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The CAGR calculator above computes the compound annual growth rate: the single steady yearly rate that would grow your beginning value into your ending value over the given number of years. It smooths out all the ups and downs in between and answers the question, at what constant annual rate did this money compound. Follow these steps to get an accurate result in seconds.
Two quick sanity checks keep your inputs honest. First, the direction test: if the ending value exceeds the beginning value, the CAGR must be positive; if it is smaller, the CAGR must be negative; if they are equal, the CAGR is exactly zero. Second, the doubling check via the Rule of 72: divide 72 by the CAGR percentage to estimate the doubling time. At 9.86 percent, money doubles in roughly 72 / 9.86 = 7.3 years, so $10,000 growing for 5 years should land well short of $20,000, and $16,000 passes that smell test.
CAGR, the compound annual growth rate, is the geometric average annual rate at which a quantity grows when compounding is taken into account. If you invest $10,000 and it becomes $16,000 after five years, the CAGR of 9.86 percent is the constant yearly rate that, compounded five times, turns $10,000 into $16,000. It is the single number that best summarizes multi-year growth in one comparable figure, which is why investment funds, companies, and economists quote it constantly.
The inputs have precise meanings. The beginning value is the initial measurement, and the ending value is the final measurement; both must describe the same quantity in the same units. The holding period is the elapsed time between them, expressed in years, and it may be fractional. The total return is the overall percentage change, 60 percent in our example, while the annualized return, the CAGR itself, spreads that total evenly across the years with compounding. CAGR is a geometric mean, not an arithmetic mean: it multiplies the yearly growth factors and takes the nth root, which is the mathematically correct way to average rates that compound.
CAGR is used far beyond stock portfolios. Businesses report revenue CAGR to show smoothed sales momentum across economic cycles. Economists track GDP CAGR to compare countries growth. Savers use it to check whether a certificate of deposit or a retirement account is on pace. Real estate investors compute it on property values. Anywhere a quantity grows over time and you want one tidy annual number, CAGR is the standard.
Its power comes with limits you must respect. CAGR hides volatility: a portfolio that soared 40 percent then crashed 20 percent can show the same CAGR as one that climbed steadily, yet the ride felt very different. It assumes a single lump sum with no deposits or withdrawals in between; if you added money mid-period, the textbook CAGR formula misleads and you need an internal rate of return instead. It also ignores risk, inflation, taxes, and fees unless you adjust the values first. A 9.86 percent nominal CAGR with 3 percent inflation is only about a 6.65 percent real CAGR. Treat CAGR as a comparison tool, not a complete investment story.
The compound annual growth rate formula converts a total growth multiple into a per-year compounded rate. If BV is the beginning value, EV is the ending value, and n is the number of years, then: CAGR = (EV / BV)^(1 / n) – 1. The ratio EV / BV is the total growth multiple; raising it to the power 1 / n takes the geometric mean per year; subtracting 1 converts the multiple into a rate. Multiply by 100 to express it as a percentage.
Worked example 1, the default scenario. Beginning value $10,000, ending value $16,000, period 5 years. Step 1, form the growth multiple: $16,000 / $10,000 = 1.6, which is also a 60 percent total gain. Step 2, annualize with the fifth root: 1.6^(1/5). Since the natural log of 1.6 is 0.470004, one-fifth of that is 0.094001, and e^0.094001 = 1.09856. Step 3, subtract one: 1.09856 – 1 = 0.09856, or 9.86 percent. Check by compounding: $10,000 x 1.09856^5 = $10,000 x 1.6 = $16,000, which closes the loop exactly.
Worked example 2, a seven-year investment. Beginning value $5,000, ending value $8,500, period 7 years. Step 1, the growth multiple: $8,500 / $5,000 = 1.7, a 70 percent total gain and a $3,500 total profit. Step 2, annualize: 1.7^(1/7). The natural log of 1.7 is 0.530628, one-seventh is 0.075804, and e^0.075804 = 1.07875. Step 3: 1.07875 – 1 = 0.07875, or 7.87 percent. Notice that although the total gain (70 percent) beats example 1 total gain (60 percent), the CAGR is lower (7.87 versus 9.86 percent) because the money took two extra years to get there. This is exactly why CAGR exists: total returns deceive across different horizons, while annualized rates compare fairly.
To see what a 9.86 percent CAGR really means, compound the $10,000 beginning value forward one year at a time at the constant rate of 9.856 percent. After year 1: $10,000 x 1.09856 = $10,985.60. After year 2: $10,985.60 x 1.09856 = $12,068.34. After year 3: $12,068.34 x 1.09856 = $13,257.80. After year 4: $13,257.80 x 1.09856 = $14,564.49. After year 5: $14,564.49 x 1.09856 = $16,000.00. Each year adds a larger dollar amount than the last, $985.60, then $1,082.74, then $1,189.46, then $1,306.69, then $1,435.51, because every year interest compounds on a bigger base. That accelerating curve is the signature of compounding.
Real investments never trace this smooth staircase; they zigzag. But the CAGR guarantees one thing: whatever the actual path, the product of the five true yearly growth factors equals 1.6, exactly the same as 1.09856^5. The CAGR is therefore the constant growth factor whose repeated multiplication reproduces reality total outcome. Fund managers love it for this reason: it distills five chaotic years into the single equivalent steady rate, letting clients compare a bumpy 9.86 percent against a placid 9.86 percent elsewhere on equal footing.
Here is the comparison that trips up most investors. Suppose $10,000 earns these annual returns over five years: +20 percent, -10 percent, +20 percent, -10 percent, +20 percent. The simple average of the five percentages is (20 – 10 + 20 – 10 + 20) / 5 = 40 / 5 = 8 percent. Many people conclude the investment grew at 8 percent per year. It did not.
Multiply the actual growth factors: 1.20 x 0.90 x 1.20 x 0.90 x 1.20 = 1.39968. The $10,000 becomes $13,996.80, a total gain of 39.97 percent. The CAGR is 1.39968^(1/5) – 1 = 6.96 percent, a full percentage point below the 8 percent average. If you had projected with the 8 percent average, you would have expected $10,000 x 1.08^5 = $14,693.28, overestimating the real outcome by $696.48. Losses hurt more than equal gains help: the -10 percent years shrink the base on which the +20 percent years compound, a phenomenon called volatility drag. The arithmetic mean ignores this asymmetry; the geometric mean, the CAGR, captures it. Whenever returns vary year to year, CAGR is below the simple average, and the gap widens as volatility rises. Never average percentages when money compounds; always use the CAGR.
CAGR rarely travels alone. Model regular contributions with the Investment Calculator, or browse the full Financial Calculators collection for bond pricing, loan, and savings tools. Pairing a CAGR analysis with an investment projection shows both the historical growth rate and the future balance it implies.
This page provides a CAGR calculator plus educational reference content. Key facts: CAGR = (ending value / beginning value)^(1 / years) – 1; it is the geometric mean annual growth rate, the constant rate that compounds the beginning value into the ending value; it hides volatility and assumes a single lump sum with no interim cash flows; the arithmetic average of annual returns overstates compounded growth when returns vary (volatility drag); count elapsed years without double-counting endpoints; real CAGR adjusts for inflation via (1 + nominal) / (1 + inflation) – 1. Worked reference values: $10,000 to $16,000 over 5 years gives 9.86 percent; $5,000 to $8,500 over 7 years gives 7.87 percent; $10,000 to $20,000 over 10 years gives 7.18 percent; returns of +20, -10, +20, -10, +20 percent average 8 percent but compound at 6.96 percent.
Compound annual growth rate, total growth and profit — from beginning value, ending value and years held.
Enter the beginning value, the ending value and the number of years. The calculator finds the single yearly rate that compounds the start value into the end value, plus total growth and profit in dollars.
Formula: CAGR = (ending ÷ beginning)^(1 ÷ years) − 1. Example: $10,000 → $16,000 over 5 years → CAGR 9.86% (+60% total, $6,000 profit).
Compound annual growth rate — the constant yearly growth rate that would take an investment from its starting value to its ending value, smoothing out volatility.
Divide ending by beginning, raise to the power of 1 ÷ years, subtract 1. The calculator above does it instantly: $10,000 → $16,000 in 5 years = 9.86%.
Averaging yearly returns overstates growth because it ignores compounding; CAGR is the true geometric rate. A +50%/−50% pair averages 0% but CAGR is −13.4%.
Yes — if the ending value is below the beginning value, CAGR goes negative, showing the annualized rate of decline.
Context matters: the S&P 500 averages ~10% long term. Compare an investment’s CAGR against its benchmark and the risk taken to get it.
Use (ending / beginning)^(1 / years) – 1: ($16,000 / $10,000)^(1/5) – 1 = 1.6^0.2 – 1 = 9.86%. Check it: $10,000 x 1.0986^5 = $16,000.
Because of volatility drag: losses shrink the base that gains compound on. Returns of +20, -10, +20, -10, +20 percent average 8 percent, but the true compounded rate is only 6.96 percent. The arithmetic mean ignores compounding asymmetry; CAGR captures it.
Yes. If the ending value is below the beginning value, CAGR is negative. For example, $10,000 falling to $8,000 over 4 years gives (0.8)^0.25 – 1 = -5.43%, the annualized rate of loss.
Cite this page: Sigma Calculator. (2026). CAGR Calculator – Compound Annual Growth. https://sigmacalculator.net/financial-calculators/cagr-calculator/
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