Calculator of Alexandria

CAGR and ROI calculator

Calculate total return on investment and compound annual growth rate (CAGR) from starting and ending values, with the difference explained.

Annualized return (CAGR)
Total return (ROI)
Gain

Formula

CAGR=(V1V0)1/t−1\text{CAGR} = \left(\frac{V_1}{V_0}\right)^{1/t} - 1
How it's derived

The formula

CAGR=(V1V0)1/t−1\text{CAGR} = \left(\frac{V_1}{V_0}\right)^{1/t} - 1 ROI=V1−V0V0\text{ROI} = \frac{V_1 - V_0}{V_0}

V0V_0 is the starting value, V1V_1 the ending value and tt the number of years.

Where it comes from

ROI is the total percentage change: how much you gained, relative to what you put in. It ignores time, so a 65% gain over 5 years and over 20 years look the same.

CAGR answers a better question: what steady yearly growth rate would turn V0V_0 into V1V_1 over tt years? Steady growth at rate gg multiplies the value by (1+g)(1+g) each year:

V0(1+g)t=V1V_0 (1 + g)^t = V_1

Divide by V0V_0, then take the tt-th root of both sides:

1+g=(V1V0)1/t1 + g = \left(\frac{V_1}{V_0}\right)^{1/t}

Real investments go up and down. CAGR smooths that out into the one rate that would have landed in the same place.

Worked example

$10,000 grows to $16,500 over 5 years:

ROI=650010000=65%CAGR=1.651/5−1=10.5%\text{ROI} = \frac{6500}{10000} = 65\% \qquad \text{CAGR} = 1.65^{1/5} - 1 = 10.5\%

Note that 65% ÷ 5 = 13% overstates the yearly return. Compounding means each year’s growth builds on the last.

Watch out for

  • Deposits and withdrawals. CAGR assumes nothing was added or taken out. If you contributed along the way, the result will overstate your return.
  • Volatility hides. Two investments with the same CAGR can have had very different rides.

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