CAGR calculator

How the formula works

The compound annual growth rate is the single constant rate that would take a beginning value to an ending value over a given number of years, as if it grew by exactly that much every year. It is the reverse of compounding: instead of asking what a rate grows to, it asks what rate got you here. With \(V_\text{begin}\) the starting value, \(V_\text{end}\) the ending value and \(n\) the number of years:

The ratio \(V_\text{end}/V_\text{begin}\) is the total growth multiple; the \(1/n\) power spreads that growth evenly across the years, and subtracting 1 turns the multiple into a rate. It is a geometric mean of the yearly growth factors, not an arithmetic average of the yearly returns — and that distinction is the whole reason CAGR exists.

Why it differs from a simple average. Averaging annual returns adds them up and divides; it ignores that each year compounds on the last. Volatility makes the two diverge, always in the same direction: the geometric mean is never higher than the arithmetic mean, and the gap widens with the size of the swings. This is volatility drag. Take a value that rises 50% one year and falls 50% the next. The arithmetic average is \((50\% - 50\%)/2 = 0\%\), which sounds like breaking even — but the money tells a different story:

A dollar became 75 cents. The arithmetic average said 0%; the CAGR says −13.4% a year, and only the CAGR agrees with what is left in the account. That is what makes CAGR the honest single-number return: it is defined so that growing the beginning value at the CAGR for \(n\) years lands exactly on the ending value, with no residual to explain away. Any rate that reproduces the real endpoints has to be the geometric one.

What each input means

Beginning value — \(V_\text{begin}\)

What the investment was worth at the start of the period. It must be positive: a growth multiple is undefined when you divide by zero or a negative starting value, which is why the worksheet guards against it.

Ending value — \(V_\text{end}\)

What it is worth now, at the end of the period. If it is below the beginning value the CAGR is negative — a real, meaningful answer, and the worksheet shows it as such rather than hiding the loss.

Number of years — \(n\)

How long the money was invested, start to end. This is calendar time, not a count of contributions. For a period measured in months, divide the months by 12 (30 months is \(n = 2.5\)); the questions below work an example.

Compare to (annual rate)

An optional benchmark rate — a savings yield, an index's long-run return, a hurdle you had in mind. The worksheet grows the beginning value at this rate over the same years and tells you whether your CAGR beat it, and by how many percentage points. Leave it at a market-like figure to see if you kept pace.

A worked example

Take the worksheet's opening numbers: $10,000 grew to $18,000 over 5 years.

• The growth multiple is $18,000 / $10,000 = 1.80× — an 80.00% total return over the whole period.
• Spread across 5 years: \((1.8)^{1/5} - 1 = 12.47%\) a year. That is the CAGR: grow $10,000 by 12.47% five times over and you land on $18,000 — the ending value, back again.
• Note what CAGR is not: 80.00% total return is not 80.00% / 5 = 16.00% a year. Dividing the total by the years ignores compounding and overstates the rate; the geometric 12.47% is the honest figure, because it is the only rate that reproduces $18,000 exactly.
• Against the 7% benchmark, $10,000 would have reached $14,026 — so this result beat it, by 5.47 pts.

Assumptions and limits

• CAGR is a smoothed rate. It draws the straight geometric line between two points and says nothing about the path between them — a holding that lurched −40% then +90% can share a CAGR with one that crept up steadily. It reports the return, not the risk or the volatility that produced it.
• It assumes a single lump sum in and a single value out. Deposits and withdrawals along the way break the two-point picture entirely; for a stream of contributions use the investment return calculator, which handles cash flows.
• Nothing is deducted: the CAGR is before taxes, fees and inflation, each of which lowers what you actually keep. Subtract expected inflation from the CAGR to read it in today's purchasing power.
• This is arithmetic, not advice. A higher CAGR looked at alone says nothing about the risk taken to earn it.

Questions people ask

What is CAGR?

CAGR — compound annual growth rate — is the constant yearly rate that grows a beginning value into an ending value over a number of years. It is \((V_\text{end}/V_\text{begin})^{1/n}-1\): the total growth multiple, spread evenly across the years and expressed as a rate. Because it is defined to land exactly on the ending value, it is the single number that honestly describes how fast an investment grew over a period.

CAGR vs average annual return — what's the difference?

CAGR is a geometric mean; the average annual return most people quote is an arithmetic mean, and the two disagree whenever returns vary. Suppose a value gains 50% one year and loses 50% the next. The arithmetic average is \((50\% - 50\%)/2 = 0\%\), which suggests you broke even. But \(1.50 \times 0.50 = 0.75\): a dollar is now 75 cents, a CAGR of \(0.75^{1/2}-1 = -13.40%\) a year. The arithmetic mean overstates the return because it ignores that each year compounds on the last — the more the returns swing, the wider the gap, and it always favors the arithmetic figure. Only the CAGR matches the money actually left in the account.

Does CAGR account for deposits or withdrawals?

No. CAGR looks only at the beginning value and the ending value, so it silently credits any money you added along the way as if it were growth, and penalizes any you took out. For an account you paid into over time it is the wrong tool — you want a money-weighted return (an IRR) or a time-weighted return instead. Use CAGR for a single lump sum left alone between two dates; use a cash-flow-aware calculator when there were contributions.

Is a higher CAGR always better?

Not on its own. CAGR measures return and ignores risk entirely — a 13% CAGR earned through stomach-churning swings is not obviously better than a 9% CAGR earned steadily, and the higher figure may reflect a much riskier holding that could as easily have gone the other way. CAGR also hides the path: two investments with the same CAGR can have felt completely different to hold. Compare CAGRs only alongside the volatility and the drawdowns that produced them.

How do I annualize a return measured over months?

Put the time in years and use the same formula. For a period of \(m\) months, \(n = m/12\): a value that grew 20% over 30 months has \(n = 2.5\), so the CAGR is \(1.20^{1/2.5}-1 \approx 7.6\%\) a year. The mechanics never change — CAGR only cares about the growth multiple and the length of time in years, so months, quarters or a decade all annualize the same way.