Work out compound annual growth rate from two values — or solve the formula backwards for the final value, the starting amount, or the years it takes.
Fill in the three you know; the fourth is what gets solved.
CAGR is a smoothed rate: it describes the single constant rate connecting two points and says nothing about the path between them. Two investments with the same CAGR can differ wildly in volatility, drawdowns and risk. Past returns do not predict future ones. For education and planning, not investment advice.
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Compound annual growth rate is the single constant rate that would take an investment from where it started to where it ended. This calculator solves the formula in all four directions — the rate, the final value, the starting amount, or the number of years — and shows every step of the arithmetic, so you can follow the derivation rather than just copy a number.
CAGR = (Ending Value ÷ Beginning Value)^(1/n) − 1, where n is the number of years. The logic is short: divide the ending value by the beginning value to get the total growth multiple, take the nth root to find the per-year multiple, then subtract one to turn a multiple into a rate. A fund that grows from $10,000 to $25,937 in ten years has a multiple of 2.5937; the tenth root of that is 1.10; subtract one and the CAGR is 10%. Because the formula only touches the endpoints, it smooths away everything in between.
Compound annual growth rate
A 60% total gain over three years and a 90% gain over six are hard to compare directly. Annualising both puts them on the same footing.
Revenue growth quoted as a CAGR is the standard in board decks and investor updates, because it strips out the year-to-year noise.
Solve for the starting amount to find what you need to invest today, or for the years to find how long a target will take at a given rate.
If a product advertises a total return over several years, converting it to a CAGR usually makes it look far more ordinary.
One formula, four unknowns. Most calculators only compute the rate. This also answers "what will it be worth", "what do I need to invest" and — uniquely — "how many years will it take".
Each mode prints the substitution, the ratio, the root and the subtraction. If you are learning the formula or checking coursework, the steps are the answer.
Your result is compared with the annualized returns of stocks, bonds, gold, property and inflation over 1928–2025 — each figure derived from published data, not asserted.
A smoothed rate says nothing about the ride. The page says so, rather than presenting a single number as the whole story.
CAGR = (Ending Value ÷ Beginning Value)^(1/n) − 1, with n in years. Divide to get the growth multiple, take the nth root for the per-year multiple, subtract one to express it as a rate. Multiply by 100 for a percentage.
Three operations. Divide the ending value by the beginning value. Raise that to the power of 1/n — on most calculators that is the x^y key with 1 divided by the number of years. Then subtract 1. For $10,000 to $25,937 over 10 years: 2.5937, then ^0.1 = 1.10, then −1 = 0.10, or 10%.
No, and the difference matters. A simple average of yearly returns ignores compounding and is always at least as high as the CAGR. Gain 100% then lose 50% and the simple average is +25%, while the CAGR is 0% — because you ended exactly where you started. CAGR is the geometric mean and is the honest one.
Solve for years with an ending value twice the beginning value. At 9% it takes about 8.04 years. The rule of 72 approximates this — 72 ÷ 9 = 8 — and stays close for rates between roughly 5% and 15%.
Yes. If the ending value is below the beginning value, the rate is negative and describes the constant annual rate of decline. This calculator reports it rather than hiding it.
The formula divides by the beginning value, so a start of zero has no defined growth rate — going from nothing to something is an infinite multiple. If you are measuring growth from zero, use the absolute change instead.
It depends entirely on the asset and the risk. For context, over 1928–2025 the S&P 500 returned about 10.0% a year with dividends, corporate bonds 6.6%, gold 5.6%, Treasuries 4.5%, real estate 4.2%, and inflation ran at 3.1%. A rate below inflation means purchasing power fell even though the number went up.
The path. Two investments that both turn $10,000 into $20,000 over seven years have identical CAGRs whether one rose steadily or crashed 60% in the middle. CAGR ignores volatility, drawdowns, and the order returns arrive in — which matters enormously if you are adding or withdrawing money along the way.
No. It compares two endpoints only. If you added or removed money during the period, the CAGR of the balance is not your return — you want a money-weighted return (IRR) instead.
Yes. Enter the period in years as a decimal — 18 months is 1.5. The formula handles fractional exponents without any special treatment.