CAGR calculator: annualized return on investment

Your brokerage shows a +150% gain on a position you have held for eight years. Is that good? You can't compare it with a fund's 10-year record or the S&P 500's long-run average until you turn it into a yearly rate. That rate is the compound annual growth rate, or CAGR — and it is not 150 ÷ 8. The calculator above gives you the right number from three inputs.

In short

• CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1.
• $10,000 → $25,000 over 8 years is +12.14% a year, not the +18.75% you get by dividing 150% by 8.
• It is the same math the SEC requires for "average annual total return" in mutual fund prospectuses.
• It only works when no money went in or out along the way.

How to use the calculator

1. Starting value — what the investment was worth at the start of the period.
2. Ending value — what it is worth at the end. Include reinvested dividends if you want a total-return figure.
3. Years — fractions are fine: 18 months is 1.5, two years and three months is 2.25.

You get the CAGR, the total return for the whole period, the growth multiple, the naive "total return ÷ years" figure for comparison, and how many years it takes to double at that rate.

The formula, and where it comes from

CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1

This is not a rule of thumb. SEC Form N-1A, which governs mutual fund prospectuses, defines a fund's average annual total return with the equation P(1 + T)^n = ERV: a hypothetical $1,000 payment (P), compounded at the yearly rate T for n years, equals the ending redeemable value (ERV). Solve it for T and you get the CAGR formula above.

Worked through for the default inputs:

Step	Calculation	Result
Growth multiple	$25,000 ÷ $10,000	2.50×
Total return	2.50 − 1	+150.00%
Take the 8th root	2.50^(1/8)	1.1214
Subtract 1	1.1214 − 1	+12.14% a year
Check	$10,000 × 1.1214⁸	≈ $25,000
Naive average	150% ÷ 8	+18.75% (overstated)
Years to double	ln 2 ÷ ln 1.1214	6.1 years

The doubling time is exact. The familiar Rule of 72 (72 ÷ 12.14 ≈ 5.9) is a close shortcut, nothing more.

Why averages overstate returns

Dividing total return by years ignores compounding, so it always overstates a positive CAGR. Averaging yearly returns has a worse flaw: it ignores volatility.

Start$10,000

After year 1 (+50%)$15,000

After year 2 (−50%)$7,500

The average of +50% and −50% is 0%, yet you lost $2,500. Enter 10,000, 7,500 and 2 in the calculator and it shows the truth: −13.40% a year. A loss takes a bigger percentage gain to undo, which is why a fund's arithmetic average return can look healthy while its CAGR lags.

When CAGR is the right tool — and when it isn't

If you added money along the way, you need time-weighted return (TWR) for comparisons with an index, or money-weighted return (MWR) for the return on your own dollars. Our guide to comparing your portfolio with the S&P 500 explains both.

More pitfalls

• Taxes and fees. A pre-tax ending value gives a higher CAGR than what you would keep after selling in a taxable account. For a like-for-like comparison with an IRA or a fund's after-tax figures, use matching values.
• Dividends. Price-only values understate a dividend stock's CAGR. Use the value with dividends reinvested, as funds do in their total-return figures.
• Cherry-picked dates. Starting at a market low flatters any CAGR. Try the same holding from a peak.

From one number to your whole portfolio

CAGR needs two values and two dates; a real portfolio with deposits needs more. After you import your brokerage history, GetHossa calculates your portfolio's return with every deposit and withdrawal taken into account and compares it with the S&P 500 over the same dates. To project a steady rate forward instead, plug your CAGR into the compound interest calculator.

The calculator only does arithmetic on the numbers you enter. Past returns don't predict future ones, and nothing here is investment advice.