What is the Formula to Calculate Population Growth Rate

by

Population Growth Rate Calculator

Calculate the growth rate of a population over a specific period using standard demographic formulas. This tool computes the total percentage change and the Compound Annual Growth Rate (CAGR).

function calculatePopulationGrowth() { // 1. Get input values using var var initialPopInput = document.getElementById('initialPopulation'); var finalPopInput = document.getElementById('finalPopulation'); var yearsInput = document.getElementById('timePeriodYears'); var resultDiv = document.getElementById('growthResult'); // 2. Parse values var initialPop = parseFloat(initialPopInput.value); var finalPop = parseFloat(finalPopInput.value); var years = parseFloat(yearsInput.value); // 3. Validate inputs if (isNaN(initialPop) || isNaN(finalPop) || isNaN(years)) { resultDiv.innerHTML = 'Please enter valid numeric values for all fields.'; return; } // Edge case handling for division by zero or invalid time frames if (initialPop <= 0) { resultDiv.innerHTML = 'Initial population must be greater than zero to calculate a growth rate.'; return; } if (years = 0) ? "increase" : "decrease"; var resultColor = (absoluteChange >= 0) ? "#28a745" : "#d9534f"; // 6. Output Results HTML var outputHTML = '
'; outputHTML += '

Results:

'; outputHTML += '
'; outputHTML += 'Absolute Population Change:'; outputHTML += '' + absoluteChangeFormatted + ' (' + direction + ')'; outputHTML += '
'; outputHTML += '
'; outputHTML += 'Total Percentage Growth (over ' + years + ' years):'; outputHTML += '' + totalGrowthFormatted + '%'; outputHTML += '
'; outputHTML += '
'; outputHTML += 'Compound Annual Growth Rate (CAGR):'; outputHTML += '' + cagrFormatted + '% per year'; outputHTML += '
'; outputHTML += '*CAGR represents the smoothed annualized growth rate required to go from the initial to the final population over the specified time.'; outputHTML += '
'; resultDiv.innerHTML = outputHTML; }

What is the formula to calculate population growth rate?

Understanding how a population changes over time is crucial for demographics, urban planning, and environmental studies. The "growth rate" can be expressed in a few ways depending on the time frame involved.

1. The Basic Percentage Growth Formula

If you want to know the total percentage change between two points in time, regardless of how many years passed between them, you use this simple formula:

Growth Rate (%) = ((Final Population – Initial Population) / Initial Population) × 100

This tells you that the population grew by X% in total over the entire period.

2. The Annualized Growth Formula (CAGR)

When dealing with population changes over multiple years, a simple average is often inaccurate because populations grow compoundingly (new members of the population also reproduce). Demographers prefer the Compound Annual Growth Rate (CAGR). This formula calculates a smoothed annualized rate.

CAGR (%) = ((Final Population / Initial Population)^(1 / Number of Years) – 1) × 100

This calculator provides both metrics, focusing on CAGR as the standard measure for annual demographic change.

Example Calculation

Let's look at a realistic demographic example using the formulas above:

  • Initial Population (Year 2010): 500,000
  • Final Population (Year 2020): 650,000
  • Time Period: 10 Years

Using the calculator above:

  • The Absolute Change is an increase of 150,000 people.
  • The Total Percentage Growth over the decade is 30.00%.
  • The Compound Annual Growth Rate (CAGR) is 2.66% per year. This means the population grew at an average compounded rate of 2.66% annually to reach the final number.

Leave a Comment