People type this into search every day: how do I calculate return on investment.
Return on investment is the gain or loss divided by the money you put in. Investor.gov’s annual return glossary calls an annual rate of return the profit or loss on an investment over a one-year period. The return on investment calculator starts with the whole holding period, then annualizes it when you type a time span.
ROI = (amount received − amount invested) ÷ amount invested
Annualized return = (received ÷ invested) ^ (1 ÷ years) − 1
The annualized line is the constant compound rate that turns the outlay into the amount received. Investor.gov’s compound interest page is that relationship: earnings on principal and on earlier earnings. Fees, tax, inflation, and cash added in the middle are left out. These examples use the amounts you type. They are not a forecast, and they are not investment advice.
Fig 1
Two amounts, then a rate
Divide the gain by what you put in
The holding-period rate uses the two amounts. Years turn that rate into a compound annual line.
Example 1. $25,000 comes back as $32,500 in three years
Calculator defaults:
- Amount invested: $25,000
- Amount received back: $32,500
- Years held: 3
Gain: 32,500 − 25,000 = $7,500.00.
Holding-period ROI: 7,500 ÷ 25,000 = 30%.
Annualized compound return: (32,500 ÷ 25,000) ^ (1 ÷ 3) − 1 = 1.3 ^ (1/3) − 1 = 9.1%.
Check the path at that 9.1% rate. Year 1: 25,000 × 1.091392883 = $27,284.82. Year 2: $29,778.46. Year 3: $32,500.00. The rate is the smooth yearly step that lands on the amount you got back.
Calculator result
Return on investment
- Amount invested
- $25,000.00
- Amount received back
- $32,500.00
- Years held
- 3 years
30%
return on investment
- Net gain or loss
- $7,500.00
- Annualized compound return
- 9.1%
- Amount invested
- $25,000.00
Fig 2 · 1/2
What the $32,500 is made of
$25,000 invested, three years
Invested
$25,000
Gain
$7,500
The amount invested is $25,000 of the $32,500 you get back.
The $7,500 gain is a 30% holding-period return.
The gain’s share of the ending pile is 7,500 ÷ 32,500 = 23.1%. That 23.1% is a different ratio. Example 8 walks what happens when the two ratios get swapped.
Fig 3 · 1/4
The 9.1% path to $32,500
Constant compound rate on $25,000
Balance
- Balance
| Point | Balance |
|---|---|
| Start | $25k |
| Year 1 | $27k |
| Year 2 | $30k |
| Year 3 | $33k |
Year 1 is $27,284.82.
Year 3 lands on $32,500.00.
Example 2. The same 30% on $2,000
- Amount invested: $2,000
- Amount received back: $2,600
- Years held: 3
Gain: 2,600 − 2,000 = $600.00.
ROI: 600 ÷ 2,000 = 30%.
Annualized: 9.1%.
The percents match example 1. A 30% return on $2,000 is a $600 gain. A 30% return on $25,000 is a $7,500 gain. The decision sits on the percent and on the dollars.
Example 3. The same dollars in one year
- Amount invested: $25,000
- Amount received back: $32,500
- Years held: 1
Gain: $7,500.00. Holding-period ROI: 30%. Annualized return: 30%.
With a one-year hold, the two rates are the same number. Investor.gov’s annual return is this case: profit or loss over a one-year period.
Example 4. The same dollars over five years and over ten
Keep $25,000 and $32,500. Change only the years.
Five years. The holding-period formula divides the gain by the amount invested, so it stays 30%. Annualized return: (1.3) ^ (1/5) − 1 = 5.4%.
Ten years. Holding-period ROI is still 30%. Annualized return: (1.3) ^ (1/10) − 1 = 2.7%.
Fig 4 · 1/2
30% held for longer
$25,000 received back as $32,500
- Holding period
- Annualized
| Category | Holding period | Annualized |
|---|---|---|
| 1 year | 30% | 30% |
| 3 years | 30% | 9.1% |
| 5 years | 30% | 5.4% |
| 10 years | 30% | 2.7% |
One year makes the holding-period rate and the annualized rate both 30%.
Ten years leaves the holding-period rate at 30% and the annualized rate at 2.7%.
A 30% holding-period return over ten years is a slow compound rate. The year field is what stops those two sentences from meaning the same thing.
Example 5. A loss: $20,000 comes back as $16,000
- Amount invested: $20,000
- Amount received back: $16,000
- Years held: 2
Gain: 16,000 − 20,000 = −$4,000.00. The calculator prints -$4,000.00.
ROI: −4,000 ÷ 20,000 = −20%. The label is loss on investment.
Annualized: (16,000 ÷ 20,000) ^ (1/2) − 1 = 0.8 ^ 0.5 − 1 = −10.6%.
The holding-period loss is 20% of the money you put in. Splitting that −20% across two years would be −10% a year. The compound line, the rate that shrinks $20,000 to $16,000, is −10.6%.
Calculator result
Return on investment
- Amount invested
- $20,000.00
- Amount received back
- $16,000.00
- Years held
- 2 years
-20%
loss on investment
- Net gain or loss
- -$4,000.00
- Annualized compound return
- -10.6%
- Amount invested
- $20,000.00
Example 6. Years left at zero
- Amount invested: $25,000
- Amount received back: $32,500
- Years held: 0
Gain: $7,500.00. ROI: 30%.
The annualized line is absent. The exponent divides by the year count, and a zero span has no exponent. Use 0 when you only want the holding-period rate, or when you do not know the dates yet.
Example 7. You double the money in five years
- Amount invested: $25,000
- Amount received back: $50,000
- Years held: 5
Gain: $25,000.00.
Holding-period ROI: 25,000 ÷ 25,000 = 100%.
Annualized: 2 ^ (1/5) − 1 = 14.9%.
The CAGR calculator on the same two balances prints 14.87%, because that page keeps two decimals. The ROI page rounds the annualized line to one decimal, 14.9%. The CAGR post walks the two-balance formula on its own. Here the same math is the annualized row under a holding-period return.
The rule of 72 estimates years to double as 72 ÷ rate. At 14.9% that estimate is 72 ÷ 14.9 = 4.8 years, close to the 5 years you typed. The ROI page solves the rate from the years. The rule of 72 estimates the years from a rate.
Example 8. Two divisions that come out as different numbers
Stay with example 1: $7,500 of gain, $25,000 invested, $32,500 received, 3 years. The holding-period ROI is 30%. The annualized rate is 9.1%.
Division A puts the gain over the amount received: 7,500 ÷ 32,500 = 23.1%. That is the gain’s share of the ending pile, the second slice in the figure above. It is the answer to “what fraction of the $32,500 is profit.” ROI divides by the $25,000 you put in.
Division B spreads the 30% evenly across the three years: 30 ÷ 3 = 10% a year. The compound line is 9.1%. The 10% figure adds the yearly rates. Compounding applies each year’s rate to a balance that already grew. The path in example 1 is the check: 9.1% a year reaches $32,500. A flat 10% a year would end higher than $32,500.
Year 1 at 10%: 25,000 × 1.10 = $27,500. Year 2: $30,250. Year 3: $33,275. That is $775 past the $32,500 you received. The 10% split overstates the yearly rate.
Example 9. The whole outlay comes back as zero
- Amount invested: $25,000
- Amount received back: $0
- Years held: 3
Gain: −$25,000.00, printed as -$25,000.00.
ROI: −25,000 ÷ 25,000 = −100%.
Annualized: (0 ÷ 25,000) ^ (1/3) − 1 = −100%.
A total loss is −100% whether you read the holding period or the annualized line. There is no lower rate hiding in the year count when the ending amount is zero. An invested amount of $0 has no rate at all. The calculator prints Need an investment, because the formula divides by that amount.
Example 10. A machine, a one-year tool, and a larger pile
The payback page recovers a $40,000 outlay at $16,000 of cash a year, which takes 2.5 years. ROI needs an ending amount, so you have to say when you stop counting.
Stop at three years. Cash received: 3 × 16,000 = $48,000.
ROI: (48,000 − 40,000) ÷ 40,000 = 20%. Gain: $8,000.00. Annualized over 3 years: 6.3%.
Stop at the payback date and treat the amount received as $40,000, the outlay itself.
ROI: (40,000 − 40,000) ÷ 40,000 = 0%. Annualized over 2.5 years: 0%.
Payback answers “when is the outlay back.” ROI on that same date answers “what did I earn past the outlay,” and the answer is zero if you stop the moment the outlay returns. Cash after that date is what makes the ROI positive. The payback formula ignores that later cash on purpose.
A one-year tool:
- Amount invested: $8,000
- Amount received back: $9,200
- Years held: 1
Gain: $1,200.00. ROI: 1,200 ÷ 8,000 = 15%. Annualized: 15%, because the hold is one year.
A larger pile over four years:
- Amount invested: $100,000
- Amount received back: $180,000
- Years held: 4
Gain: $80,000.00. ROI: 80,000 ÷ 100,000 = 80%. Annualized: (1.8) ^ (1/4) − 1 = 15.8%.
Fig 5 · 1/3
The dollar gain behind three rates
Holding-period gain, not the percent
Net gain
$2,000, 30%
$600
$25,000, 30%
$7,500
$100,000, 80%
$80,000
A 30% return on $2,000 is a $600 gain.
An 80% return on $100,000 is an $80,000 gain.
The 30% cases share a rate and differ by $6,900 of gain. The 80% case is a higher rate and a much larger pile. The compound interest post grows a balance forward. This page starts from the ending amount and solves the rate.
Calculator result
Compound annual growth rate
- Starting value
- $10,000.00
- Ending value
- $16,105.10
- Years
- 5 years
10%
compound annual growth rate
- Total change
- 61.1%
- Growth multiple
- 1.61×
- Years in the exponent
- 5
That card is the CAGR defaults: $10,000 to $16,105.10 in five years. 10,000 × 1.10 ^ 5 = 16,105.10, so the rate is 10%. Total change is 61.1%. The growth multiple is 1.61×. Same algebra as the annualized ROI line, with a starting value and an ending value.
Ten ROI cases side by side
| Example | Invested | Received | Years | Gain | ROI | Annualized |
|---|---|---|---|---|---|---|
| 1. Defaults | $25,000 | $32,500 | 3 | $7,500 | 30% | 9.1% |
| 2. Smaller pile | $2,000 | $2,600 | 3 | $600 | 30% | 9.1% |
| 3. One year | $25,000 | $32,500 | 1 | $7,500 | 30% | 30% |
| 4. Five years | $25,000 | $32,500 | 5 | $7,500 | 30% | 5.4% |
| 4. Ten years | $25,000 | $32,500 | 10 | $7,500 | 30% | 2.7% |
| 5. Loss | $20,000 | $16,000 | 2 | −$4,000 | −20% | −10.6% |
| 6. No year count | $25,000 | $32,500 | 0 | $7,500 | 30% | omitted |
| 7. Double | $25,000 | $50,000 | 5 | $25,000 | 100% | 14.9% |
| 8. Gain ÷ received | $25,000 | $32,500 | 3 | $7,500 | 23.1% is the wrong box | 9.1% is the compound line |
| 9. Total loss | $25,000 | $0 | 3 | −$25,000 | −100% | −100% |
| 10. Machine, 3 years | $40,000 | $48,000 | 3 | $8,000 | 20% | 6.3% |
| 10. Stop at payback | $40,000 | $40,000 | 2.5 | $0 | 0% | 0% |
| 10. One-year tool | $8,000 | $9,200 | 1 | $1,200 | 15% | 15% |
| 10. Larger pile | $100,000 | $180,000 | 4 | $80,000 | 80% | 15.8% |
Open the return on investment calculator with the amount you put in and the amount you got back. If the cash arrives as the same sum every year and you want the date the outlay is recovered, use the payback period page. If you have a start value and an end value and you want the smoothed yearly rate only, use the CAGR calculator.