How to Calculate CAGR: Compound Annual Growth Rate

Compound annual growth rate (CAGR) is the constant annual rate that connects a beginning value to an ending value. For an investment without intervening deposits or withdrawals, it makes the growth over different holding periods easier to compare. It is not a measure of volatility or a forecast.

The CAGR Formula

CAGR = ((Ending value / Beginning value)^{1 / Years} - 1) x 100%

The beginning value must be positive, the ending value nonnegative, and the period greater than zero. Use the actual elapsed period; our ROI calculator currently accepts whole years.

A $10,000 to $18,000 Worked Example

1. Divide the ending value by the beginning value: $18,000 / $10,000 = 1.8.
2. Take the fifth root: 1.8^1/5 = 1.124746...
3. Subtract one and multiply by 100: 12.47% per year.

The displayed rate is rounded. Compounding the unrounded rate annually gives exactly $18,000 after five years. Open this example in the ROI calculator.

The same 80% gain over ten years has a CAGR of 6.05%. A $20,000 investment falling to $14,000 over four years has a CAGR of -8.53%.

The property-value example measures price growth only. It does not measure rental income, financing, maintenance, transaction costs or taxes.

CAGR vs. Average Annual Return

A gain of 100% followed by a loss of 50% returns an investment to its starting value. The arithmetic average is (100% - 50%) / 2 = 25%, but the two-year CAGR is 0%. The arithmetic mean averages individual returns; CAGR measures compounded endpoint growth. CFA Institute explains the arithmetic and geometric means.

Annual Growth Is Not a Nominal Monthly Rate

DigiCalc's compound interest calculator divides the entered annual rate by 12 and compounds monthly. Entering 12.47% there is therefore not the same as earning a 12.47% effective annual CAGR.

To model this example with monthly compounding, convert the effective annual rate to a nominal annual rate: 12 x ((1 + CAGR / 100)^1/12 - 1) x 100. Here it is about 11.81%. Set the starting balance to $10,000, monthly contribution to $0, and horizon to five years. With the unrounded converted rate the result is $18,000; a rounded rate produces a small difference.

For a separate annual-growth scenario, $25,000 x 1.07²⁰ = $96,742, rounded to the nearest dollar. That assumes a constant 7% effective annual growth rate, no deposits, and no fees or taxes. It is an illustration, not an expected return.

What Is a Good CAGR?

There is no universal good rate. Compare the same period, investment category, risk, currency and return definition. A price-only return is not directly comparable with a total return that includes reinvested distributions. Check whether fees, taxes and inflation have been included, and do not treat a historical CAGR as a promise.

When CAGR Can Mislead

• Cash flows: Adding savings can raise the ending balance without generating investment gains. Endpoint CAGR does not adjust for the amount or timing of contributions and withdrawals. A cash-flow-aware return method is needed instead; our ROI tool does not calculate IRR or time-weighted returns.
• Volatility: CAGR does not show drawdowns or the path between the endpoints.
• Dates: Choosing a different start or end date can change the annualized result substantially.
• Inflation: With constant annual inflation, real growth is (1 + nominal growth) / (1 + inflation) - 1, using decimal rates. Simple subtraction is only an approximation.

Comparing Different Holding Periods

An 80% total gain over six years has a CAGR of 10.29%. A 55% gain over four years has a CAGR of 11.58%. Annualization helps compare the rates, but the different periods and risks still matter. See how to calculate return on investment for total return and its limitations.

Sources and Scope

The worked examples are calculated from DigiCalc's shared CAGR engine and checked by automated tests. They assume no intervening cash flows and do not provide investment advice or an independent professional review.

• CFA Institute: arithmetic and geometric means.
• SEC Investor.gov compound interest calculator, which separates the annual rate, contributions and compounding frequency.