Species-Area Relationship Calculator
Estimate species richness from habitat area using MacArthur and Wilson's S = cA^z equation.
Calculate how habitat loss reduces biodiversity in any ecosystem.
The species-area relationship (SAR) is one of ecology’s most consistent empirical patterns. Larger habitats support more species. The relationship follows a power law, first formalized by MacArthur and Wilson in 1967 as the theory of island biogeography.
The equation:
S = c x A^z
where S is the number of species, A is area, c is a constant that depends on the taxon and region, and z is the scaling exponent.
The z exponent. For true islands isolated by ocean, z is typically 0.25-0.35. For habitat fragments on land (forest patches in an agricultural landscape), z is lower, around 0.12-0.25. The difference matters. A lower z means species are more resilient to area reduction.
The c constant varies widely by taxon and region. For birds in tropical forests, c might be 5-20. For insects on a single island chain, it could be 0.1 or 500. It is best calibrated with local data.
Habitat loss prediction. If you halve the area of a forest patch, you expect to lose a fraction of species: S_new = S_old x (0.5)^z. With z = 0.25, halving the area loses about 16% of species. With z = 0.35, it loses about 22%.
This is why conservation biology focuses on maintaining connected habitat corridors. Fragmented patches behave as islands and suffer species loss at rates predicted by the SAR. A single large reserve often supports more species than several small reserves of equal total area.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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