Understanding how populations change over time is essential for urban planning, biology, economics, and environmental science. Whether you are projecting the growth of a city, a country, or a bacterial culture, the mathematical principles remain largely the same. This guide explains how to calculate future population size using the standard exponential growth formula.
The Population Growth Formula
The most common method for calculating population growth over discrete time periods (like years) is the geometric or exponential growth formula. It assumes the growth rate remains constant over the time period.
P = P₀ × (1 + r)ᵗ
Where:
P = The final population size.
P₀ = The initial population size (Current Population).
r = The growth rate expressed as a decimal (e.g., 2% becomes 0.02).
t = The time period (usually in years).
Step-by-Step Calculation Example
Let's look at a realistic scenario. Suppose a small town has a current population of 50,000 people. The town is growing at a rate of 2.5% per year. We want to know what the population will be in 10 years.
Identify the variables:
P₀ = 50,000
rate = 2.5% = 0.025
t = 10 years
Set up the equation:
P = 50,000 × (1 + 0.025)¹⁰
Add the rate to 1:
1 + 0.025 = 1.025
Apply the exponent (time):
1.025¹⁰ ≈ 1.28008
Multiply by the initial population:
50,000 × 1.28008 ≈ 64,004
After 10 years, the population of the town will be approximately 64,004.
Calculating Population Decline
This formula works equally well for shrinking populations. If a population is declining, the growth rate is negative. For example, if a species is declining by 5% per year, your r would be -0.05.
The term inside the parenthesis becomes (1 – 0.05) = 0.95. Because this number is less than 1, multiplying it repeatedly over time will result in a smaller final number.
Factors Influencing Growth Rates
While the mathematical formula provides a projection, real-world population growth is influenced by three main demographic factors:
Fertility Rates: The average number of children born to women in the population.
Mortality Rates: The number of deaths within the population.
Migration: Net migration is the difference between immigrants (people moving in) and emigrants (people moving out).
The "Growth Rate" input in the calculator above essentially combines these three factors into a single percentage to project future trends.
function calculatePopulation() {
// 1. Get Input Elements
var initialPopInput = document.getElementById('initialPop');
var growthRateInput = document.getElementById('growthRate');
var timePeriodInput = document.getElementById('timePeriod');
var resultBox = document.getElementById('resultDisplay');
var errorBox = document.getElementById('errorDisplay');
// 2. Parse Values
var P0 = parseFloat(initialPopInput.value);
var rPercent = parseFloat(growthRateInput.value);
var t = parseFloat(timePeriodInput.value);
// 3. Validation
if (isNaN(P0) || isNaN(rPercent) || isNaN(t) || P0 < 0 || t 0) {
totalPercentGrowth = ((finalPop – P0) / P0) * 100;
}
// 5. Update HTML Output
// We use Math.round because you generally can't have a fraction of a person
document.getElementById('resFinalPop').innerText = Math.round(finalPop).toLocaleString();
// Format change with + or – sign
var changeFormatted = Math.round(totalChange).toLocaleString();
if (totalChange > 0) changeFormatted = "+" + changeFormatted;
document.getElementById('resChange').innerText = changeFormatted;
document.getElementById('resPercent').innerText = totalPercentGrowth.toFixed(2) + "%";
// Show result box
resultBox.style.display = 'block';
}