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Formula
CAGR = (Ending value ÷ Beginning value)^(1 ÷ Years) − 1; Ending value = Beginning value × (1 + CAGR)^Years
- Ending value
- the value at the end of the period
- Beginning value
- the value at the start of the period (must be greater than 0)
- Years
- the length of the period in years; fractions such as 2.5 are allowed
- CAGR
- the steady yearly growth rate that links the two values, as a decimal
What the calculator works out
The CAGR calculator has two modes.
Find CAGR takes a beginning value, an ending value and the number of years, and returns:
- Compound annual growth rate (CAGR), the steady yearly rate that turns the first value into the second.
- Total growth, the overall percentage change across the whole period.
- Growth multiple, how many times larger the ending value is.
- Amount gained or lost in dollars.
- Simple average per year, shown for comparison so you can see how it differs from CAGR.
- A year-by-year path at the CAGR, for whole numbers of years.
Find ending value turns the CAGR calculator around: enter a beginning value, a CAGR and a number of years to project where the value ends up.
What CAGR means
CAGR answers one question: if something had grown at exactly the same rate every year, what would that rate be? It ignores the path in between and looks only at where the value started and finished. That makes the CAGR calculator a fair way to compare an investment held for 3 years with one held for 7, or a company’s revenue growth with a competitor’s.
Economists use the same calculation. The U.S. Bureau of Economic Analysis computes average annual growth with a variant of the compound interest formula, and the Federal Reserve annualizes monthly and quarterly changes the same way.
The CAGR formula
CAGR = (Ending value ÷ Beginning value)^(1 ÷ Years) − 1
Rearranged to project forward:
Ending value = Beginning value × (1 + CAGR)^Years
Total growth is simply (Ending value ÷ Beginning value − 1) × 100.
How to calculate CAGR by hand
Say an investment grew from $20,000 to $32,000 over 6 years.
- Growth multiple: $32,000 ÷ $20,000 = 1.6.
- Exponent: 1 ÷ 6 = 0.1667.
- Raise the multiple to the exponent: 1.6^0.1667 ≈ 1.0815.
- Subtract 1: 0.0815, or 8.15% a year.
- Total growth: (1.6 − 1) × 100 = 60%.
To check the answer, multiply $20,000 by 1.0815 six times; you land back at about $32,000. On a calculator without a power key, take the natural log instead: ln(1.6) ÷ 6 = 0.0783, and e^0.0783 − 1 = 8.15%.
To project forward, reverse the steps. $8,000 growing at 6% a year for 8 years is $8,000 × 1.06^8 = $12,750.78.
CAGR growth table
How much $1 becomes at a steady CAGR, and roughly how long it takes to double.
| CAGR | After 5 years | After 10 years | After 20 years | Years to double |
|---|---|---|---|---|
| 3% | 1.1593× | 1.3439× | 1.8061× | 23.45 |
| 5% | 1.2763× | 1.6289× | 2.6533× | 14.21 |
| 7% | 1.4026× | 1.9672× | 3.8697× | 10.24 |
| 10% | 1.6105× | 2.5937× | 6.7275× | 7.27 |
| 12% | 1.7623× | 3.1058× | 9.6463× | 6.12 |
The doubling column is close to the “rule of 72” estimate of 72 ÷ the rate (72 ÷ 8 ≈ 9 years at 8%).
CAGR versus the average growth rate
The most common mistake with growth rates is averaging them. Suppose a stock rises 50% one year and falls 50% the next. The simple average is 0%, which suggests you broke even. In fact $100 became $150 and then $75, a CAGR of −13.4% a year.
This happens because a loss is taken from a larger or smaller base than the gain before it. CAGR always reproduces the real ending value; the simple average does not. When the yearly returns vary, the simple average is always at least as high as the CAGR, so quoting it flatters the result.
Real-life uses
- Comparing investments held for different lengths of time, after the fact.
- Company and market analysis, such as revenue, earnings or users growing over several fiscal years.
- Planning, by projecting a value forward at an assumed rate in the ending-value mode of the CAGR calculator.
- Checking claims. “Revenue tripled in five years” is a CAGR of 24.57%.
For a single total percentage gain or loss, use the ROI calculator or the percentage change calculator. To model regular deposits on top of growth, use the compound interest calculator, because CAGR on a balance that includes contributions overstates the investment’s own return.
Limitations to keep in mind
CAGR hides volatility. Two investments with the same CAGR can have had very different paths, and one may have fallen sharply along the way. It also says nothing about risk, fees, taxes or inflation unless the values you enter already reflect them. Past CAGR is not a forecast of future growth.
Glossary
- Compounding. Growth on growth: each year’s increase is applied to a base that includes previous increases.
- Growth multiple. Ending value ÷ beginning value.
- Annualized. Converted to a yearly rate so periods of different lengths can be compared.
- Rule of 72. A shortcut for doubling time: 72 ÷ the yearly percentage rate.
Worked examples
An investment over five years
A $10,000 investment worth $18,000 five years later.
Inputs (Find CAGR): Beginning value = $10000; Ending value = $18000; Number of years = 5 years
Growth multiple = $18,000.00 ÷ $10,000.00 = 1.8 CAGR = 1.8^(1/5) − 1 = 0.124746 = 12.47% Total growth = (1.8 − 1) × 100 = 80%
Answer: Going from $10,000.00 to $18,000.00 in 5 years is a CAGR of 12.47% (80% in total).
Company revenue over four years
Annual revenue grew from $2.5 million to $4.1 million over four fiscal years.
Inputs (Find CAGR): Beginning value = $2500000; Ending value = $4100000; Number of years = 4 years
Growth multiple = $4,100,000.00 ÷ $2,500,000.00 = 1.64 CAGR = 1.64^(1/4) − 1 = 0.131647 = 13.16% Total growth = (1.64 − 1) × 100 = 64%
Answer: Going from $2,500,000.00 to $4,100,000.00 in 4 years is a CAGR of 13.16% (64% in total).
A portfolio that lost value
A $50,000 portfolio fell to $38,000 over three years, so the CAGR is negative.
Inputs (Find CAGR): Beginning value = $50000; Ending value = $38000; Number of years = 3 years
Growth multiple = $38,000.00 ÷ $50,000.00 = 0.76 CAGR = 0.76^(1/3) − 1 = −0.087419 = −8.74% Total growth = (0.76 − 1) × 100 = −24%
Answer: Going from $50,000.00 to $38,000.00 in 3 years is a CAGR of −8.74% (−24% in total).
Projecting a value forward at 7%
$15,000 assumed to grow at a steady 7% a year for 10 years.
Inputs (Find ending value): Beginning value = $15000; CAGR = 7 %; Number of years = 10 years
End value = $15,000.00 × (1 + 7%)^10 = $29,507.27
Answer: $15,000.00 growing at 7% a year for 10 years reaches $29,507.27 (96.72% in total).
Assumptions and limitations
- CAGR assumes smooth compounding once a year at a constant rate. Real values rise and fall from year to year; CAGR describes only the start and end points.
- The beginning value must be greater than 0. An ending value of 0 gives a CAGR of −100%. Negative values are not supported, because the formula needs a positive ratio.
- Deposits and withdrawals during the period are not accounted for. If money was added or taken out, CAGR on the account balance overstates or understates the investment's own return.
- Fractional years are allowed. The year-by-year table appears only for whole numbers of years up to 50.
- Values are shown in dollars, but the formula works for any positive quantity such as revenue, users or population.
Frequently asked questions
How do you calculate CAGR?
Divide the ending value by the beginning value, raise the result to the power of 1 divided by the number of years, and subtract 1. Growing from $20,000 to $32,000 in 6 years gives 1.6^(1/6) − 1 = 0.0815, or 8.15% a year.
How do you calculate CAGR over 5 years?
Use 5 as the number of years, so the exponent is 1/5 = 0.2. A value that grows from 100 to 150 over 5 years has a CAGR of 1.5^0.2 − 1 = 8.45%.
What is the difference between CAGR and average annual return?
The simple average adds up each year's return and divides by the number of years; CAGR is the single rate that compounds to the actual result. Returns of +20%, −10% and +15% average 8.33%, but the CAGR is 7.49%, which is the rate that actually reproduces the ending value.
Can CAGR be negative?
Yes. If the ending value is below the beginning value, CAGR is negative. Falling from $50 to $40 over 2 years is a CAGR of −10.56%.
What is a reverse CAGR calculation?
It runs the formula forward to find the ending value from a known growth rate. Use the Find ending value mode. $8,000 growing at 6% a year for 8 years reaches $12,750.78.
How is CAGR different from ROI?
ROI is the total percentage gain over the whole period, regardless of how long it took. CAGR spreads that gain over the years as a compound yearly rate. An 80% total gain is about 12.5% a year over 5 years but only about 6.05% a year over 10 years.
Sources
- How is average annual growth calculated? — U.S. Bureau of Economic Analysis. Checked October 10, 2026.
- Annualizing data — Federal Reserve Bank of Dallas. Checked October 10, 2026.
- Rates and Returns (CFA Program refresher reading) — CFA Institute. Checked October 10, 2026.
- Compound annual growth rate — Wikipedia. Checked October 10, 2026.