How do you calculate the average annual growth rate (CAGR) between two specific dates?

Change the period selector to "exact dates" and enter a start date and an end date. The calculator will calculate the actual number of days between those two dates, convert that time span into years, then calculate the annual growth rate. So an investment held from March 14, 2021 through September 2, 2025 would not be rounded to four or five years but treated as the actual number of 1,633 days. Whole years and whole months do not affect the calculation of days; by definition a month is one twelfth of a year so only the remaining days need to be considered.

Should you use a notation of 365 days or 365.2425 days for "one year"? Is that important?

The impact is small but it can explain minor differences from other tools. A period of 1826 days averages to approximately 4.9994 years in the Gregorian calendar. Another result is 5.0027 years based on a fixed 365-day cycle. When values double within that time frame, CAGR changes from 14.8717% to 14.8611%, which represents a difference of about one basis point. This usually results in your numbers and the published ones matching to three or four decimal places but not being exactly equal.

Why is the CAGR lower than the average annual return?

The average ignores the compounding effect of interest while compound interest generates further growth from existing growth. If $1,000 becomes $1,331 in three years then the total gain is 33.1% which divided by three gives an annualized return of 11.03%. The actual return is 10%. $1,000 becomes $1,100 then $1,210 and finally $1,331. The arithmetic average will always be the more pleasant of the two numbers and the longer the time period and the higher the interest rate the greater the difference. This calculator displays both values side by side to make the difference obvious at a glance.

Can I use the CAGR for a monthly investment plan?

It's not very accurate. The CAGR (compound annual growth rate) only looks at the beginning and ending values, assuming a certain amount of capital is invested over the entire period. With regular savings plans, each payment has a different investment duration, so one single growth rate from start to finish does not accurately reflect this situation. The correct indicator is the IRR (internal rate of return), and for irregular payment dates, the XIRR (extended internal rate of return). Also, the metrics that fund platforms give for such accounts are usually these. CAGR can be used when a certain amount of capital is invested or in a series of values where no new funds come in over time, like income.

CAGR Calculator

Your figures

What do you want to work out?

Growth rate (CAGR)

Ending value

Starting value needed

Time required

Starting value

Ending value

How do you want to enter the period?

Years, months and days

Exact start and end dates

Years

Months

Days

Days in a year

Only the loose days are divided by this. Whole years and months are unaffected, so the setting does nothing unless the period contains days.

Compound annual growth rate (%)

Compound annual growth rate

Total growth over the period: %
Total gain: $
Growth multiple

Simple average per year: %
Years to double at this rate
Days in the period

A steady 14.6493% a year turns $10,000 into $18,500 over 4.5 years. Spreading the same total growth evenly instead, with no compounding, would read 18.8889% a year. The gap between those two numbers is the compounding you would be ignoring.

Charts and schedule

Show the charts

The compounding curve and the period-sensitivity bars.

Show the year-by-year schedule

One row per year at the resolved rate, ending with the stub period.

Year-by-year path at the compound annual growth rate, ending with the stub period when the span is not a whole number of years.
Year	Value	Gain in the year	Cumulative growth (%)
1	11,464.93	1,464.93	14.65
2	13,144.47	1,679.53	31.44
3	15,070.04	1,925.58	50.7
4	17,277.7	2,207.66	72.78
4.5	18,500	1,222.3	85

The compound annual growth rate (CAGR) is a single annualized growth rate that represents what the equivalent constant annual growth rate would have to be in order for something to grow from its starting value to its ending value. In reality, investments or income do not change at such a steady pace. The value of CAGR lies precisely in smoothing out year-to-year noise and providing just one number with which to compare other numbers.

Most of the calculations for CAGR are very simple. The most common mistake is determining the time period. An investment held from March 14, 2021 to September 2, 2025 is neither four nor five years. This calculator allows you to enter the exact time period based on the information that you input. You can either enter the number of years, months and days or directly provide two date inputs. It also has a reverse calculation feature to determine the length of time required to reach a particular goal.

Formula:

The entire content of this page is based on the following formula:

EV = SV \times (1 + r)^{n}

SV = starting value, EV = ending value, r = CAGR (as a decimal), n = number of years. By rearranging the formula, we can solve for any one of these four variables with the calculator.

r = \left(\frac{EV}{SV}\right)^{\frac{1}{n}} - 1 \qquad EV = SV \times (1 + r)^{n}

SV = \frac{EV}{(1 + r)^{n}} \qquad n = \frac{\ln\left(\frac{EV}{SV}\right)}{\ln(1 + r)}

The last expression explains why there is a period selector. As the period consists of years, months and days it cannot simply be left blank for the solver to fill in. So calculating the required period for a given thing is treated as a separate mode with its own answer.

A complete example.

An investment went from $10,000 to $18,500 in four and a half years. Four and a half years is the same thing as 4.5 years, which means that:

r = \left(\frac{18{,}500}{10{,}000}\right)^{\frac{1}{4.5}} - 1 = 1.85^{0.2222} - 1 = 0.1465

The average annual growth rate is 14.65%. No matter how the calculation is performed, it always results in the same result.

10{,}000 \times 1.1465^{4.5} = 18{,}500.49

The 49 that is appended at the end comes from rounding off interest rates to four decimal places when recording. Calculation tools keep full accuracy and therefore agree exactly with 18,500 on recalculation.

Notice what happens when the period is rounded to five years. It takes six months longer to reach the same growth so the interest rate falls to 13.09%. This rounding makes a difference of as much as 1.5 percentage points. That's why we have included a field for the number of months.

Why duration is more important than many people think.

CAGR is calculated as an annual growth rate so each value must be divided by the number of years. Giving the wrong number of years will make the interest rate incorrect by that same amount.

The sensitivity charts on this page show the impact visually. They use start and end values to recalculate multiple periods before and after the period entered, and convert them into annual growth rates. For shorter holding periods, the bars widen quickly outward, while for longer holding periods they tend to flatten out. This is why a three-year CAGR is more impacted by the time period than a fifteen year CAGR.

There is another nuance to this problem that is often cited in advertising presentations: because the CAGR only looks at starting and ending values, if either of those end points changes, then the result will change, and anything that happened in between won't be reflected. For example, suppose an investment was worth $5,500 five years ago, fell to $3,000 three years ago, and is now worth $6,000. The annual growth rate for the last three years would be 25.99%. The annual growth rate over the entire five-year period would be 1.76%. Although both of those values are mathematically correct, in a presentation only one of them will be shown.

Entering a time period as two dates

If you switch the time period selector to a specific date, then the calculator will calculate the actual number of days between two dates and convert that time period into years. Use this mode if you do not have full years but instead have transaction confirmations, purchase dates or financial periods information.

Full years or full months are not affected by the choice of reference for calculating the number of days; since a month is defined as one twelfth of a year and has no fixed number of days, both methods of input agree. Only the remaining days need to be divided, and here differences arise from differing conventions.

What calculation method should be used?

There are differing opinions on how many days a year has and often the method used is not stated. The three methods presented here cover essentially all cases.

Basis	Days per year	When it is used
Mean Gregorian year	365.2425	The default. The true average length of a calendar year once the leap-year rules are averaged in, including the skipped century leap years.
Julian year	365.25	The simpler leap-year average, one extra day every four years. Common in scientific and older financial work.
Simple year	365	Ignores leap days entirely. Matches quick spreadsheet work and many published examples.

The actual difference is very small but it exists. For a period of 1,826 days the average works out to be 4.9994 years on the Gregorian calendar and 5.0027 years if you simply calculate using 365 days per year. If those numbers are doubled, then the CAGR changes from 14.8717% to 14.8611%, which is a difference of about one basis point. This is important when comparing your values with others and not understanding why there is a discrepancy by one place. It's usually not relevant for decisions.

The CAGR is not the average of the annual returns.

It is important to understand this fallacy because wrong numbers often look more attractive than right ones.

Assume that $1,000 grows to $1,331 within three years. The total gain is $331, which is 33.1% of the original amount. Dividing this by three gives an annualized return of 11.03%. This answer is incorrect. The correct answer is 10%. $1,000 becomes $1,100, then $1,210 and finally $1,331 because the annual increase is based on last year's higher balance.

The "Annual Simple Average" chart on this page shows the pleasant and correct version side by side, which is intentional. The same comparison is also shown in the Compound Interest graph. The curve represents capital growth with annual compounding, while the straight line represents the same total growth spread evenly over the entire period. Both start at the same point and end at the same point. The area between them represents the compound interest growth that is lost.

The higher the interest rate and the longer the time period, the larger this difference will be. That is why stating an average annual return for long investment horizons leads to a significant overestimation of the result.

Calculating how long it will take to reach a goal

The "Time Needed" mode answers a different question: How long will it take to reach the goal at this rate of growth? It solves for n in the same equation and displays the result as a decimal number of years, which is then broken down into more understandable units like years, months, and days.

In three cases there is no solution, so the calculator produces no result but leaves the fields blank. With a growth rate of zero you can't get anywhere. With positive growth you can never reach a goal below your starting point, and with negative growth you can never reach a goal above your starting point. If this mode shows blank fields it's because one of these three cases applies.

The Rule of 72 is a mental shortcut to the same calculation. By dividing 72 by the interest rate in percent, you get an approximation for how long it will take to double. At 8% it estimates that it takes 9 years, while the actual value is 9.01 years, which is fairly accurate. At 24%, it estimates that it takes 3 years but the actual value is 3.22 years, so not as accurate. The "Time to Double" chart on this page instead uses exact logarithms.

Can CAGR be negative?

Yes, that is completely normal. When the ending value is lower than the starting value, this rate represents the constant annual downward rate which has caused this decrease. The average annual downward rate of an investment that decreased from $10,000 to $7,000 over four years was 8.53%.

When the interest rate is negative there are two changes to the results. As the numbers do not tend towards doubling, there is no time period in which a doubling occurs. The growth rate falls below 1, which is usually the most understandable way of explaining the result.

Situations where CAGR is not applicable:

CAGR only compares two points in time, which is both a strength and a limitation.

It cannot be used when money is coming in or going out during the period. A monthly investment plan has both the amount invested and the time of the investment varying from month to month, and a single rate of interest from start to finish cannot represent this situation. For that problem, use the internal rate of return (IRR), and if the timing data is irregular, use the modified internal rate of return (XIRR). Standard fund platforms report this value for exactly this reason. Using CAGR for investment plans can make results look better or worse than they really are, depending on whether the market has gone up before most of the money was put in, or after.

Nor are the risks explained. Two investments may have the same average annual growth factor (CAGR), but while one has a smooth path, another might fall by half twice. The smoothing that makes these comparable is also the smoothing that obscures what's really going on.

In addition, this describes the past and is not a forecast. That a previous CAGR was 20% is a description of an event that has already happened and does not provide any insight into next year.

What is a good CAGR?

It depends entirely on what is being measured and compared to. Here are some benchmarks:

Reference	Rough annual rate	Note
Long-run broad US equity index	About 10% nominal	Before inflation, measured over many decades. Individual decades vary enormously.
Long-run inflation	About 2 to 3%	Anything below this is losing purchasing power even while the number grows.
Government bonds and cash	Low single digits	The comparison that tells you whether the risk you took was paid for.
A growing company's revenue	Very wide	Compare it to the sector's growth, not to an investment return.

A useful approach is to always compare similar things with each other. Compare asset classes of the same type and ideally also for the same time period. CAGRs calculated for different years answer different questions.

Calculate this in a spreadsheet.

If you have a starting value in cell B1, an ending value in cell B2, and the number of years in cell B3, then:

Goal	Formula
Growth rate	=(B2/B1)^(1/B3)-1
Growth rate, built in	=RRI(B3,B1,B2)
Ending value	=B1*(1+B4)^B3
Years required	=LN(B2/B1)/LN(1+B4)
Years between two dates	=YEARFRAC(B5,B6)

Make sure the cell for the interest rate is set to percentage format and do not multiply it by 100, otherwise you will end up with 14.65 being displayed as 1465%.

This tool is for analysis and planning purposes only. It describes how values have changed between two points in time but does not predict what will happen next. Therefore the projections shown here should be considered as scenarios rather than predictions.

Frequently asked questions

How do you calculate the average annual growth rate (CAGR) between two specific dates?: Change the period selector to "exact dates" and enter a start date and an end date. The calculator will calculate the actual number of days between those two dates, convert that time span into years, then calculate the annual growth rate. So an investment held from March 14, 2021 through September 2, 2025 would not be rounded to four or five years but treated as the actual number of 1,633 days. Whole years and whole months do not affect the calculation of days; by definition a month is one twelfth of a year so only the remaining days need to be considered.
Should you use a notation of 365 days or 365.2425 days for "one year"? Is that important?: The impact is small but it can explain minor differences from other tools. A period of 1826 days averages to approximately 4.9994 years in the Gregorian calendar. Another result is 5.0027 years based on a fixed 365-day cycle. When values double within that time frame, CAGR changes from 14.8717% to 14.8611%, which represents a difference of about one basis point. This usually results in your numbers and the published ones matching to three or four decimal places but not being exactly equal.
Why is the CAGR lower than the average annual return?: The average ignores the compounding effect of interest while compound interest generates further growth from existing growth. If $1,000 becomes $1,331 in three years then the total gain is 33.1% which divided by three gives an annualized return of 11.03%. The actual return is 10%. $1,000 becomes $1,100 then $1,210 and finally $1,331. The arithmetic average will always be the more pleasant of the two numbers and the longer the time period and the higher the interest rate the greater the difference. This calculator displays both values side by side to make the difference obvious at a glance.
Can CAGR be negative?: Yes. If the ending value is less than the starting value then that rate of return is the constant annual rate of decrease which has caused this decline and is a valid answer not an error. The annual rate of decrease for an investment which decreased from 10,000 to 7,000 in four years was 8.53%. If the rate of return were negative then the value would not be increasing so there would be no number required to double it.
Can I use the CAGR for a monthly investment plan?: It's not very accurate. The CAGR (compound annual growth rate) only looks at the beginning and ending values, assuming a certain amount of capital is invested over the entire period. With regular savings plans, each payment has a different investment duration, so one single growth rate from start to finish does not accurately reflect this situation. The correct indicator is the IRR (internal rate of return), and for irregular payment dates, the XIRR (extended internal rate of return). Also, the metrics that fund platforms give for such accounts are usually these. CAGR can be used when a certain amount of capital is invested or in a series of values where no new funds come in over time, like income.

Related calculators

CAGR CalculatorCalculate the compound annual growth rate (CAGR) of an investment, or solve for the starting value, ending value, or number of years. Includes total return, doubling time, a benchmark comparison, a growth chart, and a year-by-year table.

Annual Interest Rate CalculatorFind the annual interest rate on a loan or investment from the principal, final amount, and time. Solve for any variable under simple, compound, or continuous interest, and see the effective rate (APY).

Compound Interest CalculatorCalculate compound interest and the future value of a deposit, with optional regular contributions, any compounding frequency, the effective annual rate (APY), a simple-versus-compound comparison, a growth chart, and a year-by-year table. Works in reverse to solve for the rate, time, or starting amount.

Effective Annual Interest Rate CalculatorConvert a nominal interest rate into the effective annual rate (EAR / APY) for any compounding frequency, including continuous compounding, and solve the nominal rate in reverse.

Time Value of Money CalculatorSolve any time-value-of-money problem: enter four of present value, interest rate, years, payment, and future value, and the calculator finds the fifth, with compounding, payment timing, and inflation adjustment.

Appreciation CalculatorProject the future value of an appreciating asset with compound growth, then solve for the starting value, rate, or years. Includes inflation adjustment, tax on the gain, a sensitivity band, and profit and return metrics.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Investopedia - Compound Annual Growth Rate (CAGR)
Definition, formula and the standard caveats about smoothing and endpoint sensitivity.
Wikipedia - Compound annual growth rate
The geometric-mean derivation and the relationship to annualised return.
Wikipedia - Day count convention
Why 365, 365.25 and 365.2425 all appear in financial arithmetic, and what each one is for.
Microsoft - RRI function
The built-in spreadsheet function for an equivalent compound growth rate.
U.S. SEC Investor.gov - Compound interest
The regulator's plain-language explanation of growth earned on prior growth.