CAGR Calculator — Compound Annual Growth Rate
Compute the Compound Annual Growth Rate (CAGR) between any starting and ending value over a given period. Compare CAGR against the total return, the Rule of 72 doubling shortcut, and the exact doubling time.
CAGR (Compound Annual Growth Rate)
7.2%
Total return over period
100.0%
Absolute gain
$10,000
Years to double (Rule of 72 shortcut)
10.0 years
Years to double (exact compound math)
10.0 years
Projected value in 10 more years at this CAGR
$40,000
Smoothed Growth at Constant CAGR
How to read your result
The CAGR is the single constant annual rate that would grow your starting value into your ending value over the given period. It smooths out year-to-year volatility into one comparable number — the same figure investment funds report on fact sheets.
Total return is the simple percentage change from start to end, ignoring how long it took. A 100% total return over 1 year (CAGR 100%) is very different from 100% over 20 years (CAGR ~3.5%). Always pair total return with a time horizon.
The Rule of 72 doubling shortcut divides 72 by the CAGR to estimate how many years it takes to double at the same rate. The exact compound math uses log(2) / log(1 + CAGR). The two answers usually agree within a few months in the 4–12% range.
The chart shows what the growth would look like as a smooth exponential curve at the computed CAGR. Real investments rarely look this clean — actual paths are jagged, but the start and end points are the same. CAGR is the geometric mean, not the arithmetic average.
When to use this tool
- ›Comparing two investments with different time horizons. A fund that returned 60% over 5 years (CAGR ~9.86%) vs. one that returned 80% over 8 years (CAGR ~7.62%) — CAGR makes them apples-to-apples.
- ›Sanity-checking a fund's marketing material. If a brochure highlights '+150% lifetime return,' divide by the years since inception to find the CAGR — often a less impressive number than the headline.
- ›Projecting a future balance assuming the same growth rate continues. Plug your historical start and end into this tool, then read the 'projected in 10 more years' output to see what continued compounding implies.
- ›Translating revenue or user growth between investor pitch decks. '5x in 4 years' is a CAGR of about 49.5% — useful for benchmarking against industry averages or comparable companies.
Methodology
CAGR is the geometric mean rate of return: CAGR = (endValue / startValue)^(1 / years) − 1, expressed as a percent. It assumes annual compounding and a single uninterrupted holding period — no contributions, withdrawals, or fees.
We compute the exact doubling time using natural logarithm — log(2) / log(1 + CAGR) — for a precise comparison against the Rule of 72 shortcut. The chart series uses the same exponential model: balance(t) = startValue × (endValue / startValue)^(t / years).
The 'projected in 10 more years' output extrapolates the historical CAGR forward. This is a mechanical projection, not a forecast — past growth is not a guarantee of future returns, especially for periods that include market peaks or troughs at the boundaries.
Limits we acknowledge: CAGR hides volatility. Two investments with the same CAGR can have very different drawdowns and risk profiles. For volatility-sensitive comparisons, pair CAGR with a measure of variance (standard deviation, Sharpe ratio) — those are out of scope for this tool.
Site-wide methodology framework: /methodology/ · Pre-publication standards: /editorial-standards/
FAQ
Why use CAGR instead of average annual return?
Because the simple arithmetic average overstates real growth when returns vary. A portfolio that gains 50% one year and loses 50% the next has an average return of 0% but a CAGR of about −13.4% — you actually ended down 25%. CAGR reflects the compounded reality; the simple average does not.
Can CAGR be negative?
Yes. If the ending value is less than the starting value, CAGR is negative. A drop from $10,000 to $7,000 over 5 years is a CAGR of about −6.9%. The formula handles this naturally — the exact-doubling outputs become meaningless (you can't double a shrinking balance) and may show as negative or undefined.
Does CAGR account for dividends or interest?
Only if your starting and ending values include reinvested dividends and interest. If you input just the share price change, CAGR reflects price appreciation alone. For total return, use values that include all cash distributions reinvested — most fund 'total return' figures already do this.
How does CAGR differ from IRR (Internal Rate of Return)?
CAGR assumes a single starting deposit and a single ending value — no contributions or withdrawals in between. IRR handles multiple cash flows at different times. If you only deposited once and never added more, the two give the same answer; otherwise IRR is the right tool. This calculator is for the simple case.
Why does the Rule of 72 estimate differ from the exact doubling time?
The Rule of 72 is an arithmetic shortcut, exact only near a CAGR of about 7.85%. At higher rates it slightly overshoots; at lower rates it slightly undershoots. The gap is rarely more than a year for typical investment returns and is small enough that the rule remains useful for mental math.
When does CAGR become misleading?
When the start or end point is unusually high or low (cherry-picked to flatter a fund), when the time period is too short to be meaningful (less than ~3 years), or when underlying volatility makes the smooth average a poor description of what an investor would have actually experienced. Always check the actual year-by-year returns alongside CAGR.