To make population growth calculator correctly please enter, Initial Population (P₀), Annual Growth Rate (r): The yearly percentage growth rate, entered as a percentage (e.g., 2%).

Time Period (t): The number of years in the future (positive) or past (negative).

Example:

• Initial Population (P₀): 1,000,000
• Growth Rate (r): 2% (0.02)
• Time (t): 10 years

Calculation: P(t) = 1,000,000 × e^(0.02 × 10) = 1,000,000 × e^(0.2) ≈ 1,221,403

Output: The population after 10 years will be approximately 1,221,403.

A city has 100,000 residents and experiences a 2% annual growth rate, the calculator would show that after 5 years, the population would reach approximately 110,408 people.

Population Growth Chart

Population Growth Formula

The formula for calculating population growth is:

P(t) = P₀ × e^(r ⋅ t)

Where:

• P(t): Population at time t (future or past).
• P₀: Initial population size (current or starting population).
• e: Euler’s number (approximately 2.71828), representing the base of natural logarithms.
• r: Growth rate (as a decimal, e.g., 2% = 0.02).
• t: Time in years (can be positive for future projections or negative for historical estimates).

A small town with 50,000 residents growing at 1.5% annually. Using the formula:

P5 = 50,000(1 + 0.015)^5
P5 = 50,000(1.077)
P5 = 53,850 residents after 5 years

How to Calculate Growth Rate of Population?

To compute the population growth rate, you’ll need to analyze the change between time periods.

The formula is:

Growth Rate = ((Final Population - Initial Population) / Initial Population) × 100

If a region’s population increased from 200,000 to 220,000 over 5 years:

Growth Rate = ((220,000 - 200,000) / 200,000) × 100
Growth Rate = (20,000 / 200,000) × 100
Growth Rate = 0.1 × 100 = 10% total growth
Annual Growth Rate = 10% ÷ 5 = 2% per year

• Rural Village Growth: Initial: 5,000; Rate: 0.5% annual After 3 years = 5,000(1 + 0.005)^3 = 5,075 residents
• Metropolitan Expansion: Initial: 2,000,000; Rate: 3% annual After 2 years = 2,000,000(1 + 0.03)^2 = 2,121,800 residents
• Suburban Development: Initial: 75,000; Rate: 2.5% annual After 4 years = 75,000(1 + 0.025)^4 = 82,744 residents
• University Town Growth: Initial: 150,000; Rate: 1.8% annual After 1 year = 150,000(1 + 0.018) = 152,700 residents
• Industrial City Decline: Initial: 500,000; Rate: -0.5% annual After 3 years = 500,000(1 – 0.005)^3 = 492,537 residents

What is Population Growth?

Population growth represents the dynamic change in population size within a specific geographic area over time. This complex demographic phenomenon encompasses natural increase (births minus deaths) and net migration (immigration minus emigration).