Average Rate of Increase Calculator
Calculate the Compound Annual Growth Rate (CAGR) over a specific time period.
Please enter valid positive numbers. Start value cannot be zero.
Average Rate of Increase (CAGR)
0.00%
Total Absolute Growth
0.00
Total Percentage Growth
0.00%
How to Calculate Average Rate of Increase
Calculating the Average Rate of Increase is essential for understanding how a metric—such as revenue, population, or website traffic—grows over a period of time. Unlike a simple percentage change, the Average Rate of Increase (often referred to mathematically as CAGR or Compound Annual Growth Rate) smoothes out the volatility of growth over multiple periods.
The Formula
To find the average rate at which a value has grown from a starting point to an ending point over a specific number of periods, we use the following formula:
Rate = ( ( Ending Value / Starting Value ) 1 / n ) – 1
Where:
- Ending Value: The value at the end of the period.
- Starting Value: The value at the beginning of the period.
- n: The total number of time periods (e.g., years, months).
Example Calculation
Imagine a small business had a revenue of 50,000 in Year 1 (Starting Value) and 85,000 in Year 4 (Ending Value). The time difference is 3 years (n = 3).
- Divide Ending by Starting: 85,000 / 50,000 = 1.7
- Raise to the power of (1/n): 1.7(1/3) ≈ 1.1935
- Subtract 1: 1.1935 – 1 = 0.1935
- Convert to percentage: 0.1935 * 100 = 19.35%
This means the revenue grew at an average rate of 19.35% per year.
Why use this instead of Simple Average?
A simple average (adding yearly percentages and dividing by years) ignores the compounding effect of growth. The formula used in this calculator provides the geometric mean, which is the standard for accuracy in finance, statistics, and data analysis.