CAGR Calculator (compound annual growth rate)

Understanding the CAGR calculator — concept and principle

The compound annual growth rate (CAGR) is the single steady yearly rate that would turn a starting value into an ending value over a given number of years. It is the standard way to summarise investment performance, company revenue growth or any quantity that grows by compounding, and it lets you compare periods of different lengths fairly.

How it is calculated

• CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1
• Total return = ending ÷ starting − 1
• Simple average per year = total return ÷ years
• Doubling time = ln 2 ÷ ln(1 + CAGR)

Years can be fractional, for example 2.5 for two and a half years. The starting value must be positive.

The principle

Compound growth multiplies: after n years at rate g, a value becomes start × (1 + g)ⁿ. Solving that for g gives the CAGR formula, the n-th root of the growth multiple. Because growth compounds, the simple average (total return divided by years) always overstates the yearly rate for a gain; it ignores that later years grow on a larger base. CAGR also smooths out the path: two investments with very different ups and downs can share the same CAGR if they start and end at the same values.

Worked example

1. Start $10,000, end $25,000, 8 years.
2. Growth multiple = 25,000 ÷ 10,000 = 2.5; total return = 150%.
3. CAGR = 2.5^(1/8) − 1 ≈ 1.12135 − 1 = 12.14% a year.
4. Check: 10,000 × 1.1214⁸ ≈ 25,000.
5. Simple average = 150% ÷ 8 = 18.75% a year, clearly higher.
6. Doubling time = ln 2 ÷ ln 1.12135 ≈ 6.1 years (the rule of 72 gives 72 ÷ 12.14 ≈ 5.9).

How to read the result

Use CAGR to compare against a benchmark, such as a broad stock index, inflation or a savings rate over the same years. A CAGR above inflation means real growth. Remember that CAGR says nothing about volatility; look at the worst year or drawdown too. For investments with regular deposits or withdrawals, use a money-weighted return (IRR) instead, since CAGR assumes one start and one end value.

Common mistakes

• Using CAGR when money was added or withdrawn during the period.
• Counting the number of data points instead of the years between them.
• Presenting the simple average as the annual return.

Frequently asked questions

What is a good CAGR?

It depends on what you compare with; for investments, beating inflation and a low-cost index over the same period is a sensible test.

Can CAGR be negative?

Yes. If the ending value is below the start, CAGR is negative, showing the average yearly decline.

How do I calculate CAGR in Excel?

Use =(end/start)^(1/years)-1, or =RRI(years, start, end).

Sources: Standard time value of money mathematics (compound growth) · CFA Institute, Quantitative Methods curriculum (time value of money, returns)