The value at the end of each year at the constant rate, the growth added that year, and the growth so far. The last row lands on the end value.
Year
Value
Added that year
Growth so far
1
2,709,721.04
309,721.04
12.91%
2
3,059,411.71
349,690.67
27.48%
3
3,454,230.11
394,818.40
43.93%
4
3,900,000.00
445,769.89
62.50%
Enter a start value, an end value and the years between them. Switch “Solve for” to project an end value from a rate, or to find how long a rate takes to reach a target. Revenue, users and portfolios all work: the rate does not care about the unit.
Estimates only — not financial, tax, or professional advice.
Calculated in your browser — the numbers you enter are never sent to our servers.
What it calculates: CAGR, End value, Years to reach it, Total growth.
$2.4 million of revenue growing to $3.9 million in four years is a 12.90% CAGR
The compound annual growth rate answers one question: what single yearly rate, applied again and again, carries the start value to the end value in the time given? Divide the end by the start to get the growth multiple, take the n-th root for n years, and subtract one. Here 3,900,000 ÷ 2,400,000 = 1.625, the fourth root of 1.625 is 1.12905, and the CAGR is 12.90%.
CAGR = (End ÷ Start)^(1 ÷ n) − 1
Run it forward to check it: $2,400,000 grows to $2,709,721 after one year at 12.90%, then $3,059,412, $3,454,230 and exactly $3,900,000 after the fourth. The table under the calculator prints that path for your own numbers, which is the quickest way to see that one rate reproduces the whole change.
Revenue, 4 years
Start = 2,400,000, End = 3,900,000
Multiple = 1.625
CAGR = 1.625^(1/4) − 1
CAGR = 12.90%
Up 50%, then down 50%: the average says 0% a year, the CAGR says −13.40%
An arithmetic average of yearly changes ignores that each year starts from where the last one ended. A value that rises 50% and then falls 50% ends at 1.5 × 0.5 = 0.75 of where it began — a 25% loss — yet the two changes average to zero. The compound rate that matches the real result is 0.75^(1/2) − 1 = −13.40% a year.
The gap is called volatility drag, and it only ever runs one way: the average is always further from zero than the compound rate unless every year is the same. Four years of +20%, +10%, −15% and +25% average 10.00%, but they multiply to 1.4025, a CAGR of 8.82%. That is why fund reports quote compound returns, and why the simple average on this page sits next to the CAGR.
Four uneven years
1.20 × 1.10 × 0.85 × 1.25 = 1.4025
CAGR = 1.4025^(1/4) − 1 = 8.82%
Average = (20 + 10 − 15 + 25) ÷ 4 = 10.00%
At 8% a year, $10,000 becomes $21,589.25 in ten years; reaching $25,000 at 7% takes 13.54 years
Once the rate is known, the same equation runs the other two ways. For a future value, compound the start: $10,000 × 1.08^10 = $21,589.25. For the time a target needs, take logarithms: n = ln(End ÷ Start) ÷ ln(1 + rate), so reaching $25,000 from $10,000 at 7% takes ln 2.5 ÷ ln 1.07 = 13.54 years.
n = ln(End ÷ Start) ÷ ln(1 + r)
The years answer has a trap the calculator handles for you: a target below the start is never reached at a positive rate, and a target above it never at a negative one. Rather than print a negative number of years, the result says the target is not reached at this rate.
Years to a target
Start = 10,000, End = 25,000, r = 7%
n = ln 2.5 ÷ ln 1.07
n = 13.54 years
12.47% a year doubles a value in 5.90 years; the rule of 72 says 5.77
An investment that grew from $10,000 to $18,000 in five years compounded at 12.47% a year. At that rate it doubles in ln 2 ÷ ln 1.1247 = 5.90 years. The rule of 72 — divide 72 by the rate in percent — gives 5.77 years, close enough for mental arithmetic and a little short, as it always is above about 8%.
Both figures appear under every result, so the size of the shortcut’s error is visible at your own rate. The Doubling Time Calculator works the exact formula for any growth rate, including periods other than a year.
Doubling at 12.47%
Exact: ln 2 ÷ ln 1.1247 = 5.90 years
Rule of 72: 72 ÷ 12.47 = 5.77 years
The US population grew 7.4% from 2010 to 2020 — a CAGR of 0.712% a year
The Census Bureau counted 308,745,538 people in the United States on 1 April 2010 and 331,449,281 on 1 April 2020, an increase of 22,703,743, which it reported as 7.4%. As a compound annual rate over the ten years that is (331,449,281 ÷ 308,745,538)^(1/10) − 1 = 0.712% a year.
The textbook version is the same arithmetic. OpenStax’s Principles of Finance asks for the annual growth rate of revenue that rose from $30 million to $90 million over ten years: the multiple is 3, and 3^(1/10) − 1 = 11.61% a year. Both cases are in the test suite this calculator is checked against.
Census 2010 → 2020
Multiple = 331,449,281 ÷ 308,745,538 = 1.07354
CAGR = 1.07354^(1/10) − 1
CAGR = 0.712% a year
For one start and one end, CAGR and annualized return are the same number; deposits change the tool
If all you need is the yearly rate behind an investment’s start and end value, the Annualized Return Calculator gives exactly the same figure — it is the same formula under a different name. The ROI Calculator also shows it, as annualized ROI. This page exists for the other questions: projecting an end value from a rate, finding how many years a rate needs, and printing the path year by year, for revenue or users as readily as for money.
Once money is added or withdrawn along the way, a start and an end value no longer describe the growth, and CAGR overstates or understates it. That calls for an internal rate of return: the XIRR Calculator handles dated cash flows of any size.
Two endpoints decide the answer, so name them whenever you quote a CAGR
Because only the first and last values enter the formula, the choice of years is the choice of answer. Start the window in a bad year and the rate looks strong; end it in one and it looks weak. A CAGR worth quoting states its dates — “12.90% a year, 2021 to 2025” — so a reader can see the window that was picked.
The rate also needs a positive start. Growth from zero, or from a loss to a profit, has no compound rate: the ratio of end to start is infinite or negative. Report those as an absolute change instead. A zero end value is allowed and gives −100%, a total loss.
Frequently Asked Questions
What is CAGR?
The compound annual growth rate: the single yearly rate that, compounded, turns a start value into an end value over a number of years. CAGR = (End ÷ Start)^(1 ÷ years) − 1.
How do I calculate CAGR in Excel?
Use =(End/Start)^(1/Years)-1, or the built-in =RRI(Years, Start, End), which returns the same equivalent annual rate. Format the cell as a percentage.
Is CAGR the same as annualized return?
For one start value and one end value, yes — it is the same formula. When money is added or withdrawn during the period, use an internal rate of return such as XIRR instead.
Why is CAGR lower than the average annual growth rate?
The average adds yearly changes as if each started from the same base; compounding multiplies them. Unless every year is identical, the compound rate is closer to zero than the average. +50% then −50% averages 0% but is a −13.40% CAGR.
Can CAGR be negative?
Yes. If the end value is below the start value the rate is negative, and an end value of zero gives −100%.
What if the start value is zero or negative?
CAGR is undefined: the growth multiple would be infinite or negative. Describe the change in absolute terms instead.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Growth compounds once a year at a single constant rate between the two endpoints.
Nothing is added or taken out along the way; the change is all growth.
The start value is positive. Growth from zero, or from a loss, has no compound rate.
Where it stops
Only the two endpoints matter: the path between them, however bumpy, does not change the answer.
Moving either endpoint by a year can change the rate a lot; state the dates with the figure.
Contributions or withdrawals make CAGR the wrong tool; use an internal rate of return (IRR or XIRR).
It is a description of the past, not a forecast. Taxes, fees and inflation are not taken out.
Related Calculators
Annualized ReturnThe compound annual rate behind a total return, with the growth multiple alongside it.
ROISimple, date-based, and net ROI with annualised ROI (CAGR), a reverse target solver, and a two-investment comparison.
Doubling TimeHow long a quantity takes to double at a constant rate, or from two measurements — with the rule of 70 and rule of 72 measured against the exact answer.
Compound InterestSee how savings grow as interest earns interest, with adjustable contributions and compounding frequency.
XIRRThe annualised return on irregular cash flows at their own dates — the figure a simple return calculation cannot give.
InvestmentProject lump-sum and regular-contribution growth, plan a goal, and solve future vs present value, with fees and inflation.
Rule of 72Years to double from a rate, or the rate to double in a set time, by the rule of 72 — with the exact answer and the error beside it, plus the rules of 114 and 144.
Regular InvestmentProject how regular monthly contributions grow over time — SIP-style investing, dollar-cost averaging, inflation-adjusted value, and long-term goals.
Returns are assumptions, not guarantees. Actual results may vary because of market performance, taxes, fees, inflation, and timing. This is an educational projection, not investment advice.
Published the CAGR calculator: the compound annual growth rate between two values, plus the end value a rate reaches and the years it needs, with the year-by-year path, the simple-average and rule-of-72 comparisons, and cases checked against the 2020 Census and an OpenStax textbook problem.
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