Article — CAGR Calculator
CAGR calculator: compound annual growth rate, explained and forecast
Compound annual growth rate (CAGR) is the constant yearly rate that takes a beginning value to an ending value over a given number of years. The formula is (Ending Value ÷ Beginning Value)^(1/n) − 1, where n is years. If $10,000 grows to $15,000 over 5 years, CAGR is 8.45%. CAGR smooths out year-to-year volatility into one comparable number, which is why it is the standard yardstick for multi-year investment, business, and economic growth.
This calculator inverts that math instantly. Enter the start value, the end value, and the elapsed years; the CAGR percentage, total return, profit, multiplier, and doubling time appear. A forecast option projects the ending value forward at the same rate, useful for sanity-checking retirement targets or business plans.
The CAGR formula
CAGR = (EV ÷ BV)^(1/n) − 1. The exponent is the inverse of n, which is what makes this an n-th root rather than a simple division. The minus one removes the principal, leaving only the growth rate.
BV = $10,000 beginning valueEV = $15,000 ending value after 5 yearsEV / BV = 1.5 50% total return1.5^(1/5) = 1.0845 fifth rootCAGR = 8.45% annualised growth rateThe total return is 50%, but the CAGR is only 8.45% because compounding does most of the work. An investment growing 8.45% per year hits 1.5x after 5 years (1.0845^5 = 1.5). Five years of straight 10% would have ended at 1.61x — substantially more. The CAGR is doing the inverse: figuring out what annual rate produced the observed end value.
CAGR vs average growth rate
The arithmetic average of year-to-year returns and the CAGR are not the same. The average treats each year as independent. CAGR treats them as compounding on each other, which is what actually happens to invested capital.
Consider an investment that returns +20%, −10%, and +15% over three years. The arithmetic average is (20 − 10 + 15) ÷ 3 = 8.33%. The CAGR, however, is (1.20 × 0.90 × 1.15)^(1/3) − 1 = 8.17%. The 0.84 percentage point gap is volatility drag — the cost of having returns that bounce rather than compound smoothly. Over longer periods and higher volatility, the gap widens.
For an investment with returns +50% in year one and −50% in year two, the arithmetic average is 0% — but you have lost 25% of your money. (1.5 × 0.5 = 0.75.) The CAGR over those two years is −13.4%. The gap between average and CAGR widens with volatility. This is why the SEC requires mutual funds to disclose annualised returns (which use CAGR math) rather than simple averages.
CAGR and the Rule of 72
The Rule of 72 is a 17th-century mental-math shortcut: doubling time in years equals 72 divided by the CAGR in percent. At 8% growth, money doubles in 72 ÷ 8 = 9 years (the precise answer is 9.01 years). At 6%, it doubles in 12 years; at 12%, in 6 years.
- 4% CAGR = doubles in 18 years (72 / 4)
- 6% CAGR = doubles in 12 years (72 / 6)
- 8% CAGR = doubles in 9 years
- 10% CAGR = doubles in 7.2 years (rule says 7.2; true 7.27)
- 12% CAGR = doubles in 6 years
- 15% CAGR = doubles in 4.8 years (rule says 4.8; true 4.96)
The exact doubling formula is ln(2) ÷ ln(1 + CAGR). The Rule of 72 is accurate to within 1% for CAGRs between 6% and 10%, which is why it became the default approximation. For very high CAGRs (above 20%), a Rule of 70 or Rule of 69 is closer to the true continuously compounded answer.
CAGR by asset class
Long-run CAGR is the headline number for comparing investments. US large-cap stocks have produced about 10% CAGR over 30-year windows including dividends. Bonds have produced 4 to 6%. Real estate sits between, at 5 to 8%. Cash and savings accounts have historically barely kept up with inflation.
These averages mask huge dispersion. The S&P 500 had years of +30% gains and years of −38% losses. The 10% headline figure is the geometric average across all of them. Smoothing volatility into one number is exactly what CAGR is for, but the smoothing also conceals risk that any honest analysis has to add back.
CAGR for startup revenue growth
CAGR is also the dominant metric in private-company analysis. Investors evaluate revenue growth in CAGR terms across funding rounds. A typical Series B SaaS company targets 60 to 80% revenue CAGR. A Series C target is closer to 40 to 60%. By the time a company reaches IPO, sustainable CAGR has usually dropped to 20 to 30%.
CAGR over fewer than three years is unreliable because there are too few compounding cycles. A startup that triples revenue in year one (200% CAGR) almost never sustains that rate. Public-market CAGR figures below 3 years should be treated with similar caution, especially after bull or bear runs. Most analysts use 5-year CAGR as the minimum credible window.
The flipside is that very early-stage companies sometimes report CAGRs above 300%, which sound impressive but mean little. Going from $100K to $1M of revenue in a year is a 900% CAGR, but the absolute dollars are tiny. CAGR works best on amounts that are large enough to be stable.
Real vs nominal CAGR with inflation
The CAGR computed here is nominal — it does not subtract inflation. For real purchasing-power growth, the formula is real CAGR = (1 + nominal CAGR) ÷ (1 + inflation rate) − 1. The subtraction shortcut (nominal minus inflation) is only accurate for low rates.
At a 10% nominal CAGR and 3% inflation, real CAGR is (1.10 ÷ 1.03) − 1 = 6.8%. The naive subtraction (10 − 3 = 7%) is close but slightly wrong. The error grows with inflation: at 10% inflation, real CAGR is roughly (1+nominal)/(1+inflation) − 1, which deviates from naive subtraction at higher rates. The two methods diverge when both rates are high and start adding up over decades.
Long-term US equity returns are quoted in real terms at about 7%, against the 10% nominal headline. The 3-point gap is the long-run inflation drag. Other asset classes shrink similarly: a 5% nominal bond yield becomes 2% real after inflation. For retirement planning, real CAGR is the relevant figure because retirement spending also rises with inflation.
CAGR limitations and pitfalls
CAGR has three structural weaknesses. First, it depends entirely on the chosen start and end points. Cherry-picking a starting year right after a market crash inflates the CAGR; starting right before one deflates it. Honest CAGR reporting uses rolling periods (e.g., every 5-year window across 30 years) rather than a single hand-picked window.
Second, CAGR ignores intermediate path. Two investments can have identical CAGRs but vastly different volatility. An investment that grew steadily at 10% per year and one that alternated +50% / −30% returns both might end up with a 10% CAGR, but their risk profiles are nothing alike. Always look at standard deviation or maximum drawdown alongside CAGR.
Third, CAGR assumes a single lump sum at the start. It does not handle deposits, withdrawals, or rebalancing inside the period. For irregular cash flows, the right tool is the internal rate of return (IRR) or the time-weighted return — not CAGR.
Using CAGR to forecast future value
The forecast option projects the ending value forward at the same CAGR. Future value = present value × (1 + CAGR)^n. This is useful for retirement planning, valuation discounting, and quick what-ifs. It is not a prediction. Past performance does not repeat exactly, especially for individual stocks or for any time period shorter than a decade.
Use the forecast as a baseline to test against. If a retirement plan needs $2M and the historical CAGR suggests $1.5M, you know you need either higher contributions, a longer horizon, or a different asset mix. The math is only as good as the assumption that the next decade will look something like the last one, which is true on average but rarely true in detail.