Finance · Interest and investing
Calculate compounded annual growth (CAGR)
CAGR is the fictional constant annual rate that would take a starting value to an ending value in n years. It smooths the trip: a crash and a rebound disappear into one number.
Calculate
How the calculator works
Form end / start, raise to 1/n, subtract 1. That r satisfies start × (1+r)^n = end, so it is compound interest run backwards with no cash flows. n may be fractional. If end is below start, CAGR is negative. An ending value of 0 is refused.
Formula and method
CAGR = (V_arrivée / V_départ)^{1/n} − 1n is time in years. The result is shown as a percent.
V_arrivée = V_départ × (1 + CAGR)^n
Check: CAGR is the r of annual compounding that links the two points, with no in-between deposits.
CAGR does not describe year-by-year returns; it keeps only the endpoints. An asset that does +50%, −40%, +50% can show a calm CAGR while the holder lived large swings. There is no weighting by contributions: this is not IRR. ROI on the same pair ignores n; CAGR insists on n. Fees and tax appear only if you already netted them from the two values.
Worked example
$10,000 to $16,105.10 in 5 years
start $10,000, end $16,105.10, n = 5.
- Ratio = 1.61051.
- 1.61051^(1/5) = 1.10.
- CAGR = 10%.
10% CAGR. $10,000 × (1.10)^5 = $16,105.10.
Input notes
- Starting value
- Strictly positive beginning value.
- Ending value
- Strictly positive ending value. Below start produces a negative CAGR.
- Time
- Holding period n. 2.5 is allowed. Zero is not.
Assumptions and limits
Assumptions
- No cash flows between the two values.
- Annual compounding identity, not a monthly path.
Limits
- Hides volatility and drawdowns.
- Not a money-weighted return if you added cash.
- Not a forecast of the next n years.
How to read the result
10% CAGR means a constant 10% annual compound would explain the two points. It does not mean you earned 10% every year. ROI on $10,000 → $16,105 is +61.05% with no years attached — a different sentence.
Common mistakes
Calling CAGR the average of yearly returns.
The arithmetic average of yearly returns is a different statistic and is not computed here.
Using CAGR on a plan with large monthly deposits.
Endpoints then mix contributions with growth. This identity assumes no in-between cash.
Related calculations
- ROIROI here is a simple ratio of gain (or loss) to cash put in. It does not know whether the outcome took a month or a decade. CAGR is the tool that uses years.
- Compound interestGrow a single principal at a nominal annual rate with a chosen compounding frequency, including continuous compounding. The page also reports the effective annual rate. There are no recurring deposits on this form.
- Savings with monthly depositsProjects a starting balance and constant monthly deposits, credited at month-end, with an annual nominal rate converted as monthly = annual / 12. It is a fixed-rate scenario, not a market forecast.
- Inflation and purchasing powerAn amount, a constant annual rate, a period. Compound forward, or bring a later sum back to today’s purchasing power.
- Simple interestInterest is proportional to principal, rate, and time. It does not itself earn interest. Use this only when a contract is actually simple, not as a stand-in for savings compounding.
Frequently asked questions
How is CAGR different from ROI?
ROI ignores time. CAGR is an annualized compound rate over n years.
The same two dollar amounts produce one ROI and infinitely many CAGRs depending on n. Always state the number of years with CAGR.
Can CAGR be negative?
Yes, if the ending value is below the start.
That is a constant annual decline that would explain the drop, still smoothing any path in between.
Is this an expected return?
No. It describes two historical (or hypothetical) points.
Past CAGR is not a promise. This tool does not load market data.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
Gain versus cash in, no clock
If you only want (out − in) / in, ROI is the ratio without n.
Calculate ROICAGR between two positive values. Not a forecast. This is a calculator, not financial, tax, or credit advice, and not a loan or investment offer. Lenders and brokers apply their own rounding, fees, insurance, and APR. Check the actual contract and disclosures.
Category: Finance