CAGR Calculator
Turn a beginning value, ending value, and time span into an annualized growth rate, total return %, and growth multiple.
CAGR
Live toolgrowth multiple 2.50×
Check — compound it back: $10,000 × (1 + 0.1650)^6 ≈ $25,000 ✓
Assumes no money was added or removed between the two values. For accounts with ongoing deposits, use a money-weighted return (IRR) instead. If you entered share prices, the result is price-only growth that excludes dividends.
How it works
CAGR — compound annual growth rate — answers one question: if your money had grown at a single steady rate every year instead of the lumpy path it actually took, what would that rate be? Enter what you started with, what you ended with, and how long it took (fractional years are fine — 18 months is 1.5, and for day counts use days ÷ 365.25). The tool returns three numbers: the growth multiple (how many times over your starting money you ended with), the total return (the cumulative change over the whole period, not annualized), and the CAGR (that same change spread into an equivalent per-year compounded rate).
Losses are first-class citizens here: if the ending value is below the beginning value, the CAGR is simply negative — displayed with an explicit minus sign, never clamped to zero. An ending value of zero is a −100% CAGR: a total loss. And every result comes with a built-in verification step — compound the beginning value at the computed rate for the full time span and it must reproduce the ending value, up to rounding.
One assumption to keep in mind: this is a pure point-to-point comparison. The math assumes no money was added or removed between the two values, and if you enter per-share prices instead of total values, the result is price-only growth that excludes dividends.
The formula
CAGR = (ending value ÷ beginning value)1 ÷ years − 1
- Growth multiple: M = E ÷ B — the ending value divided by the beginning value; how many times over the starting money you ended with.
- Total return %: (M − 1) × 100 — the cumulative (not annualized) return, converted to a percent-number.
- CAGR as a decimal: M1 ÷ Y − 1 — the growth multiple raised to the power of one-over-the-number-of-years, minus one. It is the single constant yearly rate that, compounded once per year for Y years, turns B into E.
- CAGR %: multiply the decimal by 100 for display (0.165 becomes 16.5% per year).
Self-check identity: B × (1 + CAGR)Y = E, up to rounding — compounding the beginning value at the computed rate for Y years must reproduce the ending value. Units cancel in every formula, so any consistent currency works.
Worked example
Inputs: beginning value B = $10,000; ending value E = $25,000; years Y = 6.
- Growth multiple: M = 25,000 ÷ 10,000 = 2.5000 → displayed 2.50×.
- Total return: (2.5 − 1) × 100 = 1.5 × 100 = 150.00%.
- Exponent: 1 ÷ Y = 1 ÷ 6 = 0.1666667.
- Root via logs: ln(2.5) = 0.9162907; 0.9162907 × 0.1666667 = 0.1527151; e0.1527151 = 1.1649931. So M1/6 = 1.1649931.
- CAGR: 1.1649931 − 1 = 0.1649931 → 0.1649931 × 100 = 16.4993 ≈ 16.50% per year.
- Verify by compounding back: $10,000 × (1.1649931)6: 1.1649931² = 1.3572089; 1.3572089 × 1.1649931 = 1.5811390; 1.5811390² = 2.5000005 → $10,000 × 2.5000005 ≈ $25,000 ✓.
Emitted growthRate = 16.5 (percent-number: 16.5 means 16.5%).
Negative-CAGR example (a loss is still valid): B = $40,000; E = $32,000; Y = 2. M = 32,000 ÷ 40,000 = 0.8000 (0.80×). Total return = (0.8 − 1) × 100 = −20.00%. CAGR = 0.81/2 − 1 = 0.8944272 − 1 = −0.1055728 → −10.56% per year. Verify: $40,000 × 0.8944272² = $40,000 × 0.8000000 = $32,000 ✓.
FAQ
What is CAGR?
Compound annual growth rate — the single constant yearly rate that would grow a beginning value into an ending value over a given number of years, with compounding. It smooths a lumpy path into one comparable annual figure.
What is the CAGR formula?
CAGR = (ending value ÷ beginning value)^(1 ÷ years) − 1, expressed as a percent. For $10,000 growing to $25,000 over 6 years: 2.5^(1/6) − 1 ≈ 16.50% per year.
Can CAGR be negative?
Yes. If the ending value is below the beginning value, CAGR is negative — for example, $40,000 falling to $32,000 over 2 years is a CAGR of about −10.56% per year.
How is CAGR different from total return?
Total return is the cumulative change over the whole period (150% in the example above); CAGR spreads that same change into an equivalent per-year compounded rate (16.50%). Over multi-year periods total return is always the larger-looking number.
Does CAGR account for deposits, withdrawals, or dividends?
No. Point-to-point CAGR assumes no money was added or removed between the two values — for an account with ongoing deposits it overstates growth, and a money-weighted return (IRR) is the right measure. If you enter share prices, the result is price-only growth that excludes dividends.
Can I use fractional years, like 18 months?
Yes — enter 1.5 years (or days ÷ 365.25). Be careful annualizing periods under a year: a short-term gain extrapolated to a full year is a hypothetical rate, not an expected return.
Continue your analysis
Educational disclaimer
This calculator is for educational purposes only and is not financial, investment, or tax advice. A historical CAGR is a description of the past, not a forecast — carrying it into the compound-interest or DCF tools as growthRate is an assumption you are choosing to make, and past growth does not guarantee future results. The calculation assumes no contributions or withdrawals between the two values: for accounts with ongoing deposits, CAGR overstates growth and a money-weighted return (IRR) is the right measure. If you enter share prices, the result excludes dividends (price-only growth). This matters doubly here because the emitted growthRate travels into other tools. When the time span is under one year, treat the annualized figure as an extrapolation of a short-term result, not an expected yearly return.