What it is and when to use it
This calculator computes Simpson's Index of Diversity from a list of species counts (individuals per species) in a sample. It answers a specific question: if you pick two individuals at random from the sample, how likely is it that they belong to different species? A value close to 1 means high diversity (many species, evenly represented), while a value close to 0 means low diversity (the sample is dominated by one or a few species).
Use it in ecology fieldwork, classroom labs, or habitat monitoring whenever you have counted individuals of each species in a plot, trap, or quadrat and want a single comparable number. It works for any set of counts — plants in a survey quadrat, insects from a pitfall trap, or fish from a netting survey — as long as every individual has been assigned to a species.
D = Σ[n(n-1)] / [N(N-1)] | Simpson's Index of Diversity = 1 - D
Worked example
A quadrat survey counts four species with 20, 15, 10, and 5 individuals, for a total N = 50. Σn(n-1) = (20×19) + (15×14) + (10×9) + (5×4) = 380 + 210 + 90 + 20 = 700. N(N-1) = 50 × 49 = 2,450. D = 700 / 2,450 = 0.2857. Simpson's Index of Diversity = 1 - 0.2857 = 0.7143, entered into the calculator as "20,15,10,5" and matching its output of 0.7143.
Common mistakes and how to interpret the result
- Entering relative abundances or percentages instead of raw counts. The formula needs actual individual counts (whole numbers) for n(n-1) to be meaningful; percentages will produce a mathematically valid but ecologically meaningless number.
- Comparing indices from samples of very different total sizes without caution. Simpson's Index is somewhat sensitive to sample size, so comparing a 50-individual sample to a 500-individual sample can be misleading even if both are calculated correctly.
- Confusing Simpson's Index (D) with Simpson's Index of Diversity (1-D). Some sources report D directly, where lower means more diverse — this calculator reports 1-D, where higher means more diverse. Check which convention a paper or textbook is using before comparing values.
- Leaving out rare species. Omitting singletons (species seen only once) because they feel negligible will inflate the apparent diversity score; include every species observed, however rare.
Frequently Asked Questions
What does a Simpson's Index of Diversity value actually mean?
Why does the formula use n(n-1) instead of just n?
Is a higher biodiversity index always better for an ecosystem?
Can I use this calculator for species richness instead of diversity?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |