CAGR Calculator – One Steady Rate Behind Any Growth
CAGR — compound annual growth rate — answers a deceptively simple question: at what single steady rate would a value have to grow, year after year, to travel from where it started to where it ended? Enter a beginning value, an ending value and the years between them, and this page finds that rate. Or flip the tabs: solve for the end value a given rate produces, or for the time a target takes. Every answer arrives with a year-by-year table and a doubling time, so the one smooth number never has to be taken on trust.
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The full picture
What this means
From $10,000.00 to $20,000.00 over 5.00 years works out to a CAGR of 14.87%. Total growth across the whole period is +100.00% — the value multiplied by 2.00. Growing at that pace, the value doubles every 5.00 years. CAGR is one smoothed rate between two points: the real path may have swung well above and below it, and this number hides every one of those swings on purpose.
Read the rate with its period. A CAGR quoted without the years it covers is only half an answer — the same doubling is 14.87% a year over five years and 7.18% a year over ten.
- CAGR is the single steady rate that would carry a value from start to finish, year after year — $10,000 to $20,000 is 14.87% a year over five years.
- The period is the quiet lever: the same $10,000 to $20,000 is only 7.18% a year over ten years, so a CAGR quoted without its period is only half an answer.
- At 14.87% a year the doubling time is 5.00 years — and the year-by-year table proves the rate by landing exactly on the ending value.
- The growth, year by year
- How it works, in 3 steps
- How each figure is worked out
- Deep dives
- The CAGR ladder: same start, different finishes
- Running the formula forward: what $10,000 becomes
- Doubling times, exact and rule-of-thumb
- The average-return trap, with a second example
- Checking a CAGR claim in the wild
- CAGR questions, answered
The growth, year by year
A CAGR is only believable if the balance actually lands on the ending value — so here is the same answer unfolded, one year at a time, at exactly the rate above.
| Year | Value | Gain in year | Total growth |
|---|---|---|---|
| Year 0 (start) | $10,000.00 | — | 0.00% |
| Year 1 | $11,486.98 | +$1,486.98 | +14.87% |
| Year 2 | $13,195.08 | +$1,708.10 | +31.95% |
| Year 3 | $15,157.17 | +$1,962.09 | +51.57% |
| Year 4 | $17,411.01 | +$2,253.85 | +74.11% |
| Year 5 | $20,000.00 | +$2,588.99 | +100.00% |
How it works, in 3 steps
Start with the two values
The beginning value is what the asset, account or business was worth at the start; the ending value is what it is worth now. On the default, $10,000 grows to $20,000. Take both values on the same basis — if you want a real, after-inflation rate, use inflation-adjusted figures at both ends, not just one.
Add the time between them
Count the years as exactly as the values deserve: five calendar years is 5, and two years and six months is 2.5. The period is the quiet lever in this formula — the same $10,000 to $20,000 is 14.87% a year over five years but only 7.18% a year over ten — so a CAGR quoted without its period is only half an answer.
Read the rate — then flip the question
The answer is the steady yearly rate that connects the two values: 14.87% here. Then use the other two tabs on the same figures: what end value would 8% produce instead, and how long would 10% take to double the money? The three modes are one formula wearing three hats, and checking a claim in two directions is how smooth numbers get caught out.
How each figure is worked out
The default, worked through. Ending divided by beginning: 20,000 ÷ 10,000 = 2. Raised to the power of one fifth — because the period is five years — 21/5 = 1.148698. Minus 1 leaves 0.148698, which is a CAGR of 14.87%. The proof runs backwards: $10,000 growing at exactly that rate for five years lands on $20,000.00 to the cent, as the year-by-year table above shows. Quote the rate rounded to 14.87% and the five-year check lands within a cent or two — the table always uses the full-precision rate.
Solving for the end value instead. At 8% for ten years the multiplier is 1.0810 = 2.158925, so $10,000 becomes $21,589.25 — total growth of +115.89%, and a doubling time of 9.01 years, which is why ten years at 8% a little more than doubles the money.
Solving for time. To double at 10%, the years are ln(2) ÷ ln(1.10) = 0.6931 ÷ 0.0953 = 7.27 years. Nothing in that answer depends on the amount: doubling time is a property of the rate alone, which is why the same 7.27 years appears whether the beginning value is ten dollars or ten million.
Deep dives
CAGR describes a journey as if it were a ramp. The money almost certainly did not travel that way: it lurched, stalled and sprinted, and the single rate irons all of that flat. That is not a defect to apologise for — a summary that repeated every twist would be the raw data, not a summary — but it does mean two investments with identical CAGRs can have felt completely different to live through, and one of them may have come close to wiping out on the way.
The extreme case is worth memorising. An investment that falls 50% in year one and rises 100% in year two ends exactly where it started: $100 becomes $50, then $100 again. Its CAGR is 0.00% — honest, and the only single rate that connects start to finish. Its simple average return, though, is +25% a year, a number that sounds like strong growth while describing a round trip to nowhere. Whenever a return is quoted as an average of yearly percentages, this gap is sitting inside it.
Volatility is what opens the gap. Steadier sequences sit closer to their CAGR; wilder ones fall further below their average. That is the real information a CAGR carries beyond the endpoints: it is the growth rate the money actually experienced, per year, after every setback has been charged against every gain. For comparing two finished journeys it is hard to beat. For predicting the next one, remember it says nothing about how rough the ride will be.
CAGR looks backwards; compound interest looks forwards. CAGR is measured from two real values at two real moments, and it asks what steady rate explains the trip. Compound interest takes a rate you choose and projects what a balance would become if that rate held. The end-value and years tabs above are compound-interest questions wearing CAGR’s clothes — the same mathematics, run in the opposite direction.
APY is the third cousin, and the one most often confused with CAGR. Annual percentage yield folds the compounding frequency into the rate: interest credited monthly starts earning its own interest sooner, so a quoted APY sits slightly above the nominal yearly rate behind it. CAGR, by convention, compounds once a year. Comparing a savings account’s APY with an investment’s CAGR is at least a comparison of two effective yearly rates; the real trap is comparing either of them with a nominal rate that ignores compounding altogether.
And CAGR is easy to abuse, because it needs only two observations. Pick a start at the bottom of a crash and an end at the top of a boom and almost anything looks brilliant. Honest use means honest windows — whole cycles where possible, the same window for everything being compared, and the period always quoted beside the rate, exactly as this page insists on doing.
The CAGR ladder: same start, different finishes
Every row below starts at $10,000 and applies this page’s own formula, CAGR = (ending ÷ beginning) raised to (1 ÷ years), minus 1. The base row and the ten-year row are the page’s own worked examples; the $30,000 row was run through the calculator’s rate tab, and the remaining rows follow the same formula the page prints.
| Ending value | Years | Total growth | CAGR | Doubling time at that rate |
|---|---|---|---|---|
| $15,000 | 5 | +50.00% | 8.45% | 8.55 years |
| $20,000 | 5 | +100.00% | 14.87% | 5.00 years |
| $20,000 | 10 | +100.00% | 7.18% | 10.00 years |
| $30,000 | 5 | +200.00% | 24.57% | 3.15 years |
| $50,000 | 10 | +400.00% | 17.46% | 4.30 years |
The second and third rows are the pair that teaches the period lesson. Doubling the money in five years is 14.87% a year; doubling it in ten years is only 7.18% a year — less than half the rate for the same total growth, because compounding has twice as long to work. Any CAGR quoted without its period, as the page’s guide warns, is only half an answer, and this table shows why: the same +100% total growth supports two rates that differ by more than seven points, depending entirely on how long the money took.
The first and last rows show the other lever, the multiple. Growing by half in five years needs 8.45% a year, while growing fivefold in ten years needs 17.46% — a rate that looks only twice as large for a total gain eight times as large, because compounding rewards patience geometrically rather than arithmetically. And the doubling-time column is not a separate fact: it is the same formula run backwards, years = ln(2) ÷ ln(1 + CAGR), which is why the 14.87% row doubles in exactly 5.00 years and the 7.18% row in exactly 10.00. Quote the rate and the period together, and the doubling time follows for free.
Running the formula forward: what $10,000 becomes
The page’s end-value tab runs the same formula in reverse: end value = beginning × (1 + rate) raised to the years. The 8% ten-year row is the page’s own worked example; the other rows were run through the calculator’s end-value tab.
| Rate | Years | End value | Total growth |
|---|---|---|---|
| 6% | 10 | $17,908.48 | +79.08% |
| 8% | 10 | $21,589.25 | +115.89% |
| 10% | 10 | $25,937.42 | +159.37% |
| 8% | 20 | $46,609.57 | +366.10% |
Two points of rate are worth more than they look. At ten years, moving from 6% to 8% adds $3,680.77 to the ending value, and moving from 8% to 10% adds a further $4,348.17 — the second step adds more than the first, because the higher rate compounds on a larger base every year. That is the same geometric effect as the ladder above, viewed from the other end: small rate differences, left alone for a decade, become large dollar differences, which is why fees and return assumptions that look like rounding deserve the same attention as the headline rate.
Time is the larger lever still. Ten years at 8% turns $10,000 into $21,589.25, a little more than double, as the page’s guide says. Twenty years at the same rate turns it into $46,609.57 — not double the ten-year figure, but more than double, because the second decade compounds on the $21,589.25 the first decade built, not on the original $10,000. The twenty-year total growth of +366.10% is the product of two ten-year growth factors, not their sum, and any projection that adds decade returns together instead of multiplying them will understate the result by exactly that compounding-on-compounding.
Doubling times, exact and rule-of-thumb
The doubling time at a rate is years = ln(2) ÷ ln(1 + rate), the page’s own years-tab formula with the ending value set to twice the beginning value. The rule of 72 — 72 divided by the rate — is the familiar shortcut, and the table below puts the two side by side so the shortcut’s error is visible rather than rumoured.
| Rate | Exact doubling time | Rule of 72 | Shortcut error |
|---|---|---|---|
| 6% | 11.90 years | 12.00 years | +0.10 years |
| 8% | 9.01 years | 9.00 years | −0.01 years |
| 10% | 7.27 years | 7.20 years | −0.07 years |
| 12% | 6.12 years | 6.00 years | −0.12 years |
The shortcut is good, and the table shows how good: across 6% to 12% it never misses by more than about a tenth of a year, roughly five weeks, and at 8% it is essentially exact. That is why it survives: for a back-of-the-envelope doubling question it is faster than logarithms and close enough to decide with. But the exact column is what this calculator returns, and for a dated plan — a retirement year, a loan term, a target date — five weeks of error is still error, and the page’s years tab exists to remove it. Use the rule of 72 to sense-check, and the calculator’s exact figure to plan.
One further property deserves stating, because the page’s guide states it and it is easy to miss: doubling time depends on the rate alone, never on the amount. The 7.27 years at 10% is the same whether the beginning value is $10 or $10,000,000, because the ratio of ending to beginning is 2 in both cases and the amount cancels out of the logarithm. A claim that a larger sum doubles faster at the same rate is confusing the dollars gained — which do scale with the amount — with the time taken, which does not.
The average-return trap, with a second example
The page’s deep dive already gives the classic trap: an investment that falls 50% and then rises 100% ends where it started, with a CAGR of 0.00% but a simple average return of +25% a year. Here is a gentler version of the same trap, with smaller numbers, so the mechanism is visible without the drama.
Take $100 that falls 20% in year one, to $80, then rises 30% in year two, to $104. The simple average of the two yearly returns is (−20% + 30%) ÷ 2 = +5.00% a year, which sounds like steady growth. The CAGR is the square root of 1.04 minus 1, which is 1.98% a year — less than half the average — because the 30% rise applies to the reduced $80, not to the original $100, and the average ignores that shrinkage. The $4 of real gain over two years is 1.98% a year compounded, not 5%, and any projection that carries the 5% average forward will overstate the future by more than double the true rate.
The general rule is the one the page’s deep dive states: steadier sequences sit closer to their CAGR, and wilder ones fall further below their average, because losses shrink the base that later gains must rebuild. Whenever a return is quoted as an average of yearly percentages, the gap is sitting inside it, and the size of the gap grows with the volatility, not with the return. That is why CAGR, for all its smoothing, is the honest single number for a completed journey: it is the rate the money actually experienced, after every setback has been charged, and it is the only single rate that reconnects the starting value to the ending value.
One omission is stated here rather than smoothed over: CAGR says nothing about the path’s risk, and two investments with identical CAGRs can have felt completely different to live through, as the page’s deep dive also warns. A smooth 8% and a wild ride that ends at the same place share a CAGR and nothing else — the wild ride may have come close to wiping out on the way, and no single endpoint rate can tell you whether it did. Judge the rate together with the ride, never instead of it.
Checking a CAGR claim in the wild
CAGR claims arrive in fund marketing, business pitches and social posts, usually without the workings. This page’s three tabs give you everything needed to check one in under a minute, and the two claims below show the check working in both directions.
Claim one passes. A fund says it grew $10,000 at 20% a year for three years. Run the end-value tab: $10,000 × 1.20 raised to 3 is $10,000 × 1.728 = $17,280. If the fund’s ending value is $17,280, the claim is exactly right, and the total growth of +72.80% over three years is consistent with a 20% CAGR. The check is the multiplication, and it either lands on the claimed figure or it does not — there is no room for interpretation once the endpoints and the period are fixed.
Claim two fails, and the failure is instructive. A pitch says $10,000 became $20,000 in five years at 10% a year. Run the same tab: $10,000 × 1.10 raised to 5 is $10,000 × 1.61051 = $16,105.10, not $20,000 — nearly $4,000 short. The true CAGR for doubling in five years is 14.87%, as this page’s default shows, so the pitch understates the required rate by almost five points. The error is usually innocent — someone averaged, or carried a rate from a different period — but the consequence is not: a plan built on 10% where 14.87% is needed will arrive years late, if it arrives at all.
Four questions catch most bad claims before the arithmetic even starts. First, is the period stated? A CAGR without years, as the page’s guide warns, is only half an answer, and the same doubling is 14.87% over five years but 7.18% over ten. Second, are both endpoints on the same basis — both before inflation, or both after, and both before or both after fees and withdrawals? A starting value net of fees against an ending value gross of them invents growth. Third, were contributions or withdrawals made along the way? The formula assumes nothing added or withdrawn, and a growing account fed by regular deposits will show a flattering CAGR if the deposits are counted as growth. Fourth, is the quoted figure a CAGR at all, or an average of yearly returns? If it is the average, the volatile-journey gap from the previous section sits inside it, and the true compounded rate is lower. A claim that survives all four questions and then lands on its ending value in the end-value tab is a claim worth trusting; one that fails any of them deserves a second look before a single dollar follows it.
One final caution belongs to every checked claim: a verified past CAGR is not a promised future one. The formula describes a completed journey exactly, and says nothing about the next five years, which is why this page’s guide treats CAGR as a summary of what happened rather than a forecast. Use it to compare completed journeys honestly, and to test whether a promised journey is even arithmetically possible — then judge the future on its own evidence, not on the past rate.
CAGR in Excel: one formula, four ways to write it
CAGR is (end divided by start) to the power (1 divided by years), minus 1. In Excel that is =(End/Start)^(1/Years)-1 — and RATE and RRI give the same answer, which is the check that catches sign and year-count errors.
With the beginning value in B2, the ending value in B3, and the years in B4, the direct formula is =(B3/B2)^(1/B4)-1, formatted as a percentage. The parentheses matter: the exponent is 1 divided by years, applied to the ratio, and the minus 1 comes after the power. The RATE function gives the same result as =RATE(B4,0,-B2,B3), with the beginning value negative by sign convention and no periodic payments; RRI gives it as =RRI(B4,B2,B3) with no sign change. All three are the same mathematics, and if they disagree, one has a sign or a year-count error. The year count is the elapsed time — the intervals between dates, not the count of data points — so 2020 to 2025 is 5 years, not 6.
The same rate sustained for 3, 5, and 10 years produces $66,550, $80,526, and $129,687 from $50,000 at 10%, and CAGR recovers 10.00% from any of those endpoints. An uneven history shows what CAGR hides: $50,000 to $60,000 in 3 years is 6.27%, to $55,000 in 5 years is 1.92%, and to $110,000 in 10 years is 8.21% — the 10-year figure hides the mid-period fall entirely. For accounts with contributions and withdrawals on irregular dates, XIRR, not CAGR, is the right tool, because it prices each flow by its timing. The companion guide works all four Excel methods, the 3, 5, and 10-year examples on one history, the negative and zero cases where CAGR breaks, and the comparability rules for comparing two CAGRs fairly.
CAGR questions, answered
What is CAGR?
CAGR — compound annual growth rate — is the single steady yearly rate that would carry a beginning value to an ending value over a set number of years, assuming growth compounds once a year and nothing is added or withdrawn along the way. If $10,000 becomes $20,000 in five years, the CAGR is 14.87%: growing by exactly that percentage every year lands precisely on $20,000. Real investments almost never grow at one steady rate — CAGR is the smoothed average that best summarises the whole trip in one number.
How do you calculate CAGR?
Three steps. Divide the ending value by the beginning value. Raise the result to the power of 1 divided by the number of years. Subtract 1, and read the answer as a percentage. On this page’s default: 20,000 ÷ 10,000 = 2; 2 raised to the power of 1/5 is 1.148698; minus 1 gives 0.148698, a CAGR of 14.87%. The formula is CAGR = (ending ÷ beginning) raised to (1 ÷ years), minus 1 — and the tabs above run it in every direction: rate, end value or years.
What is a good CAGR?
Good depends entirely on what is growing. Over very long periods, a broad US stock market index has compounded at roughly 10% a year before inflation, while cash in a savings account has usually grown far more slowly, and a business or a rental property sits wherever its own numbers put it. Judge a CAGR against its peers and against inflation: a rate below inflation is growth on paper and shrinkage in buying power. And the longer the period behind a CAGR, the more it can be trusted — a spectacular rate over three months says almost nothing.
Can CAGR be negative?
Yes. If the ending value is below the beginning value, the formula returns a negative rate, and this calculator shows it rather than hiding it. $20,000 shrinking to $10,000 over five years, for example, is a CAGR of −12.94%: the value falls by that percentage, compounded, every year. A negative CAGR over a short window is common even in assets that do well over decades — which is one reason the period you choose matters so much to the answer.
What is the difference between CAGR and an average return?
An average return adds the yearly percentages up and divides — and it flatters. Grow 50% one year and fall 50% the next and the average return is 0%, yet $100 became $150 and then $75: you lost a quarter of your money. The CAGR for that trip is −13.40%, because the square root of (75 ÷ 100), minus 1, is −0.1340 — the only single rate that actually connects the start to the end. Whenever yearly returns vary, the CAGR is lower than the simple average, and the CAGR is the honest one.
How long does it take money to double at a given CAGR?
Exactly ln(2) divided by ln(1 + rate). At 10% that is 0.6931 ÷ 0.0953 = 7.27 years. The old rule of 72 gives a fast mental estimate — 72 ÷ 10 = 7.2 years — close enough for conversation, but this page always shows the exact figure. Doubling time is the same whatever the amount: a dollar and a million both double in 7.27 years at 10%, which is why the rate, not the balance, is the number worth chasing.
What CAGR turns $10,000 into $30,000 in five years?
24.57% a year, with a doubling time of 3.15 years at that rate. The working is (30,000 ÷ 10,000) raised to (1 ÷ 5), minus 1: the multiple is 3.00, total growth is +200.00%, and the steady yearly rate that connects the two values is 24.57%. Compare it with doubling in five years, which needs only 14.87%: tripling in the same time needs nearly ten points more a year, because the third $10,000 must itself compound.
Is the rule of 72 accurate enough to use?
For a quick sense-check, yes; for a dated plan, use the exact figure. Between 6% and 12% the rule of 72 never misses the exact doubling time by more than about a tenth of a year — 12.00 years against an exact 11.90 at 6%, and 6.00 against an exact 6.12 at 12% — and at 8% it is essentially exact at 9.00 against 9.01. That is close enough to judge a claim in conversation, but a retirement date or a loan term deserves the calculator’s exact logarithm, not a five-week approximation.
Why is my average yearly return higher than my CAGR?
Because the average ignores the shrinking base after a loss. A $100 investment that falls 20% to $80 and then rises 30% to $104 has a simple average return of +5.00% a year, but a CAGR of only 1.98% a year, since the 30% rise applies to the reduced $80 rather than the original $100. The wider the swings, the wider the gap between the average and the CAGR, which is why a return quoted as an average of yearly percentages always flatters a volatile journey.
Does a bigger starting amount double faster at the same rate?
No. Doubling time depends on the rate alone, because it is ln(2) divided by ln(1 + rate), and the amount cancels out of the calculation. At 10% the doubling time is 7.27 years whether the beginning value is $10 or $10,000,000. The dollars gained do scale with the amount — a larger sum gains more dollars in the same time — but the time taken to double does not, and confusing the two is one of the commonest misreadings of a growth claim.
Why do my CAGR formula and RATE function disagree?
Almost always a sign or a year-count error. RATE needs the present value as a negative number, =RATE(Years,0,-Start,End), with the payment argument 0. The direct formula needs the exponent as 1 divided by years, applied to the whole ratio: =(End/Start)^(1/Years)-1. If both are entered correctly they agree exactly, so a disagreement is a signal to check the inputs, not to pick the more convenient answer.
Does CAGR account for money added along the way?
No. CAGR uses only the starting value, the ending value, and the elapsed time, and it ignores every interim flow. An account with contributions and withdrawals needs XIRR, which takes each cash flow with its date and returns the annualised internal rate of return. For a single lump sum with no interim flows, CAGR and XIRR agree; in every other case they differ, and the difference is the timing of the flows.
Is a higher CAGR always better?
Not without the period, the value definition, and the path. A 5-year CAGR of 12% and a 10-year CAGR of 8% are not directly comparable if the periods differ, and a CAGR that includes dividends reinvested is higher than a price-only CAGR for the same investment. Two investments with the same CAGR can have very different volatility and drawdowns, which CAGR does not show. Compare like with like, and read the year-by-year figures alongside the rate.
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A description of a finished period — not a forecast, and not financial advice.
CAGR is computed from the two values and the time you enter; growth at any rate in the past is no guarantee of growth at the same rate in the future. The figures take no account of taxes, fees, inflation or money added or withdrawn along the way, all of which change the return actually kept. Market averages mentioned in the text are long-run historical generalities, not promises. For decisions that matter, run the numbers here, then test them against statements and, where the sums justify it, a qualified adviser.