How to Calculate Growth Rate for a Population

Population Growth Rate Calculator

Calculate Annual Growth Rate and Total Percentage Change

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How to Calculate Growth Rate for a Population

Understanding how a population changes over time is fundamental in demographics, ecology, biology, and urban planning. The population growth rate tells us the percentage change in the size of a population over a specific period.

The Growth Rate Formula

While there are several ways to measure growth, the most common method for calculating the average annual growth rate over multiple years is using the Geometric Growth Rate (similar to Compound Annual Growth Rate or CAGR). This accounts for the compounding effect of growth.

r = ( ( P_t / P_0 )^(1/t) – 1 ) × 100

Where:

• r = Annual Growth Rate (%)
• P_t = Final Population Size
• P_0 = Initial Population Size
• t = Time Period (Number of Years)

Example Calculation

Let's say a small town had a population of 10,000 people 5 years ago. Today, the population is 12,500. What is the annual growth rate?

1. Step 1: Divide Final by Initial: 12,500 / 10,000 = 1.25
2. Step 2: Raise to power of (1/t): 1.25^(1/5) = 1.25^0.2 ≈ 1.0456
3. Step 3: Subtract 1: 1.0456 – 1 = 0.0456
4. Step 4: Multiply by 100: 0.0456 × 100 = 4.56%

The town grew at an average rate of 4.56% per year.

Total Percentage Growth

If you only need to know how much the population grew in total, regardless of how many years it took, use the simple percentage change formula:

((Final Population – Initial Population) / Initial Population) × 100

In our example: ((12,500 – 10,000) / 10,000) × 100 = 25% Total Growth.

Doubling Time (Rule of 70)

A useful metric derived from the growth rate is the "Doubling Time." This estimates how many years it will take for the population to double in size at the current rate. It is calculated by dividing 70 by the growth rate percentage.

70 / 4.56 ≈ 15.35 years to double.

function calculateGrowth() { var initPop = document.getElementById('initialPop').value; var finalPop = document.getElementById('finalPop').value; var timePeriod = document.getElementById('timePeriod').value; var errorMsg = document.getElementById('errorMsg'); var resultsArea = document.getElementById('resultsArea'); // Reset error errorMsg.style.display = 'none'; resultsArea.style.display = 'none'; // Validation if (initPop === "" || finalPop === "" || timePeriod === "") { errorMsg.innerHTML = "Please fill in all fields."; errorMsg.style.display = 'block'; return; } var P0 = parseFloat(initPop); var Pt = parseFloat(finalPop); var t = parseFloat(timePeriod); if (isNaN(P0) || isNaN(Pt) || isNaN(t)) { errorMsg.innerHTML = "Inputs must be valid numbers."; errorMsg.style.display = 'block'; return; } if (P0 <= 0 || t 0) { var dt = 70 / annualRatePercent; doublingTime = dt.toFixed(1) + " Years"; } else if (annualRatePercent 0 ? "+" : ""; document.getElementById('resTotalPercent').innerHTML = sign + totalPercent.toFixed(2) + "%"; sign = annualRatePercent > 0 ? "+" : ""; document.getElementById('resAnnualRate').innerHTML = sign + annualRatePercent.toFixed(2) + "%"; document.getElementById('resDoublingTime').innerHTML = doublingTime; document.getElementById('resProjection').innerHTML = Math.round(projection).toLocaleString(); // Show results resultsArea.style.display = 'block'; }