Carrying Capacity Calculator
Calculate the maximum sustainable population size using the logistic growth model
Calculate Carrying Capacity
Number of individuals at measurement time
Rate of population change at current time
Intrinsic rate of increase per individual (birth rate minus death rate)
Carrying Capacity Results
Formula: K = N / (1 - (Cp / (r × N)))
Growth Phase: Exponential Growth
Population Growth Analysis
Example Calculations
Rabbit Population Example
Current Population (N): 22,000,000 rabbits
Population Change (Cp): 49,120,000 rabbits/year
Intrinsic Growth Rate (r): 2.3
Calculation: K = 22,000,000 / (1 - (49,120,000 / (2.3 × 22,000,000)))
Result: K ≈ 752,000,000 rabbits
Bacteria Culture Example
Current Population (N): 100 CFU/ml
Population Change (Cp): 25 CFU/ml per hour
Intrinsic Growth Rate (r): 0.27
Result: K = 1,350 CFU/ml
Logistic Growth Phases
Exponential Phase
0-25% capacity
Unlimited resources, rapid growth
Rapid Growth
25-75% capacity
Resources becoming limited
Plateau Phase
75-100% capacity
Growth slowing, reaching equilibrium
Limiting Factors
Food availability and quality
Water resources and access
Living space and territory
Disease and parasites
Climate and weather conditions
Predation and competition
Understanding Carrying Capacity
What is Carrying Capacity?
Carrying capacity (K) is the maximum number of individuals that an environment can sustainably support over time. It represents the point where population growth stabilizes due to limited resources and environmental constraints.
The Logistic Growth Model
Unlike exponential growth, the logistic model accounts for environmental resistance. As population approaches carrying capacity, growth rate decreases due to resource competition, creating an S-shaped (sigmoid) growth curve.
Applications
- •Wildlife management and conservation
- •Fisheries and agriculture planning
- •Microbiology and cell culture
- •Human population studies
Mathematical Formula
K = N / (1 - (Cp / (r × N)))
Derived from the logistic equation
- K: Carrying capacity (individuals)
- N: Current population size
- Cp: Current population change rate
- r: Intrinsic growth rate per individual
Logistic Differential Equation
dN/dt = r × N × (1 - N/K)
Rate of change depends on current population and remaining capacity