ROI Calculator (Return on Investment and Annualized ROI)

Enter the amount invested and the amount returned (the money you got back). Set the period by dates or in years, and the gain or loss, ROI (return on investment) and annualized ROI are calculated together.

Amount invested ($)

Amount returned ($)

How to set the period

Start date (invested)

End date (returned)

Years invested

Enter amounts in dollars as plain numbers. It also works when the amount returned is smaller than the amount invested (a loss). If you only need the ROI, any period (for example, 1 year) is fine.

Result and graph

Enter the amount invested and the amount returned on the left and press "Calculate". The result and a graph will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the amount invested and the amount returned, and get the gain or loss, ROI (return on investment), annualized ROI and investment period all at once
Set the period either by dates (start date and end date) or by length in years (decimals such as 2.5 years are fine)
Investments held for different lengths of time can be compared on the same scale, "% per year", with annualized ROI
Includes a bar chart that shows the gain or loss at a glance, an explanation of the formulas, and copy-and-paste formulas for Excel, Google Sheets and Python

ROI here is a math calculation that does not include fees or taxes. What you actually keep from a real investment changes by the trading fees and taxes. This page is for calculating and learning and does not recommend any investment.

What is this calculation used for?

Deciding on an equipment purchase (manufacturing, restaurants and more)

"If we buy a $30,000 machine, cost savings and extra sales should bring back $45,000 in total over 5 years." Treat that $45,000 as the amount returned: the ROI is $(45000 - 30000) \div 30000 = 0.5$ (50%), or about 8.4% a year annualized.
ROI is a standard input when a company approves equipment or system purchases. Future profits are only estimates, though, so it is good practice to also run the numbers with a cautious estimate.

Measuring advertising results (marketing ROI)

If you spend $10,000 on ads and the gross profit from those ads is $15,000, the marketing ROI is $(15000 - 10000) \div 10000 = 0.5$ (50%).
In online advertising, the basic approach is to move budget toward campaigns with a positive ROI. Just be careful to calculate with profit (revenue minus the cost of goods, that is, gross profit), not revenue, or you will overestimate the effect.

Getting a feel for the return on education

If you take a $3,000 course, earn a certification, and your salary goes up by $5,000 in a new job, the ROI is about 67% from the first year alone. "Investing in yourself" can be pictured with the same formula.
Of course, raises and passing exams are not guaranteed, and knowledge and confidence have value that does not show up in dollars. Use the number as a calm guide to whether the cost seems worth it.

How ROI relates to rental property yield

If a $300,000 property brings in $18,000 of rent a year, $18000 \div 300000 = 0.06$ (6%) is its gross rental yield. This is the income per year as a share of the amount invested, a relative of annualized ROI.
ROI looks at the total over the whole period, while yield looks at one year from the start. Gross yield does not include property management, repairs, taxes, insurance or vacancies, so what you actually keep is less. (Investors use the cap rate, based on net operating income, to include those costs.)

Comparing investments held for different lengths of time

Fund A returned +30% in 3 years and fund B returned +45% in 5 years. Which did better? By ROI alone B wins, but annualized, A earned about 9.1% a year and B about 7.7% a year, so A did better per year.
Results over different lengths of time can only be compared fairly after you turn them into annualized ROI. Keep in mind that past performance does not guarantee future results.

Formulas and figures

Formula for ROI (return on investment)

Figure

Standard notation (the usual math form)

$\mathrm{ROI}$ $=$ $($ $R$ $-$ $C$ $)$ $\div$ $C$

In words (symbols replaced with words)

④ ROI: return on investment $=$ $($ ① $R$: amount returned $-$ ② $C$: amount invested $)$ $\div$ ③ $C$: amount invested

The formula in words

① From the $R$: amount returned

② subtract the $C$: amount invested to get the gain or loss

③ divide it by the $C$: amount invested

④ and you get the ROI: return on investment (multiply by 100 to write it as a %)

Quick example

If you invest $10,000 and get $15,000 back, the ROI is

ROI: return on investment $=$ $($ amount returned ($15,000) $-$ amount invested ($10,000) $)$ $\div$ amount invested ($10,000)

$(15000 - 10000) \div 10000 = 5000 \div 10000 = 0.5\ \ (50\%)$

Key idea

ROI is the percentage of profit compared with the money you invested. As math, it is exactly the same as a percentage change (a rise or fall in value), with "old value" replaced by the amount invested and "new value" by the amount returned (see "Percentage Change Calculator" in the related pages). If the amount returned is smaller than the amount invested, both the gain and the ROI are negative (a loss).

Annualized ROI (ROI per year)

Figure

Standard notation (the usual math form)

$G$ $=$ $R$ $\div$ $C$

$A$ $=$ $G$ $1/n$ $-$ $1$

In words (symbols replaced with words)

③ $G$: growth multiple $=$ ① $R$: amount returned $\div$ ② $C$: amount invested

⑤ $A$: annualized ROI $=$ $G$: growth multiple ④ to the power $1/n$ $-$ $1$

The formula in words

① Divide the $R$: amount returned

② by the $C$: amount invested

③ to get the $G$: growth multiple (how many times the money grew)

④ raise it to the power $1/n$ ($n$ = years invested) to turn it into a growth factor per year

⑤ then subtract 1 (the original money), and you get the $A$: annualized ROI (multiply by 100 to write it as a %)

Quick example

If $10,000 grows to $20,000 (2 times) in 2 years, the annualized ROI is

growth multiple (2) $=$ amount returned ($20,000) $\div$ amount invested ($10,000)

$A$: annualized ROI $=$ growth multiple (2) to the power $1/2$ (for 2 years) $-$ $1$

$20000 \div 10000 = 2$

$2^{1/2} = \sqrt{2} \approx 1.414$

$1.414 - 1 = 0.414\ \ (41.4\%)$

Key idea

ROI has one weakness: it ignores time. "ROI of 100% in 10 years" and "ROI of 100% in 1 year" are very different, yet the ROI number is the same. Annualized ROI fixes this: it is the % per year you would get if the money grew by the same factor every year (averaging the yearly factors by multiplication, the idea of a geometric mean). Always use it when you compare investments held for different lengths of time. Raising to the power $1/n$ finds the number that gives the original number when raised to the power $n$ (the $n$th root). In the example, $2^{1/2}$ is "the number that gives 2 when squared" = $\sqrt{2} \approx 1.414$.

Formula for the years invested from dates

Figure

Standard notation (the usual math form)

$n$ $=$ $d$ $\div$ $365.25$

In words (symbols replaced with words)

② $n$: years invested $=$ ① $d$: number of days $\div$ $365.25$

The formula in words

① Divide the $d$: number of days by the average length of a year, 365.25 days

② and you get the $n$: years invested

Quick example

If you invest on January 1, 2026 and get your money back on July 1, 2026 (181 days later), the years invested are

$n$: years invested $=$ number of days (181) $\div$ $365.25$

$181 \div 365.25 \approx 0.496$

Key idea

To even out leap years (once every 4 years, a year has 366 days), it is common to divide by 365.25 instead of 365. When the period is longer than 1 year, this page counts whole years up to the same calendar date as exact years, and converts only the remaining days (less than 1 year) with this formula. For example, from January 1, 2020 to January 1, 2023 is exactly 3.000 years.

ROI, found as "gain or loss ÷ amount invested", is the report card of an investment. But it ignores time, so when you compare investments held for different lengths of time, compare their annualized ROI (the growth turned into a factor per year).

Symbols and terms

Symbols

ROI	R O I	Return on investment. The gain or loss as a % of the money invested. (Example - if $10,000 becomes $15,000, the ROI is 50%.)
$C$	C	The amount invested (cost). All the money you put into the investment.
$R$	R	The amount returned. All the money that finally came back from the investment, such as the sale price and distributions (the whole amount, including your original money, not just the profit).
$G$	G	The growth multiple. How many times the amount invested grew ($R \div C$). (Example - $10,000 → $15,000 is 1.5 times.)
$n$	n	The years invested. The time from investing to getting the money back, in years; it can be a decimal such as 2.5 years.
$d$	d	The number of days from the start date to the end date. Divide by 365.25 to turn it into years.
$A$	A	Annualized ROI. The ROI turned into "% per year", used to compare investments held for different lengths of time.
$G^{1/n}$	G to the one over n	The growth multiple $G$ to the power $1/n$: the number that gives $G$ when raised to the power $n$, which is the average growth factor per year. (Example - doubling in 2 years is $2^{1/2} \approx 1.414$ times per year.)

Terms

ROI (return on investment)	The profit on an investment as a share of the money invested. It is found as "gain or loss ÷ amount invested" and written as a %. It is one of the most widely used measures in business.
annualized	Restated as "% per year", so that results over different lengths of time can be compared fairly. Financial documents may call it the annualized return or CAGR (compound annual growth rate).
geometric mean	An average taken by multiplication. Unlike the usual average (the arithmetic mean: add up and divide), you multiply all $n$ numbers together and raise the product to the power $1/n$. It is the right average for amounts that build up by multiplication, such as growth factors and growth rates.
nth root	The number that gives a given number when raised to the power $n$. It can be written as the power $1/n$. (Example - the cube root of 8, $8^{1/3}$, is the number that gives 8 when cubed, which is 2.)
marketing ROI	ROI that treats advertising and promotion spending as an investment. It is "(profit added by the ads − ad spend) ÷ ad spend". Be careful to use profit (gross profit), not revenue, or you will overestimate the effect.
yield	The income per year as a share of the amount invested. ROI looks at the total over the whole period, while yield looks at one year from the start. It is used for rental property and bonds, and is a relative of annualized ROI.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Percents (Grades 6–7)	Knowing that a percent is found as "part ÷ whole" Being able to switch between decimals and percents, such as 0.5 and 50%
Positive and negative numbers (Grades 6–7)	Writing a loss as a negative number Knowing that a negative number divided by a positive number is negative
Exponents and roots (Grade 8 to Algebra 2)	Knowing that a power is repeated multiplication of the same number, as in $2^3 = 2 \times 2 \times 2$ Knowing that the power $1/n$ finds the number that gives the original number when raised to the power $n$ (the $n$th root; used in annualized ROI)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table for ROI (return on investment)

Amount invested	10000
Amount returned	15000
ROI (%)	=(B2-B1)/B1*100

Table for annualized ROI

Amount invested	10000
Amount returned	15000
Years invested	3
Annualized ROI (%)	=((B2/B1)^(1/B3)-1)*100

Table for the years invested from dates

Start date	2026-07-03
End date	2030-12-31
Years invested	=(B2-B1)/365.25

In the first table, enter the amount invested in B1 and the amount returned in B2, and B3 shows the ROI as a % number (the example shows 50, which is 50%).
The second table adds the years invested in B3 and gives the annualized ROI (about 14.47 in the example, 14.47% a year). "^" is a power, and "^(1/B3)" is the part that finds the number that gives the total growth when raised to the power B3 (the growth factor per year).
The third table subtracts one date from the other to get the number of days and divides by 365.25 to turn it into years (about 4.496 years in the example). If the result cell shows a date, change the cell format to Number. For periods of exactly a whole number of years, the result can differ from this page by about 1/1000 of a year because of leap years.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table for ROI (return on investment)

Amount invested	10000
Amount returned	15000
ROI (%)	=(B2-B1)/B1*100

Table for annualized ROI

Amount invested	10000
Amount returned	15000
Years invested	3
Annualized ROI (%)	=((B2/B1)^(1/B3)-1)*100

Table for the years invested from dates

Start date	2026-07-03
End date	2030-12-31
Years invested	=(B2-B1)/365.25

The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace column B with your own numbers. Subtracting dates works the same way.

How to calculate it in Python

from datetime import date

invested = 10000   # amount invested ($)
returned = 15000   # amount returned ($)
years = 3          # years invested

gain = returned - invested                                # gain or loss
roi = gain / invested * 100                               # ROI (%)
annualized_roi = ((returned / invested) ** (1 / years) - 1) * 100  # annualized ROI (%)

print(f"Gain or loss: ${gain}")
print(f"ROI: {roi:.2f}%")
print(f"Annualized ROI: {annualized_roi:.2f}%")

# To set the period by dates, divide the number of days by 365.25 to get years
days = (date(2030, 12, 31) - date(2026, 7, 3)).days
years_from_dates = days / 365.25
print(f"Years invested: {years_from_dates:.3f}")

Runs with the standard library only. "**" is a power, and "** (1 / years)" is the part that turns the growth into a factor per year. Change the amount invested, amount returned and years at the top, then run it.

How to write it in LaTeX and other math languages (copy and paste)

Formula for ROI (return on investment)

ROI = (R − C) ÷ C

\mathrm{ROI} = \frac{R - C}{C}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>ROI</mi>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>R</mi><mo>&#x2212;</mo><mi>C</mi></mrow>
      <mi>C</mi>
    </mfrac>
  </mrow>
</math>

ROI = (R - C) / C

(r - c)/c

ROI := (r - c)/c;

ROI = (r - c)/c;

ROI = (R − C)/C

Annualized ROI (ROI per year)

A = \left(\frac{R}{C}\right)^{1/n} - 1

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>A</mi>
    <mo>=</mo>
    <msup>
      <mrow>
        <mo>(</mo>
        <mfrac><mi>R</mi><mi>C</mi></mfrac>
        <mo>)</mo>
      </mrow>
      <mrow><mn>1</mn><mo>/</mo><mi>n</mi></mrow>
    </msup>
    <mo>&#x2212;</mo>
    <mn>1</mn>
  </mrow>
</math>

A = (R/C)^(1/n) - 1

(r/c)^(1/n) - 1

A := (r/c)^(1/n) - 1;

A = (r/c)^(1/n) - 1;

A = (R/C)^(1/n) − 1

Formula for the years invested from dates

n = d ÷ 365.25

n = \frac{d}{365.25}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>n</mi>
    <mo>=</mo>
    <mfrac>
      <mi>d</mi>
      <mn>365.25</mn>
    </mfrac>
  </mrow>
</math>

n = d / 365.25

d/365.25

n := d/365.25;

n = d/365.25;

n = d/365.25

How to have ChatGPT do the calculation

You are an investment calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

I invested $10,000, and 3 years later I got $15,000 back.
Find each of the following:
1. The gain or loss (in dollars)
2. The ROI (return on investment, in %, to 2 decimal places)
3. The annualized ROI (in %, to 2 decimal places) = (amount returned ÷ amount invested) to the power (1/years) − 1

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula

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ROI	R O I	Return on investment. The gain or loss as a % of the money invested. (Example - if $10,000 becomes $15,000, the ROI is 50%.)
\(C\)	C	The amount invested (cost). All the money you put into the investment.
\(R\)	R	The amount returned. All the money that finally came back from the investment, such as the sale price and distributions (the whole amount, including your original money, not just the profit).
\(G\)	G	The growth multiple. How many times the amount invested grew (\(R \div C\)). (Example - $10,000 → $15,000 is 1.5 times.)
\(n\)	n	The years invested. The time from investing to getting the money back, in years; it can be a decimal such as 2.5 years.
\(d\)	d	The number of days from the start date to the end date. Divide by 365.25 to turn it into years.
\(A\)	A	Annualized ROI. The ROI turned into "% per year", used to compare investments held for different lengths of time.
\(G^{1/n}\)	G to the one over n	The growth multiple \(G\) to the power \(1/n\): the number that gives \(G\) when raised to the power \(n\), which is the average growth factor per year. (Example - doubling in 2 years is \(2^{1/2} \approx 1.414\) times per year.)

ROI Calculator (Return on Investment and Annualized ROI)

Table of Contents

What you can do on this page

What is this calculation used for?

Formulas and figures

Symbols and terms

Symbols

Terms

Good to know before you start

How to calculate it in Excel

How to calculate it in Google Sheets

How to calculate it in Python

How to write it in LaTeX and other math languages (copy and paste)

How to have ChatGPT do the calculation

How to Use

DataChef Features

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Payback Period Calculator (Simple and Discounted Payback)

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Average Return Calculator (Annualized Geometric Average and Cumulative Return)

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ROAS Calculator (Return on Ad Spend and Break-Even ROAS)

ROAS is revenue as a share of ad spend. See how it differs from ROI (based on profit), and find the break-even ROAS from your gross margin

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