Enter your Current Population Size (N), Intrinsic Growth Rate (r), Time Period, and Population Change Rate (dN/dt), then choose a Calculation Method to find your population's Carrying Capacity (K) — along with Population at Time T, % of Carrying Capacity, and the Growth Limiting Factor keeping that population in check.
Carrying Capacity (K)
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Population at Time T
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% of Carrying Capacity
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Growth Limiting Factor
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Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely without degrading the habitat. It represents the balance point where birth rates equal death rates due to resource limitations.
The carrying capacity can be calculated from the logistic equation: dN/dt = r × N × (1 - N/K). Rearranging this formula when dN/dt = 0 (equilibrium), we get K = N × r / (r - dN/dt per individual).
Limiting factors include food availability, water supply, shelter, disease, predation, competition for resources, and environmental conditions like temperature and pH. These factors create environmental resistance that prevents unlimited population growth.
Population growth follows a logistic curve: initially exponential when population is small, then slowing as resources become limited, finally leveling off at the carrying capacity where growth rate approaches zero.
When population exceeds carrying capacity, it experiences overshoot followed by die-back due to resource depletion, increased competition, disease, or environmental degradation. The population typically crashes below the original carrying capacity.
Yes, carrying capacity can change due to environmental factors like climate change, habitat destruction, introduction of new species, technological advances (for humans), or changes in resource availability.
Exponential growth assumes unlimited resources and constant growth rate, while logistic growth accounts for environmental resistance and resource limitations, resulting in an S-shaped curve that levels off at carrying capacity.