ROI Formula

What is the ROI formula?

The standard ROI formula is [(final value − initial investment) ÷ initial investment] × 100, which scales total gain or loss to every dollar originally invested.

That investment return expression assumes one clear buy-in and one clear exit (or mark-to-market) value. When periods differ, annualized ROI adjusts the same idea to a per-year rate; uneven cash flows may call for IRR instead of a single ROI percentage.

The ROI formula expresses the return on an investment as a percentage of the amount invested: ROI = [(Final Value − Initial Investment) / Initial Investment] × 100. It is used to compare profitability across investments and is the basis for annualized ROI when holding periods differ.

This page provides a structured explanation of the ROI formula, variants, and notation used in financial return calculation, including formulas, examples, limitations, and comparisons with related financial metrics.

When to Use This Calculation

  • Evaluating investment profitability
  • Comparing multiple opportunities
  • Estimating return over time

Limitations of This Metric

  • Does not account for time value of money
  • Depends on assumptions
  • May not reflect risk

What Is ROI (Return on Investment)?

Return on Investment (ROI) is a financial metric used to evaluate the profitability of an investment relative to its cost.

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 ROI = (Net Gain ÷ Initial Investment) × 100.
  • Include all costs in "initial investment" for accurate ROI.
  • Use annualized ROI when comparing investments with different holding periods.

How to Calculate ROI

  1. Determine total investment cost.
  2. Calculate total return or profit.
  3. Subtract cost from return.
  4. Divide profit by investment.
  5. Multiply by 100 to express as a percentage.

Basic Formula

The standard ROI formula is:

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

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

The numerator (Vf − 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: Vf = $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 = [(Vf / 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.

Related ROI Topics