Population Growth Calculator
Estimate future population, annual compound growth rate, years to a target population, doubling time, and demographic change from births, deaths, and migration.
How to Use the Population Growth Calculator
Use this population growth calculator to calculate future population, annual growth rate, time to a target population, doubling time, and demographic change from births, deaths, immigration, and emigration.
Step 1
Choose the calculator mode: future population, growth rate, time to target, or births and migration.
Step 2
Enter the starting population and the inputs shown for that mode.
Step 3
Use annual growth rates as percentages. For example, enter 2.5 for 2.5% per year.
Step 4
Read the projected population, total change, annual growth rate, doubling time, or demographic balance results.
Population Growth Formula
Population growth can be described with a compound growth formula, a growth-rate formula, a doubling-time formula, or a demographic balance equation. Use the formula that matches the inputs you actually know, and compare long-range assumptions with UN World Population Prospects.
The demographic balance equation follows the same components of population change: births, deaths, immigration, and emigration.
Population Growth Example
If a city starts with 1,000,000 people and grows at 2.5% per year for 10 years, the compound projection is 1,000,000 x 1.025^10 = 1,280,084.54. Rounded to whole people, the future population is 1,280,085.
Start
1,000,000 people
Rate
2.5% per year
After 10 years
1,280,085 people
Exponential vs Linear vs Logistic Population Growth
This calculator uses compound exponential growth for percentage-rate projections. Linear models use a fixed numeric change, while logistic growth and carrying capacity models require an upper limit assumption.
Exponential or compound growth
Short-term projections with a stable percentage growth rate.
P(t) = P0 x (1 + r)^tLinear growth
Cases where population changes by a fixed number each period.
P(t) = P0 + ktLogistic growth
Longer projections where growth slows near a carrying capacity.
P(t) approaches KWhen to Use This Calculator
Limitations of Population Growth Projections
Frequently Asked Questions
Common inquiries about population projection and growth calculations solved.
How do you calculate population growth?
For constant compound growth, use P(t) = P0 x (1 + r)^t. Enter the starting population, annual growth rate as a decimal or percentage, and time period.
What is the population growth formula?
The main compound population growth formula is P(t) = P0 x (1 + r)^t. The demographic balance formula is P1 = P0 + births - deaths + immigration - emigration.
How do I calculate future population?
Choose future population mode, enter the starting population, annual growth rate, and years, then read the projected population and total percentage change.
What is the difference between population growth rate and CAGR?
CAGR is the constant annual percentage rate that connects a starting population to an ending population over a fixed period. In this calculator, the growth-rate mode returns that annualized rate.
Can population growth be negative?
Yes. A negative growth rate models decline. It can forecast a lower future population and calculate time to a lower target when the rate is greater than -100%.
What is doubling time in population growth?
Doubling time is the number of years required for a population to become twice as large at a constant positive growth rate.
What is the difference between exponential and logistic population growth?
Exponential growth assumes the same percentage rate continues indefinitely. Logistic growth assumes growth slows as the population approaches a carrying capacity.
How do births, deaths, immigration, and emigration affect population growth?
Births and immigration increase population. Deaths and emigration decrease it. The net change is births minus deaths plus immigration minus emigration.