Evenness (J′) & Simpson’s (1−D) Calculator

Compute Shannon H′, Pielou evenness J′, Simpson’s Diversity (1−D), and Hill number exp(H′).

Shannon-Wiener Diversity Index (H′)
1.235 nats
Pielou’s Evenness Index (J′ = H′/ln S) 0.891 J′ (0–1)
Simpson’s Diversity Index (1 − D) 0.682 1−D
Effective Number of Species (exp H′) 3.44 species
Inputs
⚡ Scenarios:
count
Abundance count of Species / Category 1.
count
Abundance count of Species / Category 2.
count
Abundance count of Species / Category 3.
count
Abundance count of Species / Category 4.
Results & Graph
Shannon-Wiener Diversity Index (H′)
1.235 nats
Pielou’s Evenness Index (J′ = H′/ln S)
0.891 J′ (0–1)
Simpson’s Diversity Index (1 − D)
0.682 1−D
Effective Number of Species (exp H′)
3.44 species

Shannon-Wiener Diversity Index (H′)

Graph 1 • Shannon & Simpson Diversity • Domain Architecture & Live Telemetry Maps Species1 Count, Species2 Count, Species3 Count through Shannon & Simpson Diversity Formula.
Shannon-Wiener Diversity Index: 1.235 nats Shannon & Simpson Diversity • Invariants & Metrics Shannon-Wiener Diversity Ind 1.235 nats Pielou’s Evenness Index (J′ 0.891 J′ (0–1) Simpson’s Diversity Index (1 0.682 1−D Effective Number of Species 3.44 species
Graph 2 • Shannon-Wiener Diversity Index (H′) Across Species1 Count Sweep (40% → 160%) Evaluates H′ = −Σ p_i·ln(p_i); J′ = H′ / ln(S); D = Σ n_i(n_i − 1) / [N(N − 1) across 7 operating points (current input highlighted).
0 nats 0.719 nats 1.44 nats 1.31 18count 1.30 27count 1.27 36count 1.24 45count 1.20 54count 1.16 63count 1.11 72count
Graph 3 • Joint Sensitivity: Species1 Count × Species2 Count Compares Shannon-Wiener Diversity Index (H′) when Species2 Count is shifted +25% (solid) vs. −25% (dashed).
0 nats 0.716 nats 1.43 nats --- Species2 Count @ 75% 1.26 -30% 1.25 -15% 1.23 +0% 1.20 +15% 1.18 +30%
Summary: Across 4 species (N=100), Shannon H′ is 1.2353 (Effective Species e^H′ = 3.44), Pielou Evenness J′ is 0.8911, and Simpson’s Diversity (1−D) is 0.6818.
Summary: Across 4 species (N=100), Shannon H′ is 1.2353 (Effective Species e^H′ = 3.44), Pielou Evenness J′ is 0.8911, and Simpson’s Diversity (1−D) is 0.6818.
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Formula & Mathematical Methodology: Shannon & Simpson Diversity Formula

H′ = −Σ pi·ln(pi)
J′ = H′ / ln(S)
D = Σ ni(ni − 1) / [N(N − 1)]
EffectiveSpecies = eH′
H′ = −Σ p_i·ln(p_i); J′ = H′ / ln(S); D = Σ n_i(n_i − 1) / [N(N − 1)]; EffectiveSpecies = e^(H′)
  • species1Count: Species1 Count (count)
  • species2Count: Species2 Count (count)
  • species3Count: Species3 Count (count)
  • species4Count: Species4 Count (count)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: Shannon & Simpson Diversity

Compute Shannon H′, Pielou evenness J′, Simpson’s Diversity (1−D), and Hill number exp(H′).

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: H′ = −Σ p_i·ln(p_i); J′ = H′ / ln(S); D = Σ n_i(n_i − 1) / [N(N − 1)]; EffectiveSpecies = e^(H′).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Shannon & Simpson Diversity via H′ = −Σ p_i·ln(p_i); J′ = H′ / ln(S); D = Σ n_i(n_i − 1) / [N(N − 1)]; EffectiveSpecies = e^(H′).

Frequently Asked Questions

How does the Shannon-Wiener Diversity Index (H′), Pielou Evenness (J′) & Simpson’s (1−D) Calculator compute the solution?

It evaluates H′ = −Σ p_i·ln(p_i); J′ = H′ / ln(S); D = Σ n_i(n_i − 1) / [N(N − 1)]; EffectiveSpecies = e^(H′) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Probability Distributions & Survival Analysis

Shannon-Wiener Diversity Index (H′), Pielou Evenness (J′) & Simpson’s (1−D) Calculator: inputs, method, and how to read the result

Compute Shannon H′, Pielou evenness J′, Simpson’s Diversity (1−D), and Hill number exp(H′).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Species1 Count: Abundance count of Species / Category 1.
  • Species2 Count: Abundance count of Species / Category 2.
  • Species3 Count: Abundance count of Species / Category 3.
  • Species4 Count: Abundance count of Species / Category 4.

What the calculation includes

With the default values shown, Shannon-Wiener Diversity Index (H′) is 1.235 nats. The calculation follows Shannon & Simpson Diversity Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Species1 Count from 45 count to 50 count changes Shannon-Wiener Diversity Index (H′) from 1.235 nats to 1.213 nats. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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