Annualized return calculator

Turn a total gain into a single yearly rate. For a lump sum that's the CAGR. Once you add contributions, the honest number is the money-weighted return — and it's not the same figure.

How the math works

Annualized return answers one question: what single yearly rate, compounded, reproduces the growth you actually got? For a lump sum with nothing added or taken out, that's the compound annual growth rate.

Where the ratio is your total growth multiple and the exponent spreads it across the years. A balance that grows from $10,000 to $20,000 in ten years didn't earn 100% a year — it earned 2^(1/10) − 1, or about 7.18% a year, compounded.

The moment you add money along the way, that formula breaks. Deposits and withdrawals are external cash flows, and CAGR has no way to account for when they landed. The right tool is the money-weighted return, or internal rate of return (IRR): the single rate that sets the present value of every dated cash flow to zero.

Each contribution counts as a negative flow on the date you made it, the ending balance counts as one positive flow at the end, and the calculator solves for r. A dollar you added last month gets credited for one month of return, not ten years of it. That's the difference the "With contributions" mode above computes.

Worked example

Start with the clean case. Put $10,000 into a fund tracking the S&P 500, whose long-run average annual nominal return is 10.2%. After ten years at that rate the balance is $26,413. Feed $10,000 in, $26,413 out, ten years — the calculator returns 10.2%. That's the annualized return, and it's the number you'd compare against any other investment held for any other length of time.

Now change one thing. Instead of a lump sum, you invest $500 a month over those same ten years — $60,000 of your own money in — and the fund still earns 10.2% a year. The account grows to about $100,980. Drop your $60,000 in and that ending value into a plain CAGR and it reports about 5.34% a year. You did not earn 5.34%. The fund earned 10.2%, and so did you, on every dollar for the time it was invested. The CAGR reads low because it pretends all $60,000 sat there for the full decade, when most of it arrived in the last few years. The money-weighted return, which counts each deposit from its own date, comes back to 10.2%.

Same fund, same performance, two numbers nearly a factor of two apart. The gap is entirely about how the calculation treats the timing of your money.

When this calculator is wrong

An annualized return is a compression of a messy history into one clean rate, and the compression throws things away. The rate is honest arithmetic; the trouble is in what people read into it.

• CAGR on a contributed account is the wrong number. This is the big one. If you added money over time and you compute a plain begin-to-end CAGR, you get a figure that describes no real investment. Use the money-weighted mode. The two answers can differ by half, as the worked example shows.
• An average of yearly returns is not the annualized return. The arithmetic average is always the higher number the moment returns vary at all. A year of +50% followed by a year of −50% averages to zero, but a dollar that rode both is down to 75 cents — a compound annual return of about −13.4%. The gap is the cost of volatility, and it is why a fund quoting its "average annual return" is quoting the flattering figure, not the one your account lived.
• It's a nominal, pre-tax number. A 10.2% annualized return with post-WWII inflation running 3.3% is closer to a 6.7% real return in purchasing power, and a taxable account hands some of the rest to the IRS. The annualized figure flatters until you net those out.
• Past return is not a forecast. A fund's past performance has near-zero predictive power for its future relative performance — one of the most-replicated findings in finance. An annualized return measures what happened. It is not a rate you get to assume going forward.

What to do with the result

Use the annualized return to compare, not to celebrate. Its whole job is to put investments held for different lengths of time on the same footing: a 63% gain over four years and a 22% gain over eighteen months only rank against each other once both are annualized. When you run that comparison, make sure both numbers are the same kind — two CAGRs, or two money-weighted returns, never one of each.

If you were contributing the whole time, the money-weighted number is the one to keep. It's what your dollars actually earned, and it's the fair figure to hold a fund, an advisor, or your own timing against. If it lands well below a plain index return over the same stretch, the usual culprit isn't the fund — it's fees or the timing of when the money went in, and both are worth a closer look.

Common questions

Is annualized return the same as CAGR?

For a single lump sum with no deposits or withdrawals, yes — CAGR is the annualized return. Once money moves in or out along the way, "annualized return" splits into the money-weighted return (what your dollars earned) and the time-weighted return (what the fund earned). CAGR is the no-cash-flow special case of both.

Why is my annualized return lower than my total return?

Because it's spread across the years. A 164% total gain over ten years is a 10.2% annualized return — the same growth, expressed as a yearly rate instead of a lifetime one. The longer you held, the further the annualized number sits below the total.

Should I use money-weighted or time-weighted return?

Money-weighted (IRR) if you want to know what your own dollars earned, timing included — the honest personal number. Time-weighted if you want to judge the investment itself, stripped of when you happened to add money. This calculator gives the money-weighted return in contributions mode, since that's the one that answers "what did I actually make?"

Can annualized return be negative?

Yes. If the ending value is below what you put in, the rate is negative — a total loss annualizes to −100%. The math handles it the same way; the sign just flips.

Does the calculator account for inflation and taxes?

No. It returns a nominal, pre-tax rate. To get the real return, subtract inflation — post-WWII it has averaged 3.3% a year. For an after-tax figure, the gain in a taxable account is reduced by capital gains tax when you sell.