Population Growth Calculator
This population growth calculator estimates how a population changes over time based on various factors such as birth rates, death rates, and migration.
Suppose a city has an initial population of 100,000 and experiences a 2% annual growth rate. Using the population growth calculator, you can determine that after 10 years, the population would grow to approximately 121,899 people, assuming consistent growth.Population Growth Calculation Chart
| Year | Initial Population | Growth Rate | Population Increase | Final Population |
|---|---|---|---|---|
| 1 | 100,000 | 2% | 2,000 | 102,000 |
| 2 | 102,000 | 2% | 2,040 | 104,040 |
| 3 | 104,040 | 2% | 2,081 | 106,121 |
| 4 | 106,121 | 2% | 2,122 | 108,243 |
| 5 | 108,243 | 2% | 2,165 | 110,408 |
Population Growth Formula
The basic formula for population growth is:
P(t) = P₀ × (1 + r)ᵗWhere:
- P(t) is the population after time t
- P₀ is the initial population
- r is the growth rate (as a decimal)
- t is the time period
Using our previous example:
- P₀ = 100,000
- r = 0.02 (2% expressed as a decimal)
- t = 10 years
P(10) = 100,000 × (1 + 0.02)¹⁰ = 121,899How do you calculate population growth rate?
To calculate the population growth rate the formula is:
r = (P(t) / P₀)^(1/t) - 1For example, if a town’s population increased from 50,000 to 65,000 over 5 years:
- P₀ = 50,000
- P(t) = 65,000
- t = 5 years
r = (65,000 / 50,000)^(1/5) - 1
r ≈ 0.0539 or 5.39% per yearMore Math Tools