ROI Formula

The ROI formula expresses the return on an investment as a percentage of the amount invested. Understanding each component and how they interact is essential for correct calculation and interpretation.

Basic Formula

The standard ROI formula is:

ROI = [(Final Value − Initial Investment) / Initial Investment] × 100

In notation: ROI = [(V_f − I) / I] × 100%, where:

• V_f = Final value (proceeds from sale, redemption, or current market value)
• I = Initial investment (amount originally invested)

The numerator (V_f − I) is the net gain or loss. Dividing by I scales the return to the size of the investment. Multiplying by 100 converts the result to a percentage.

Alternative Form

Some sources write ROI as:

ROI = (Net Gain / Cost of Investment) × 100

This is equivalent. Net gain equals Final Value − Initial Investment, and Cost of Investment equals Initial Investment. The result is the same.

Including Costs

In practice, the "initial investment" often includes more than the purchase price. Transaction fees, commissions, and other costs reduce the effective return. A more comprehensive formula is:

ROI = [(Final Value − Total Cost) / Total Cost] × 100

where Total Cost = Purchase Price + Fees + Other Costs. Similarly, Final Value may be reduced by selling costs or taxes. The principle remains: compare what you end up with to what you put in. For a formal treatment of profit, see net profit.

Step-by-Step Example

You invest $25,000 in a mutual fund. After four years, you sell for $32,000. There were no fees.

1. Identify initial investment: I = $25,000
2. Identify final value: V_f = $32,000
3. Calculate net gain: $32,000 − $25,000 = $7,000
4. Divide by initial investment: $7,000 / $25,000 = 0.28
5. Multiply by 100: 0.28 × 100 = 28%

ROI = 28%. This is the total return over four years. To compare with investments held for different periods, use annualized ROI.

Annualized ROI Formula

Annualized ROI converts a multi-year return into an equivalent annual rate:

Annualized ROI = [(V_f / I)^1/n − 1] × 100

where n is the number of years. For the example above: (32,000/25,000)^(1/4) − 1 ≈ 0.0634, or about 6.34% per year. This reflects compound growth.

Handling Losses

When Final Value is less than Initial Investment, ROI is negative. Example: invest $10,000, sell for $8,000. Net gain = −$2,000. ROI = (−2,000 / 10,000) × 100 = −20%. Negative ROI indicates a 20% loss.

Common Errors

Avoid dividing by zero: Initial Investment must be positive. Avoid mixing periods: if Final Value and Initial Investment are in different currencies or at different times, adjust for consistency. Do not confuse simple ROI with annualized ROI when comparing investments with different holding periods. For more on pitfalls, see ROI Limitations.