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Calculator Answers

CAGR Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A CAGR calculator (Compound Annual Growth Rate) is a financial utility that measures the annual growth rate of an investment over a specified period, assuming it grew at a steady rate. The calculator applies the algebraic formula CAGR equals the ending value divided by the starting value, raised to the power of one over the number of years, minus one. This metric smooths out volatile annual returns to facilitate direct comparison. Investors and analysts use this tool to evaluate mutual funds, stock portfolios, and business growth.

Enter the beginning value, ending value, and number of years. The calculator returns CAGR, total return, and the growth multiple. Useful for comparing investments and business growth over different time spans.

See also: ROI and Rate of Return Calculator, Compound Interest Calculator, and Stock Profit Calculator.

Quick Answer

Calculate the compound annual growth rate (CAGR) of an investment. Enter the starting value, ending value, and time period to find the annual rate.

Inputs

$
$

Fractional years are fine (e.g. 3.5).

What CAGR is (and is not)

  • CAGR is the smooth annual growth rate that takes the beginning value to the ending value over the period.
  • It assumes a single deposit at the start and no additions or withdrawals along the way.
  • It hides volatility. An investment that doubled then halved each year can have the same CAGR as one that grew steadily.
  • For series with ongoing contributions, use the future value or savings calculator instead.

Educational estimate. Not investment, financial, or tax advice. Past performance does not predict future returns.

Growth rate

CAGR

12.475%

5 years; $10,000.00 → $18,000.00

Beginning value$10,000.00
Ending value$18,000.00
Years5
Growth multiple1.8x
Total return80.00%
CAGR (annualized)12.475%

CAGR is useful for comparing investments and businesses over different time spans. A 100% total return over 10 years is roughly 7.18% CAGR; the same 100% return over 2 years is 41.4% CAGR.

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Examples

$10,000 to $18,000 over 5 years

CAGR ≈ 12.47%; total return 80%

$25,000 to $50,000 over 7 years

CAGR ≈ 10.41%; multiple 2x

$100,000 to $200,000 over 10 years

CAGR ≈ 7.18%

$5,000 to $4,000 over 3 years

CAGR ≈ −7.17% (loss)

How it works

Formula · CAGR = (ending value / beginning value)^(1 / years) - 1. The inverse of the growth factor, a geometric mean; it is arithmetic and carries no source because none would make it more true

CAGR is the constant rate that grows the beginning value into the ending value over the period. It is the nth root of the growth multiple minus one, where n is the number of years.

CAGR · CAGR = (ending / beginning)^(1 / years) − 1

Total return = (ending − beginning) / beginning. Multiple = ending / beginning.

What the number is, and what it is not

CAGR is the single constant rate that would have carried the starting value to the ending value over the span. That is all it is. It is a SMOOTHED, BACKWARD-LOOKING summary of two endpoints, it describes no year that actually happened, and it forecasts nothing.

Everything that happened between the endpoints is discarded. The order of the returns, the worst drawdown, whether the value ever halved on the way, none of it survives into the answer. That is not a flaw to be corrected, it is what a geometric mean does, but it does mean the figure answers a narrower question than people usually ask of it.

Working it out by hand

Ten thousand growing to eighteen thousand over five years.

  1. Divide the end by the start: 18,000 ÷ 10,000 = 1.8. That is the multiple, and it is also the total return plus one.
  2. Take the fifth root, because there were five years: 1.81/5 = 1.124746. On a calculator with no root key, raise 1.8 to the power 0.2.
  3. Subtract one: 0.124746.
  4. As a percentage, 12.4746% a year.
  5. Check it forwards: 10,000 × 1.1247465 = 18,000. If that does not come back to your ending value, one of the three inputs is wrong.

The total return over the whole period is 80 percent, and 80 divided by 5 is 16, which is NOT the answer. Dividing total return by years ignores compounding and overstates the rate every time the return is positive.

Two portfolios, one CAGR

This is the demonstration worth sitting with, because it is the whole argument about what the number leaves out.

YearSteadyVolatile
Start100.00100.00
After 1110.00 (+10%)200.00 (+100%)
After 2121.00 (+10%)121.00 (−39.5%)
CAGR10.0000%10.0000%

Identical to four decimal places. One of these never had a losing year and the other lost nearly forty percent in its second. If the difference between them matters to you, and for most people it does, CAGR is not the number that will tell you about it.

Why it is lower than the average return

Take five years of +30%, −20%, +25%, −15%, +20%. The arithmetic average of those is 8.000%. The CAGR is 5.806%. The gap of 2.194 percentage points is usually called volatility drag, and the standard approximation for it, half the variance of the returns, gives 2.230 points here.

The mechanism is simple: a loss shrinks the base that the next gain is applied to. A 50 percent fall needs a 100 percent rise to undo it. The geometric mean is never above the arithmetic mean, and the two are equal only when every period returns exactly the same thing. The sharper version of the same point: +100% followed by −50% averages +25% a year and leaves you with exactly what you started with, a CAGR of zero.

Edge cases and where the answer stops meaning anything

  • Under a year, it annualises. 100 to 110 over three months is a CAGR of 46.41%, because the arithmetic asks what rate sustained for a full year compounds to that. Correct, and not a number to quote as a return.
  • Money in or out breaks it. The formula sees two values and a span. A deposit along the way inflates the ending value and the CAGR credits it as growth. For a portfolio with contributions the right question is the money-weighted return, an internal rate of return, which is a different calculation.
  • Some inputs have no answer. A start at or below zero has no multiple to take a root of. An end at or below zero cannot be reached by any constant positive rate. A span of zero is a rate over no time. The calculator returns nothing rather than printing nonsense.
  • Losses work, and hide the same way. 10,000 down to 6,000 over three years is about −15.66% a year. One catastrophic year and a slow steady decline can give the identical figure.
  • Nominal, not real. To adjust for inflation you divide rather than subtract: an 8% CAGR with 3% inflation is 4.854% real, not 5%.
  • The window is a choice. Only the first and last values matter, so ending a month before a crash and a month after it are the same investment and very different numbers. Compare like with like, and say what the window is.

What this page will not do

It computes arithmetic from the three numbers you type and takes no position on any investment. It does not know your fees, your taxes, your cash flows, your time horizon or your circumstances, and it will not tell you whether a rate is good, whether one holding beats another, or what to do next. Where a figure here depends on something outside the arithmetic, the page says so rather than quietly assuming it.

The formula itself carries no source line, deliberately. It is the geometric mean of a growth factor, it is true by arithmetic, and citing a body for it would add authority the algebra does not need and this page has not verified. Rules DO exist for how investment performance may be advertised; they are a separate matter and nothing here is written to satisfy them.

Nothing you type leaves this page. The arithmetic runs in your browser. The values are not sent to a server, are not written into the address bar, and are gone when you close the tab. There are no accounts and nothing to sign up for.

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Frequently asked questions

CAGR (compound annual growth rate) is the constant annual growth rate that would take the beginning value to the ending value over the period, as if growth were perfectly smooth. It is the standard way to express the annualized return of an investment.

CAGR = (ending / beginning)^(1 / years) − 1. Express the result as a percentage. For example, $10,000 growing to $18,000 over 5 years gives (1.8)^(1/5) − 1 ≈ 12.47%.

Total return is the percent change between the two values: (ending − beginning) / beginning. CAGR annualizes that total return so different time horizons can be compared on the same scale.

No. CAGR assumes a single deposit at the start and no flows in or out. For series with ongoing deposits, use the future value or savings calculator. To compute a return with contributions, look up money-weighted return (IRR) or time-weighted return.

CAGR is a smoothed average. A volatile path with the same start and end as a smooth path produces the same CAGR. Two investments with identical CAGRs can have very different risk profiles. Always look at year-to-year returns or standard deviation alongside CAGR.

No. CAGR is just arithmetic on two numbers. Picking investments, planning retirement, or evaluating businesses involves many factors beyond CAGR; consult a qualified financial professional for advice.

Almost never. It is the one constant rate that would have taken the starting value to the ending value over the span, which is a different question from what the investment did. A holding that returned 30, then minus 20, then 25, then minus 15, then 20 percent has a CAGR of 5.806 percent, and 5.806 percent is not among those five numbers. The figure is a summary of the endpoints, not a description of the path.

No, and this is the single most important thing to understand about the number. VOLATILITY IS INVISIBLE TO IT. Take 100 dollars growing steadily to 110 and then 121. Now take 100 dollars that doubles to 200 and then falls to 121. Both start at 100, both end at 121, both took two years, and both have a CAGR of exactly 10 percent. One of them never lost a penny and the other lost 39.5 percent in its second year. If you need to know which is which, CAGR is not the number that tells you.

No, and treating it as one will mislead you in a specific direction. Suppose a holding gains 100 percent and then loses 50 percent. The arithmetic average of those two returns is plus 25 percent. The money is back where it started, so the CAGR is 0 percent. The arithmetic mean answers what a typical year looked like; the geometric mean, which is what CAGR is, answers what you ended up with. The second is the one your balance obeys.

No. It is a description of a period that has already finished, and this page will not dress it up as anything else. Nothing in the arithmetic knows why the value moved, whether the conditions that produced it still hold, or what happens tomorrow. A five-year CAGR computed through a bull market and the same figure computed through a crash are the same kind of number and neither one forecasts.

It annualises, and you should be careful with the result. A value going from 100 to 110 over three months is a CAGR of 46.41 percent, because the arithmetic asks what rate, sustained for a full year, would compound to that. That is a real answer to a real question and it is also a number nobody should quote as a return. The shorter the window, the more the annualising exaggerates whatever happened in it.

Only if they are already inside the two numbers you type. The calculator has no view on any of them. If your ending value is before fees, the CAGR is before fees. If dividends were paid out rather than reinvested, they are not in the ending value and the CAGR understates total return. And the figure is nominal: to make it real you divide rather than subtract, so an 8 percent CAGR with 3 percent inflation is 4.854 percent real, not 5.

Because for some inputs the question has no answer. A starting value of zero or less has no multiple to take a root of. An ending value of zero or less cannot be reached by any constant positive growth rate. A span of zero years is a rate over no time. The calculator returns nothing in those cases rather than printing a number that would be arithmetic nonsense.

Divide the ending value by the starting value to get the multiple. Raise that to the power of one over the number of years. Subtract one. For 10,000 growing to 18,000 over five years: the multiple is 1.8, the fifth root of 1.8 is 1.124746, and subtracting one leaves 0.124746, so 12.4746 percent. On a calculator without a root key, 1.8 to the power of 0.2 is the same thing.

Neither. It is arithmetic, the geometric mean of a growth factor, and it needs no authority to be correct. That is why this page carries no source line for it: there is nothing to cite that would make the algebra more true, and inventing a citation would be worse than none. What IS governed is how investment performance may be ADVERTISED, which is a separate matter with its own rules, and nothing on this page should be read as satisfying them.

No. The arithmetic runs in this page in your browser. The values you enter are not sent to a server, are not written into the address bar, and are gone when you close the tab. There are no accounts and nothing to sign up for.