Species-Area Relationship Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The expected number of species on a given area is calculated with S = c × A^z, where c is a constant depending on the taxon and region, A the area, and z an exponent typically between 0.20 and 0.35.
Explanation
The species-area relationship is one of the few near-universal laws in ecology: the larger a studied area, the more species are recorded, but following a power law rather than simple proportionality — hence the exponent z, which controls how fast species richness grows with area. This relationship complements the Shannon diversity index, which measures diversity within an already-sampled community, while the species-area relationship predicts how many species one can expect to find as a function of the studied zone's size. The exponent z varies systematically with geographic context: on contiguous continental areas, where species can easily migrate between zones, z generally lies between 0.20 and 0.35; on isolated island archipelagos, where distance limits colonization, z is lower, typically between 0.12 and 0.17, reflecting an overall lower species richness that is less sensitive to area. The theoretical value z≈0.27, often cited as a reference, derives from Frank Preston's model (1962), which assumes a log-normal distribution of species abundances within a community. This relationship directly underlies conservation recommendations favoring large, continuous nature reserves over many small, fragmented ones, since a fragmented protected area mechanically loses expected species richness compared to an equivalent, unfragmented area. That same species richness, once recorded in the field, can also be compared across samples of different sizes using our Margalef richness index calculator, which corrects for sampling effort rather than geographic area.
Example: c = 5, z = 0.25, area = 100 km²
Inputs
Constant c: 5. Exponent z: 0.25. Area: 100 km².
Calculation
Number of species = 5 × 100^0.25 = 5 × 3.1623 ≈ 15.8.
Result
On this 100 km² area, about 16 species are estimated to be present according to this relationship.
Frequently asked questions
Where do the c and z values for my ecosystem come from?
These two parameters are estimated empirically by surveying species on plots of different sizes in the studied region, then fitting the relationship S=cA^z to that data (usually by regression on logarithms, where log(S) = log(c) + z×log(A) becomes a straight line). They are specific to each taxon (birds, plants, insects...) and each biogeographic region: there is no universal value.
Why is the exponent z lower on islands than on the mainland?
Because geographic isolation limits species' ability to colonize new islands, which reduces the total species richness available in the archipelago compared to an equivalent continental area. Richness therefore grows more slowly with island area, hence a lower z, generally between 0.12 and 0.17 versus 0.20 to 0.35 on the mainland.
Does this relationship really justify preferring one large reserve over several small ones?
It's an important theoretical argument in favor of large, continuous protected areas (the so-called SLOSS debate, single large or several small), but it isn't the only factor: connectivity between reserves, the presence of low-population species, and ecological corridors also matter. The species-area relationship gives an average prediction, not an absolute rule applicable to every specific case.