Carrying Capacity Calculator
Calculate the maximum sustainable population size using the logistic equation. Analyze population dynamics, environmental limits, and ecological sustainability.
Understanding Carrying Capacity
Carrying capacity (K) is the maximum population size an environment can sustain indefinitely. It's determined by limiting factors like food, space, water, and other resources.
Formula: K = N ÷ (1 - (Cp ÷ (r × N))) where N = current population, Cp = population change rate, r = intrinsic growth rate
Population Examples
Population Parameters
Current number of individuals in the population
Net change in population size per time period (births - deaths + migration)
Maximum per capita growth rate under ideal conditions
Carrying Capacity Results
Carrying Capacity
1.35K
% of Capacity
7.4%
Growth Phase
Early Growth
Time to Capacity
50.0 years
Population Status: Population has significant room for growth
Population Analysis
Logistic Equation:
dN/dt = r × N × (1 - N/K)
Where dN/dt = population change, r = intrinsic rate, N = population, K = carrying capacity
Management Recommendations
Population can grow safely
Monitor growth trajectory
Ensure habitat quality
Maintain genetic diversity
Population Growth Phases
Exponential Phase
Population grows rapidly with abundant resources and minimal competition.
Logistic Phase
Growth slows as resources become limited and competition increases.
Equilibrium Phase
Population stabilizes at carrying capacity with balanced births and deaths.
Real-World Examples
Australian Rabbit Population (1859-1930)
- • Initial: 12 rabbits introduced
- • Growth Rate: r = 2.3 per year
- • Peak: 750 million individuals
- • Lesson: Invasive species can rapidly exceed carrying capacity
Human Population Growth
- • 1800: 1 billion people
- • 2024: 8+ billion people
- • Estimates: Carrying capacity 7-11 billion
- • Challenge: Balancing growth with sustainability
Limiting Factors
Food Resources
Availability of nutrition
Living Space
Physical habitat area
Water Access
Fresh water availability
Environmental Stress
Disease, predation, climate