# Return on Investment (ROI)

> Return on investment says how much profit you made for each dollar you spent, so you can compare a small investment with a large one.

Page: https://formulabro.yunusemrevurgun.com/finance/return-on-investment/  
Category: Finance  
Published: 2026-10-23  
Updated: 2026-10-23

## Formula

$$
\text{ROI} = \frac{\text{gain} - \text{cost}}{\text{cost}}
$$

Read it out loud: "R O I equals gain minus cost, all divided by cost. ROI means return on investment. The gain is the total money that came back, and the cost is the money you put in at the start."

## Before you start

- **Ratio and percent**: A **ratio** compares two amounts by dividing one by the other. A **percent** is the same ratio multiplied by 100 and read as 'out of 100'. So 0.75 is 75%, 1 is 100% and 1.5 is 150%. In a formula, a percent is usually written as a decimal first.
- **Cost, gain and profit**: The **cost** of an investment is the money put in at the start, in dollars. The **gain** is the total money that comes back, in dollars. The **profit** is the gain minus the cost, which is the extra money left over. If the gain is smaller than the cost, the profit is negative, which means a loss.
- **Fractions and brackets**: A fraction $\frac{a}{b}$ means $a$ divided by $b$. The top is the **numerator** and the bottom is the **denominator**. The division bar also works like brackets: everything above it is worked out first, so $\frac{50 - 20}{20}$ means subtract 20 from 50, then divide by 20.
- **Investment**: An **investment** is money put in now in the hope of getting more back later. It can be ingredients for a lemonade stand, a machine for a shop or shares in a company. The **return** is what comes back from it.
- **Negative numbers**: A **negative number** is smaller than zero and is written with a minus sign, such as $-20$. When money is involved, a negative result means a loss: a result of $-20$ dollars means 20 dollars was lost.

More notation help: https://formulabro.yunusemrevurgun.com/math-basics/

## What each symbol means

- $\text{ROI}$: **Return on investment**, a plain ratio that says how much profit came back for each dollar spent. It has no unit of its own. Written as a percent, it is multiplied by 100, so a ratio of 1.5 is 150%.
- $\text{gain}$: The **total money that came back** from the investment, in dollars, such as the sales a stand took in. It includes the cost itself, so it is not yet the profit.
- $\text{cost}$: The **money put in** at the start, in dollars, such as the price of ingredients. It is the amount the investment is measured against.

## The formula piece by piece

- $\text{cost}$: Start with the money put in at the start, in dollars. It is the bottom of the fraction, because the whole return is measured against what was spent.
- $\text{gain}$: The total money that came back, in dollars. It includes the cost itself, so it is not yet the profit.
- $\text{gain} - \text{cost}$: Subtract the cost from the gain to get the profit, which is the money that is extra. A negative answer means the investment lost money.
- $\frac{\text{gain} - \text{cost}}{\text{cost}}$: Divide the profit by the cost. This gives the profit for each dollar spent, as a plain ratio that can be compared with other investments.
- $\text{ROI} = \frac{\text{gain} - \text{cost}}{\text{cost}}$: The whole formula in one sentence: **return on investment is the profit divided by the cost, which tells you how many dollars of profit came back for each dollar put in.**

## What the formula is doing, and why

Return on investment, or ROI, answers one question: **for the money I spent, how much did I make?** It turns a profit in dollars into a share of what was spent, so you can compare a small venture with a large one. The formula subtracts the cost from the gain to find the profit, and then divides by the cost.

**Why subtract the cost?** The gain counts all the money that came back, and that includes the money that was only put in to begin with. Subtracting the cost leaves the profit, which is the money that is genuinely extra. A result of zero means you got back exactly what you paid. A negative result means you lost money.

**Why divide by the cost?** Dividing puts the profit on a per-dollar basis. Thirty dollars of profit from a 20 dollar outlay is a much better result than thirty dollars of profit from a 300 dollar outlay, and the division shows that at once. The bigger the cost, the more profit you need to reach the same ROI.

**Why people write it as a percent.** The formula gives a plain ratio, such as 1.5. Multiplying by 100 writes the same number as a percent, 150%. A percent is easy to read and easy to compare, which is why ROI is usually quoted this way. An ROI of 100% means the profit equals the cost, so the money has doubled.

**What ROI leaves out.** The formula has no time in it. A 50% return earned in one week and a 50% return earned over ten years give the same ROI, but they are very different results per year. To compare investments over different lengths of time, people use an annual rate such as CAGR or IRR.

## An everyday picture

Think of planting seeds in a garden. A bag of seeds costs a certain amount, and at harvest you sell the crop for more money. The ROI is the harvest's extra value compared with the seed money, measured per dollar of seed: what came back, minus what was planted, divided by what was planted. It tells you how well each dollar of seed worked, but not how long the crop took to grow.

## Worked example: Which lemonade stand did better?

Two stands sell lemonade on the same afternoon. The first stand spends 20 dollars on lemons, sugar and cups, and sells lemonade for 50 dollars. The second stand spends 40 dollars on a bigger setup and sells lemonade for 70 dollars. Which stand has the better return on investment?

1. **Write down the cost and the gain for the first stand.** The stand spent 20 dollars, so the cost is 20 dollars. Over the afternoon it took in 50 dollars from sales, so the gain, which is the total money that came back, is 50 dollars.
2. **Find the profit.** Subtracting the cost from the gain removes the money that was only spent on ingredients, which leaves the profit: $50 - 20 = 30$ dollars. Thirty dollars is the extra money the stand kept after paying for its supplies.
3. **Divide the profit by the cost.** The ROI formula divides the profit by the cost, so $\text{ROI} = \frac{50 - 20}{20} = \frac{30}{20} = 1.5$. The ratio 1.5 means the stand made 1.5 dollars of profit for every dollar it spent.
4. **Turn the ratio into a percent.** Multiplying by 100 says the same thing as a percent: $1.5 \times 100 = 150$, so the ROI is 150%. Because the profit is larger than the cost, the ROI is above 100%.
5. **Find the ROI for the second stand.** This stand spent 40 dollars and got back 70 dollars, so its profit is $70 - 40 = 30$ dollars, the same as the first stand. Dividing by its cost gives $\frac{70 - 40}{40} = \frac{30}{40} = 0.75$, which is 75%. The two stands made the same profit, but the first earned more on each dollar it spent.
6. **Note what the ROI does not show.** The formula has no time in it, so it does not say how long each stand traded. If both ran for the same afternoon, the comparison is fair. If one ran for a month, the ROI does not tell you which stand earned more per day.

**Answer:** The first stand has the better return on investment: **150%**, against 75% for the second. Both made 30 dollars of profit, but the first earned 1.5 dollars for every dollar it spent, while the second earned only 0.75 dollars.

## Common mistakes

- Subtracting the cost twice. In the formula the gain is the total money that came back, so the cost is subtracted exactly once. Treating the profit as the gain and subtracting the cost again understates the return.
- Dividing by the gain instead of the cost. Dividing by the gain gives a different measure, and it no longer shows the return on the money spent, which is what ROI is for.
- Comparing ROIs measured over different lengths of time as if they were fair. A 50% ROI in one week and a 50% ROI over ten years look the same in the formula, but they are very different per year.
- Reading a 150% ROI as 150 dollars of profit. ROI is a ratio. The dollars of profit come from the subtraction, and in the example they are 30 dollars.

## Where you will meet it

- Marketing, where a company divides the extra sales from an advert by what the advert cost.
- Personal money decisions, such as whether a training course or a tool pays back its price.
- Business reports, where managers compare projects by the profit each one returns for every dollar spent.
- Fund and portfolio reports, which quote the total return over a period as a percent of the money invested.

## Questions people ask

### Is ROI the same as profit?

No. Profit is an amount in dollars, while ROI is that profit divided by the cost, so it is a ratio. Two investments with the same profit can have very different ROIs when they cost different amounts.

### Can ROI be negative?

Yes. If the gain is smaller than the cost, the top of the fraction is negative, and so is the ROI. For example, spending 50 dollars and getting back 40 dollars gives $\frac{40 - 50}{50} = -0.2$, which is minus 20%.

### Why does ROI ignore time?

The formula only compares the money put in with the money that came back. It does not include how long the money was tied up. To account for time, people use a yearly rate such as CAGR, or the IRR when cash comes in and goes out at different times.

### Is a high ROI always good?

Not on its own. A high ROI can come from a small or risky investment, and the percent hides the size of the stake. Look at the cost, the time taken and how certain the gain is before deciding.

## Related formulas

- [Compound Annual Growth Rate (CAGR)](https://formulabro.yunusemrevurgun.com/finance/compound-annual-growth-rate/)
- [Internal Rate of Return (IRR)](https://formulabro.yunusemrevurgun.com/finance/internal-rate-of-return/)
- [Net Present Value (NPV)](https://formulabro.yunusemrevurgun.com/finance/net-present-value/)

## Sources

- [Return on investment, Wikipedia](https://en.wikipedia.org/wiki/Return_on_investment)
- [Rate of return, Wikipedia](https://en.wikipedia.org/wiki/Rate_of_return)
- [Investment, Wikipedia](https://en.wikipedia.org/wiki/Investment)

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