What Is CAGR? Compound Annual Growth Rate Formula and Calculation

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CAGR, short for compound annual growth rate, is the constant yearly rate at which a value would have had to grow, with each year’s gain compounding on the last, to move from its beginning value to its ending value over a given number of years. It reduces a multi-year path, however uneven, to one annualized percentage. If a portfolio went from $10,000 to $14,641 in four years, its CAGR is 10%. That holds whether it actually rose 10% every year or swung between large gains and losses along the way.

In finance, CAGR describes the growth of investments, revenue, earnings, customer counts, market sizes and almost any other quantity measured at two points in time. It is a representational figure, not a return any investor necessarily earned in a given year.

What CAGR means

The three words in the name each do work. Compound means growth is assumed to build on previous growth, so profits are treated as reinvested at the end of each period. Annual means the result is expressed per year, regardless of how long the measurement period is. Growth rate means the output is a percentage change, not a dollar amount.

Put together, CAGR answers one question: what single, steady yearly rate connects these two numbers? It does not describe what happened in any particular year. A stock with a five-year CAGR of 8% may have gained 25% in one year and lost 15% in another. The 8% is the rate that, applied evenly for five years, lands on the same ending value.

Because CAGR depends on only three inputs (start, end and time), it can be calculated by hand or in one spreadsheet cell. That simplicity explains its wide use. It also explains its blind spots, covered further below.

The CAGR formula

The standard compound annual growth rate formula is:

CAGR = (EV / BV)^(1 / n) - 1

where:

• EV = ending value
• BV = beginning value
• n = number of years between the two values

Multiply the result by 100 to express it as a percentage.

How to calculate CAGR step by step

1. Divide the ending value by the beginning value. This gives the total growth multiple (for example, 1.50 means the value grew 50% in total).
2. Raise that multiple to the power of 1 divided by the number of years. This converts the total multiple into a per-year multiple.
3. Subtract 1 to turn the per-year multiple into a growth rate.
4. Multiply by 100 to get a percentage.

In Excel or Google Sheets, the calculation is =(EV/BV)^(1/n)-1. Excel also has a built-in function, =RRI(n, BV, EV), which returns the same rate.

Counting the periods correctly

The most common calculation error is getting n wrong. The number of years is the number of intervals between the first and last values, not the number of data points. Revenue figures for 2019, 2020, 2021, 2022, 2023, 2024 and 2025 are seven data points but six years of growth, so n = 6. Using 7 would understate the CAGR.

Handling partial years

Investments are rarely bought on January 1 and sold on December 31. When the holding period includes a partial year, convert the whole period into years, usually by dividing the number of days held by 365.25 (the extra quarter day approximates leap years).

Hypothetical example: $10,000 is invested and sold 1,500 days later for $15,000.

• n = 1,500 / 365.25 = 4.107 years
• CAGR = (15,000 / 10,000)^(1 / 4.107) - 1 = 1.5^0.2435 - 1 ≈ 10.38%

Rounding the period to four years would give about 10.67%, and five years would give about 8.45%. A fractional n gives the accurate answer.

Worked example: CAGR vs. the average of annual returns

Hypothetical example: a portfolio starts at $10,000 and has these year-end values:

The CAGR is:

(14,641 / 10,000)^(1/4) - 1 = 1.4641^0.25 - 1 = 10.00%

Check it by compounding: $10,000 × 1.10 × 1.10 × 1.10 × 1.10 = $14,641. A steady 10% each year reproduces the real ending value exactly.

Now take the simple (arithmetic) average of the four annual returns: (30 - 10 + 10 + 13.76) / 4 = 10.94%. Applying 10.94% for four years to $10,000 would produce about $15,151, which is more money than the portfolio ever held. The arithmetic average overstates growth because it ignores that a 10% loss followed by a 10% gain does not bring you back to even: $100 falls to $90, then rises only to $99.

This is why CAGR is described as a geometric mean. It is the average that compounding actually delivers. Whenever returns vary from year to year, the arithmetic average will exceed the CAGR, and the gap widens as the swings get larger.

Quick example: a stock that tripled in 10 years

If a stock tripled over 10 years, the total gain is 200%. Dividing by 10 suggests 20% a year, but that ignores compounding. The CAGR is:

3^(1/10) - 1 ≈ 11.61% per year

At 11.61% compounded annually, $1 becomes about $3 after a decade. At 20% compounded annually, $1 would have become roughly $6.19.

How CAGR is used

Comparing investments with different paths

CAGR puts dissimilar assets on the same footing. A savings account paying a fixed 2% has a CAGR of 2%. A stock fund that went up and down might show a five-year CAGR of 9%. Neither number shows how bumpy the ride was, but both state the steady rate that links the start and end, so they can be compared directly. The same applies to assets that move independently of each other, such as stocks and real estate, or bonds and emerging markets. In any given year one may rise while the other falls, which makes year-by-year comparison noisy.

CAGR also lets you compare an investment with a benchmark. A fund’s 10-year CAGR can be set against the 10-year CAGR of an index such as the S&P 500 over the same dates, as long as both figures are calculated the same way (for example, both including reinvested dividends).

Measuring business growth

In company analysis, revenue CAGR is one of the most quoted figures. Hypothetical example: a company’s revenue grows from $2 million to $5 million over six years. Its revenue CAGR is (5 / 2)^(1/6) - 1 ≈ 16.50%.

The same calculation applies to earnings, free cash flow, subscribers, store count, market share or customer satisfaction scores. Comparing the CAGRs of different metrics inside one company shows where it is improving and where it is slipping. If revenue compounds at 12% a year while customer satisfaction declines at 1% a year, growth may be coming at a cost. Comparing the same metric across competitors adds context: a 1% annual decline in satisfaction looks less alarming if a rival’s score is falling 6% a year over the same period.

Market research reports often state an industry’s projected CAGR. Those figures are forecasts built on assumptions, not measured results, and they deserve the same scrutiny as any other projection.

Planning: required returns and future values

Rearranging the CAGR formula turns it into a planning tool.

Required rate of return. Hypothetical example: you have $20,000 today and need $40,000 in 12 years. The rate needed is (40,000 / 20,000)^(1/12) - 1 = 2^(1/12) - 1 ≈ 5.95% a year. This works as a hurdle rate: an investment expected to compound below it will not reach the goal on its own.

Future value. Given a rate, the formula projects forward: FV = BV × (1 + CAGR)^n. At an assumed 7% CAGR, $10,000 grows to 10,000 × 1.07^10 ≈ $19,672 after 10 years.

Present value. Working backward, PV = FV / (1 + CAGR)^n tells you how much to invest today. To have $50,000 in 15 years at an assumed 8%, you would need 50,000 / 1.08^15 ≈ $15,762 now.

Doubling time. The rule of 72 gives a quick approximation: divide 72 by the CAGR (as a whole number) to estimate the years needed to double. At 8%, that is about 9 years; the exact figure is ln 2 / ln 1.08 ≈ 9.01 years.

All of these rearrangements assume the rate holds steady, which is a modeling convenience, not a promise.

What is a good CAGR?

There is no universal threshold. A good CAGR depends on what you are measuring, the alternatives available and the risk taken to get there.

• Opportunity cost. A 6% CAGR from a low-risk holding may be excellent when safe alternatives pay less, and disappointing when they pay more.
• Peer and industry context. A company growing revenue at 25% a year looks weak in an industry compounding at 30%, and strong in one compounding at 10%.
• Risk. Two investments with the same CAGR are not equal if one had far larger swings or deeper drawdowns along the way.
• Inflation. A nominal CAGR includes rising prices. The real CAGR is (1 + nominal CAGR) / (1 + inflation rate) - 1. A 7% nominal CAGR during years of 3% average inflation is about a 3.88% real CAGR. Historical figures are in U.S. inflation rates by year.
• Size and stage. Small businesses and early-stage companies can post high growth rates from a low base that larger firms rarely sustain, so comparisons work best between companies of similar size.

Limitations of CAGR

It hides volatility

CAGR describes a smooth line through what is usually a jagged path. Apart from instruments with fixed, contractual returns, such as deposits or bonds held to maturity, investment returns are uneven. Two portfolios can share a 10% CAGR while one moved steadily and the other fell 40% before recovering. The investor who needed money during the drawdown had a very different experience. CAGR should be read alongside measures of volatility and maximum drawdown.

It ignores deposits and withdrawals

The formula only sees the starting and ending balances. Money added during the period is counted as growth, and money withdrawn is counted as loss.

Hypothetical example: a portfolio starts at $10,000 and earns 5% in year one, reaching $10,500. The investor then deposits $5,000, bringing it to $15,500, and it earns another 5% in year two, ending at $16,275. Plugging the start and end into the CAGR formula gives (16,275 / 10,000)^(1/2) - 1 ≈ 27.57%, even though the investments earned exactly 5% in each year. For accounts with contributions or withdrawals, a time-weighted return or IRR is the correct tool.

It depends heavily on the start and end dates

Because only two points matter, the choice of dates can change the story entirely.

Hypothetical example: a fund’s year-end values over five years are $100,000, $80,000, $60,000, $75,000, $90,000 and $105,000. Measured over the last three years, from the $60,000 low, its CAGR is (105 / 60)^(1/3) - 1 ≈ 20.51%. Measured over the full five years, it is (105 / 100)^(1/5) - 1 ≈ 0.98%. Both figures are arithmetically correct. The three-year number simply starts at the bottom. When a CAGR is quoted, check the dates, and compare it across several windows and the full history where possible.

Past rates do not carry forward

A steady historical CAGR does not mean the same rate will continue. The shorter the measurement period, the less reliable it is as a guide to future results, because a few unusual years have more weight. High growth rates also become harder to sustain as a business gets larger.

It needs a positive starting value

The formula requires a beginning value above zero, and in practice an ending value at or above zero. A company whose earnings went from a loss to a profit has no meaningful earnings CAGR, and a starting value near zero produces enormous, uninformative percentages.

Short periods get exaggerated

Annualizing a period shorter than a year assumes the short-term result would repeat. A 5% gain in one month annualizes to about 79.6% (1.05^12 - 1), a figure with little practical meaning. CAGR is most informative over multiple years.

CAGR vs. related measures

CAGR vs. average annual return

The arithmetic average adds annual returns and divides by the number of years. CAGR compounds them. With any variation in returns, the arithmetic average comes out higher, as the worked example above shows. The arithmetic average describes a typical single year; CAGR describes what the whole period actually produced.

CAGR vs. simple or total growth rate

A simple growth rate compares two values without regard to time: going from $100 to $150 is 50% growth whether it took two years or ten. Return on investment works the same way; see ROI. CAGR adds the time dimension and compounding, which allows periods of different lengths to be compared. A single bad year can drag a one-year growth rate sharply down but has a much smaller effect on a long-period CAGR.

CAGR vs. IRR

The internal rate of return is the discount rate that sets the net present value of all cash flows to zero. For a single investment with one inflow at the start and one value at the end, IRR and CAGR give the same answer. They diverge when money moves in and out over time, as with private equity funds, real estate projects or a brokerage account with regular contributions. IRR accounts for the size and timing of each cash flow; CAGR cannot. IRR usually requires a financial calculator, Excel’s IRR or XIRR functions, or portfolio software, while CAGR can be done by hand.

CAGR vs. annualized return

For a holding with no interim cash flows, an annualized total return and CAGR are the same calculation. Whether dividends are included depends on the inputs: a CAGR built on price alone understates the growth of a dividend-paying investment compared with one built on total return with dividends reinvested.

Risk-adjusted CAGR

Because CAGR ignores risk, some investors use a simple risk-adjusted version: multiply the CAGR by one minus the investment’s standard deviation of returns.

Risk-adjusted CAGR = CAGR × (1 - standard deviation)

Hypothetical example: Fund A has a CAGR of 10% and a standard deviation of 15%, giving 10% × 0.85 = 8.5%. Fund B has a CAGR of 12% and a standard deviation of 30%, giving 12% × 0.70 = 8.4%. Despite its higher raw CAGR, Fund B scores slightly lower once volatility is considered. If the standard deviation is zero, the risk-adjusted CAGR equals the CAGR, and the higher the standard deviation, the larger the reduction.

This is a rough shortcut rather than a standard industry measure. More established approaches compare return per unit of risk, such as the Sharpe ratio, which compares return in excess of a risk-free rate with volatility.

The bottom line

CAGR turns a starting value, an ending value and a number of years into one compounded annual rate. That makes it a clean way to compare investments, track business growth and set planning targets such as a required return. Its simplicity is also its weakness: it smooths away volatility, cannot handle money flowing in and out, shifts with the chosen dates and says nothing about what comes next. Use it as a summary of where a value started and finished, paired with risk measures and cash-flow-aware returns when the path matters.

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