CAGR Calculator
Work out the compound annual growth rate between a start and end value, or reverse it to find an end value or the number of years needed to reach a target.
Compounded growth path
| Year | Value | Gain that year | Total growth |
|---|
The path shows smooth growth at a constant CAGR. Real investments rise and fall from year to year; CAGR only describes the start and end points. Estimates only, not financial advice.
How to use the CAGR Calculator
- Choose what to work out: Find CAGR, Target end value or Required years.
- Enter the start value, such as the first-year revenue or the amount invested.
- Enter the end value or the growth rate, depending on the mode.
- Set the period in years and months, or tick the box to use two dates.
- Press Calculate to see the result, the formula with your numbers, the growth chart and the year-by-year table.
The CAGR formula with a worked example
CAGR = (End value ÷ Start value)1 ÷ years − 1
Example: an investment grows from $1,000 to $2,000 in 5 years. The growth multiple is 2,000 ÷ 1,000 = 2. Raising 2 to the power 1 ÷ 5 = 0.2 gives 1.1487, and subtracting 1 leaves 0.1487, so the CAGR is 14.87% a year. Check: 1,000 × 1.14875 = 2,000.
The same formula can be rearranged. To project an end value: End = Start × (1 + CAGR)years. To find how many years a target takes: years = ln(End ÷ Start) ÷ ln(1 + CAGR). For example, doubling at 10% a year takes ln(2) ÷ ln(1.10) ≈ 7.27 years.
CAGR vs simple average growth
Suppose a portfolio of $10,000 rises 50% in year one to $15,000, then falls 50% in year two to $7,500. The simple average of the two yearly returns is (50% − 50%) ÷ 2 = 0%, which suggests you broke even. The CAGR tells the real story: (7,500 ÷ 10,000)1/2 − 1 = −13.4% a year. Because CAGR is a geometric average, it always reproduces the actual start and end values, which is why it is the standard way to compare investments, revenue growth or user growth over time.
How long it takes to double at different growth rates
| CAGR | Years to double | Value of 1,000 after 10 years | Growth multiple after 10 years |
|---|---|---|---|
| 3% | 23.4 | 1,343.92 | 1.34× |
| 5% | 14.2 | 1,628.89 | 1.63× |
| 7% | 10.2 | 1,967.15 | 1.97× |
| 10% | 7.3 | 2,593.74 | 2.59× |
| 15% | 5.0 | 4,045.56 | 4.05× |
| 20% | 3.8 | 6,191.74 | 6.19× |
A quick mental shortcut is the rule of 72: divide 72 by the growth rate in percent to estimate the years to double. At 8% a year, 72 ÷ 8 ≈ 9 years.
Limits of CAGR
CAGR only looks at the first and last values, so it hides volatility and says nothing about the path in between. Two investments with the same CAGR can carry very different risk. It also ignores money added or withdrawn during the period; for investments with regular contributions, a money-weighted return such as IRR is more accurate. Use CAGR to compare growth on a like-for-like basis, not as a forecast of future returns.
Frequently asked questions
What is CAGR?
CAGR, the compound annual growth rate, is the constant yearly rate at which a value would have to grow, with growth compounding each year, to go from its start value to its end value over a given period. It smooths out the ups and downs in between.
What is the CAGR formula?
CAGR = (End value ÷ Start value) raised to the power 1 ÷ number of years, minus 1. For example, growing from 1,000 to 2,000 in 5 years gives 2 to the power 0.2 minus 1, which is about 0.1487, or 14.87% a year.
How is CAGR different from average annual return?
A simple average adds up each year's percentage change and divides by the number of years, which overstates growth when returns are volatile. CAGR is a geometric average that always reproduces the actual start and end values.
Can CAGR be calculated with a negative or zero start value?
No. The formula divides by the start value and takes a root of the ratio, so a zero or negative start value gives an undefined result. In that case look at the absolute change instead, or measure from a later positive value.
Can CAGR be negative?
Yes. If the end value is lower than the start value, CAGR is negative and shows the average yearly rate of decline. If the end value falls to zero, CAGR is −100%.
How do I use CAGR for a period that is not a whole number of years?
Enter extra months, or tick the dates option and choose a start and end date. The calculator converts the period to fractional years (days ÷ 365.25) before applying the formula.