Return on Investment Calculator

Return on investment is net gain expressed as a fraction of what you put in:

$ROI = \frac{\text{net gain}}{\text{cost}} = \frac{V_{\text{end}} - V_{\text{begin}}}{V_{\text{begin}}}$

Multiply by 100 for a percentage. A complete net gain counts everything that moved:

$\text{net gain} = (\text{sale proceeds} + \text{income received}) - (\text{purchase cost} + \text{fees and costs})$

Income means dividends, interest, coupons or rent collected while holding; costs mean commissions, spreads, management fees and any expense of owning the position. Leaving either out is the most common way an ROI figure ends up wrong.

The two useful rearrangements:

$V_{\text{end}} = V_{\text{begin}}(1 + ROI), \qquad V_{\text{begin}} = \frac{V_{\text{end}}}{1 + ROI}$

ROI is dimensionless and timeless — it says how much, never how fast. That is its central weakness, and the next section is the fix.

Putting returns on a per-year basis

Two returns are only comparable once they cover the same length of time:

$ROI_{\text{annual}} = (1 + ROI)^{1/t} - 1$

with $t$ the holding period in years, fractions allowed. This is the compound annual growth rate — the constant yearly rate that reproduces the same ending value. Going the other way, $ROI = (1 + ROI_{\text{annual}})^{t} - 1$.

Dividing total return by $t$ is not the same and always overstates the yearly figure, because it ignores compounding.

Total return versus price return

Price return counts only the change in price. Total return adds reinvested income, and over long horizons the gap is large. Say which one you are quoting.

Real return

To express a return in purchasing power, deflate it exactly rather than by subtraction:

$ROI_{\text{real}} = \frac{1 + ROI}{1 + \pi} - 1$

Every figure here is arithmetic on numbers you supply. Past return is a measurement, not a projection, and this page makes no recommendation about any investment.

• Dividing by the ending value: the denominator is what you invested. Using $V_{\text{end}}$ understates every positive return.
• Comparing returns over different horizons: 40% over 5 years is worse per year than 18% over 2. Annualise before ranking anything.
• Dividing total return by the number of years: $48.2\%$ over 3.5 years is not $13.8\%$ a year. Take the root of the growth factor instead.
• Ignoring fees and taxes: commissions and spreads come out of the gain; tax treatment depends on your jurisdiction, so enter your own figures.
• Forgetting dividends and interest: excluding income turns total return into price return and understates the result.
• Adding contributions to the numerator: money you paid in later is not a gain. Either treat each contribution as its own investment or use a money-weighted measure.
• Reporting ROI on a loss without the sign: a negative ROI is a negative number; dropping the minus sign inverts the meaning.