CAGR Calculator
Enter a beginning value, an ending value and the number of years, and the calculator returns the compound annual growth rate (CAGR) with the working shown, the total growth, the doubling time and a year-by-year path. Switch modes to project a value forward at a given rate or to find how long it takes to reach a target. Free, no sign-up.
Your numbers
Fractions work: 2.5 means two and a half years.
Results
12.135%
Compound annual growth rate
150%
Total growth
2.5×
Growth multiple
15,000
Gain over the period
18.75%
Simple average per year
6.0518
Doubling time (years)
Working
CAGR = (ending ÷ beginning)^(1 ÷ years) − 1 = (25,000 ÷ 10,000)^(1 ÷ 8) − 1 = 12.135%
Total growth = ending ÷ beginning − 1 = 25,000 ÷ 10,000 − 1 = 150%
Simple average = total growth ÷ years = 150% ÷ 8 = 18.75%
Doubling time = ln 2 ÷ ln(1 + rate) = 6.0518 years
The smooth path
| Year | Value at this rate | Growth since the start |
|---|---|---|
| 0 | 10,000 | 0% |
| 1 | 11,213.5339 | 12.135% |
| 2 | 12,574.3343 | 25.743% |
| 3 | 14,100.2724 | 41.003% |
| 4 | 15,811.3883 | 58.114% |
| 5 | 17,730.1539 | 77.302% |
| 6 | 19,881.7682 | 98.818% |
| 7 | 22,294.4882 | 122.945% |
| 8 | 25,000 | 150% |
CAGR smooths the path. It says nothing about the ups and downs along the way, and it is not the same as the average of the yearly growth rates. Compare it only over the same start and end points.
How to Use the CAGR Calculator
- 1. Choose what to find. The default finds the growth rate between two values. Choose the second option to project a starting value forward at a rate, or the third to find how many years a target takes.
- 2. Enter the values. Give the beginning value and the ending value (or the target). Values can be revenue, population, a share price, GDP or any positive quantity; the unit does not matter.
- 3. Give the time. Type a number of years (fractions such as 2.5 are fine) or switch to a start year and an end year, and the span is the difference.
- 4. Read the result. You get the CAGR, the total growth, the growth multiple, the simple average growth per year for comparison, the doubling time and a table and graph of the smooth path.
The CAGR Formula
The compound annual growth rate is the single constant yearly rate that would carry the beginning value to the ending value over the same number of years, with each year's growth building on the last. It is the geometric average growth rate, which is why it is the right tool whenever growth compounds: investments, revenue, population and GDP.
Growth formulas
CAGR
(Ending value ÷ Beginning value)^(1 ÷ years) − 1
Project forward
Ending value = Beginning value × (1 + rate)^years
Time to a target
years = ln(Target ÷ Beginning) ÷ ln(1 + rate)
Doubling time
ln 2 ÷ ln(1 + rate)
Worked Example: 10,000 to 25,000 in 8 Years
The calculator opens with a value that grows from 10,000 to 25,000 over eight years. The ratio is 2.5, so the CAGR is 2.5^(1 ÷ 8) − 1 = 12.135%. A constant 12.135% a year gives 11,213.53 after one year, 12,574.33 after two, and reaches 25,000 in year eight. Total growth is 150%, the doubling time is 6.05 years, and the quick rule of 72 gives 72 ÷ 12.135 = 5.93 years, close to the exact figure.
| Mode | Inputs | Result |
|---|---|---|
| Find the rate | 10,000 to 25,000 over 8 years | 12.135% a year |
| Project forward | 1,000 at 5% for 10 years | 1,628.89 |
| Time to a target | 1,000 to 2,000 at 5% a year | 14.21 years |
CAGR Versus the Average of Yearly Growth Rates
The calculator shows a simple average (total growth ÷ years) next to the CAGR so the difference is visible: 150% ÷ 8 = 18.75% a year, but the compound rate is 12.135%, because simple division ignores compounding. The arithmetic mean of the actual yearly growth rates is different again. A value that goes 100 → 150 → 90 → 120 grew +50%, −40% and +33.3%, whose arithmetic mean is 14.4%, yet it ends 20% higher after three years, a CAGR of only 6.27%. Volatility drags the compound rate below the arithmetic mean, and only the CAGR matches where you actually ended up.
When Not to Use CAGR
- Cash flows in between. If money was added or withdrawn during the period, CAGR misstates the return. Use an internal rate of return instead.
- Zero or negative values. A ratio of end to start must be positive, so a series that starts or ends at zero or below has no CAGR.
- As a forecast. CAGR describes the past path between two dates. Growth that was smooth on paper may have been uneven, and past growth does not set the next period's rate.
- Different endpoints. Two CAGRs are only comparable over the same start and end dates; starting a year later, at a lower point, can change the answer a lot.
Frequently Asked Questions
- How do you calculate CAGR?
- Divide the ending value by the beginning value, raise the result to the power of 1 divided by the number of years, and subtract 1. For 10,000 growing to 25,000 in 8 years, 2.5^(1/8) − 1 = 12.135%.
- What is a good CAGR?
- It depends on what is growing. Compare it with a benchmark for the same kind of thing over the same dates, such as inflation for a price, an index for an investment or national GDP growth for a company's sales. A CAGR is good only relative to alternatives and to risk.
- Can CAGR be negative?
- Yes. If the ending value is lower than the beginning value, the ratio is below 1 and the CAGR is negative. A value that falls from 100 to 50 in five years has a CAGR of −12.94%.
- What is the difference between CAGR and average annual growth rate?
- The average annual growth rate usually means the arithmetic mean of the yearly percentage changes. CAGR is the geometric mean, which accounts for compounding and always reproduces the actual ending value. The arithmetic mean is the same or larger, and the gap grows with volatility.
- How do you calculate CAGR for periods shorter than a year?
- Express the span in years: 18 months is 1.5 years and 9 months is 0.75 years. The result is still a rate per year, so a very short span can produce a dramatic figure that would not be sustained.
- How is CAGR related to the rule of 72?
- The rule of 72 is a shortcut for doubling time: divide 72 by the rate in percent. The exact doubling time at a rate r is ln 2 ÷ ln(1 + r). At 12.135% that is 6.05 years against 5.93 from the rule, which is why the rule is called an approximation.