How do I calculate the rate of return on an investment?

Work out the net profit first, which is the final value plus any income received minus the initial value, then divide it by the initial value. Buying at 10,000, selling at 12,500 and collecting 400 of dividends gives a net profit of 2,900 and a rate of return of 29 percent over the holding period. That is the total return for the whole time you held it, not a yearly figure.

What is the difference between the rate of return and the annualized return?

The rate of return covers the entire holding period; the annualized return spreads it over the years and compounds it. On the default case 29 percent over three years annualizes to 8.859 percent. Dividing 29 by three would give 9.667 percent, which is a different convention, and the compounded figure is the one printed here because it answers what an equivalent steady annual rate would have been.

Why is there a separate box for income received?

Because dividends and interest are part of your return and the final value does not contain them. If a position sold for 12,500 and paid you 400 along the way, the final value is 12,500, not 12,900 — folding the income into the price would misstate what the holding was worth when you closed it. Put the sale price in one box and the income in the other, and the net profit comes out right at 2,900.

Can the rate of return be positive if the price did not move?

Yes, and that is the ordinary case for an income holding. Buy at 10,000, hold for four years, sell at 10,000 and collect 1,200 of dividends, and the net profit is 1,200 with a rate of return of 12 percent and an annualized return of 2.874 percent. A growth-only calculation would report zero on all three, because it cannot see the income. This is what a flat-trading dividend payer, a bond held to maturity or a savings account looks like.

Can the rate of return be negative?

Yes. Sell at 10,000 something you paid 12,000 for, having collected 500 of income in two years, and the net profit is −1,500 with a rate of return of −12.5 percent. If the value goes all the way to zero the rate of return is −100 percent, and so is the annualized return, because losing everything is losing everything regardless of how long it took. Income softens a loss but does not turn it into a gain.

Is the rate of return the same as CAGR?

They coincide when there is no income. With the same initial value, the same final value, the same number of years and no dividends, this page and the CAGR calculator return identical figures — 25 percent and 7.722 percent on 10,000 growing to 12,500 over three years. They differ once the holding paid you something, because the CAGR calculation has no income box, and they also differ in emphasis: the CAGR page leads with the annualized figure while this page leads with the total return.

Does the holding period have to be a whole number of years?

This page takes whole years, because the annualized return raises the growth to the power of one over the number of years and a fractional exponent from a partial year would imply compounding over a fraction of a period. If you held something for eighteen months, the cleanest approach is to annualize over the exact fraction using the same formula elsewhere, or to treat the period in months consistently and multiply the monthly return by twelve if you want the linear convention instead.

Rate of Return Calculator

Result

29.00%

Rate of return (%)

Annualized return: 8.859%
Net profit: 2,900.00

This page answers the question you ask after a position is closed: what did it actually return, and what does that work out to per year? Two inputs come from the trade itself, the initial value and the final value, and one comes from everything that arrived in between — dividends, interest, distributions, any income the holding paid out while you owned it. That third box is the whole reason the page exists. The final value is the price you sold at, not the price plus the income, because folding 400 of dividends into a sale price of 12,500 would say the position ended at 12,900, which it did not. It ended at 12,500 and separately paid you 400. Given 10,000 in, 12,500 out, 400 received and three years held, the net profit is 2,900 and the rate of return is 29 percent — a figure most people would read as a good three years. Beside it the page prints the annualized return, 8.859 percent, which is where that 29 percent actually sits once it is spread across the years and compounded rather than divided. The gap between those two numbers is the point of showing them together: 29 divided by three is 9.667, and the honest figure is 8.859, because a return that compounds does not divide evenly. The reference table takes one holding and walks the income from nothing to 1,500, which shows how much of a return can come from being paid rather than from the price moving at all.

One holding, 10,000 to 12,500 over 3 years, at six levels of income

Income received	Net profit	Rate of return	Annualized return
0	2500	25	7.722
200	2700	27	8.293
400	2900	29	8.859
700	3200	32	9.696
1000	3500	35	10.521
1500	4000	40	11.869

Only the income changes across these rows, so the table isolates the one input that separates this page from a plain growth calculation. The first row is 2500 of net profit, 25 percent and 7.722 percent — and that row is where this page and the CAGR calculator return the same three numbers, because with no income the two calculations are the same calculation. Read down from there and every column moves together: an extra 1,500 of dividends turns 2,500 of profit into 4,000, 25 percent into 40 percent, and 7.722 percent into 11.869 percent, on a price that never changed. The last row is the one to notice, because 1,500 of the 4,000 of net profit — more than a third — came from being paid rather than from the price. That is what an income box is for, and it is why leaving it out understates the return on anything that pays you while you hold it.

Formula

Net profit = final value + income received − initial value Rate of return = net profit ÷ initial value × 100 Annualized return = ((initial value + net profit) ÷ initial value) ^ (1 ÷ years) − 1

Initial value: What the position cost when it was opened — the base every percentage on this page is measured against
Final value: What it was worth when it was closed, not counting any income it paid out — dividends and interest go in the next box instead of being folded into this one
Income received: Everything the holding paid you while you owned it: dividends, interest, distributions, and for a bond the coupons
Years: How long the position was held, which is what the annualized return is spread over and the exponent it is compounded at
Net profit: Final value plus income received minus initial value — what you are actually ahead by, and the numerator of the rate of return

Use it when you have closed or are reviewing a position and want to know what it returned, especially if it paid you along the way. The income box is what separates this page from a plain growth calculation: if the holding sent you dividends or interest, that money is part of your return and leaving it out understates the result, while adding it to the final value would misstate what the position was worth at the end. Keep the two separate and this page handles the rest. It is also the page for the question of whether a big-looking total was actually good — three years of 29 percent is an annualized return of 8.859 percent, and seeing both numbers side by side is how you tell a strong run from a long one. The annualized return here is compounded, not the rate of return divided by the number of years. Those two conventions both exist and both come from regulators, so the choice is worth knowing about: dividing 29 percent by three gives 9.667 percent, and compounding gives 8.859 percent. This page prints the compounded figure because that is the one that answers what an equivalent steady annual rate would have been. Note also that the annualized return is a rate, not a forecast — a holding that returned 8.859 percent a year over three years is not promised to keep doing so, and a single three-year window is a small sample.

Worked examples

10,000 in, 12,500 out, 400 of dividends, held 3 years
1. Net profit: 12,500 + 400 − 10,000 = 2,900
2. Rate of return: 2,900 ÷ 10,000 × 100 = 29.00%
3. Annualized return: (12,900 ÷ 10,000)^(1 ÷ 3) − 1 = 8.859%
4. Note what the annualized figure is not: 29 ÷ 3 = 9.667%, which is the linear reading
The default case, and the pair of numbers this page is built around. A 29 percent total over three years sounds better than it is, because compounding means the equivalent steady rate is 8.859 percent, not the 9.667 percent you get by dividing. If the 2,900 had come entirely from the price moving, the position would have had to end at 12,900; it ended at 12,500 and paid 400, which is why the income has its own box.
The same holding with no income — 25% and 7.722%
1. Net profit: 12,500 + 0 − 10,000 = 2,500
2. Rate of return: 2,500 ÷ 10,000 × 100 = 25.00%
3. Annualized return: (12,500 ÷ 10,000)^(1 ÷ 3) − 1 = 7.722%
This is where this page and the CAGR calculator overlap, and it is worth being precise about it. With the same two endpoints, the same three years and no income, the two pages return the identical figures — 25 percent and 7.722 percent. That is a mirror rather than a duplicate, and the test is which pieces of paper you are holding. If all you have is what you paid, what you sold for and how long you held it, the CAGR page is the one you want. If there is also a dividend statement sitting on the desk — a piece of paper that page has nowhere to put — then this is the page. Their defaults do not overlap: the CAGR page defaults to ten years.
The price went nowhere and you still made 12% — 1,200 of income over 4 years
1. Net profit: 10,000 + 1,200 − 10,000 = 1,200
2. Rate of return: 1,200 ÷ 10,000 × 100 = 12.00%
3. Annualized return: (11,200 ÷ 10,000)^(1 ÷ 4) − 1 = 2.874%
The most informative case on the page, because the endpoints are identical and a growth-only calculation would report three zeros. Nothing happened to the price over four years and the position still returned 12 percent, all of it income. This is the ordinary situation for an income holding — a utility that trades flat and pays a dividend, a bond held to maturity, a savings account — and it is exactly what the income box exists to capture. It also shows why the annualized return is worth reading rather than the total: 12 percent over four years is 2.874 percent a year compounded, which is a different claim from the headline.

Limitations

Both ends of the calculation are single points in time, so a position bought in instalments, sold in tranches, or added to along the way is not represented by one pair of numbers — for a series of contributions use an investment or dollar-cost-averaging page instead. All the income is treated as if it arrived at the end, because none of these figures is dated: a dividend paid in year one and reinvested is worth more than the same dividend paid in year three, and this page cannot tell the difference. It ignores tax, and the difference matters, because dividends and interest are generally taxed as they are received while an unrealised price gain is not taxed until you sell — so two positions with the same pre-tax return here can have different after-tax returns. It ignores fees, commissions and spreads, all of which reduce what you keep. The annualized return is compounded, which is one of two conventions in use. The other is linear: dividing the rate of return by the years held, which gives 9.667 percent on the default case rather than 8.859, and the United States Securities and Exchange Commission's own investor education glossary describes this convention for annualizing a shorter-period return, saying that a monthly rate of return multiplied by 12 expresses an annual rate of return, often called the annual percentage rate. Both conventions are in circulation and the gap between them widens with the size of the return: on a position that doubles over seven years the compounded answer is 10.409 percent a year and the linear one is 14.286, and on one that gains 1,150 percent over fifty years the two are 5.181 and 23. Only the compounded figure is printed here, because putting two differently-defined numbers both labelled as an annual return on the same panel would be worse than choosing one. Finally, this is a historical measure of what happened, not an estimate of what will.

Frequently asked questions

How do I calculate the rate of return on an investment?: Work out the net profit first, which is the final value plus any income received minus the initial value, then divide it by the initial value. Buying at 10,000, selling at 12,500 and collecting 400 of dividends gives a net profit of 2,900 and a rate of return of 29 percent over the holding period. That is the total return for the whole time you held it, not a yearly figure.
What is the difference between the rate of return and the annualized return?: The rate of return covers the entire holding period; the annualized return spreads it over the years and compounds it. On the default case 29 percent over three years annualizes to 8.859 percent. Dividing 29 by three would give 9.667 percent, which is a different convention, and the compounded figure is the one printed here because it answers what an equivalent steady annual rate would have been.
Why is there a separate box for income received?: Because dividends and interest are part of your return and the final value does not contain them. If a position sold for 12,500 and paid you 400 along the way, the final value is 12,500, not 12,900 — folding the income into the price would misstate what the holding was worth when you closed it. Put the sale price in one box and the income in the other, and the net profit comes out right at 2,900.
Can the rate of return be positive if the price did not move?: Yes, and that is the ordinary case for an income holding. Buy at 10,000, hold for four years, sell at 10,000 and collect 1,200 of dividends, and the net profit is 1,200 with a rate of return of 12 percent and an annualized return of 2.874 percent. A growth-only calculation would report zero on all three, because it cannot see the income. This is what a flat-trading dividend payer, a bond held to maturity or a savings account looks like.
Can the rate of return be negative?: Yes. Sell at 10,000 something you paid 12,000 for, having collected 500 of income in two years, and the net profit is −1,500 with a rate of return of −12.5 percent. If the value goes all the way to zero the rate of return is −100 percent, and so is the annualized return, because losing everything is losing everything regardless of how long it took. Income softens a loss but does not turn it into a gain.
Is the rate of return the same as CAGR?: They coincide when there is no income. With the same initial value, the same final value, the same number of years and no dividends, this page and the CAGR calculator return identical figures — 25 percent and 7.722 percent on 10,000 growing to 12,500 over three years. They differ once the holding paid you something, because the CAGR calculation has no income box, and they also differ in emphasis: the CAGR page leads with the annualized figure while this page leads with the total return.
Does the holding period have to be a whole number of years?: This page takes whole years, because the annualized return raises the growth to the power of one over the number of years and a fractional exponent from a partial year would imply compounding over a fraction of a period. If you held something for eighteen months, the cleanest approach is to annualize over the exact fraction using the same formula elsewhere, or to treat the period in months consistently and multiply the monthly return by twelve if you want the linear convention instead.

References

17 CFR 230.482(d)(3) — quotations of average annual total return, for one, five and ten year periods, must be computed by the methods prescribed in Form N-1A; the rule governing how an annualized return is presented in fund advertising — U.S. Securities and Exchange Commission regulation, via the Electronic Code of Federal Regulations (United States)
Annual Return — Investor.gov glossary: an annual rate of return is the profit or loss over a one-year period, and the glossary describes annualising a shorter period by multiplying it, the linear convention this page does not use — U.S. Securities and Exchange Commission, Investor.gov (United States)
IRS Publication 550, Investment Income and Expenses — how dividends, interest and other amounts paid on a holding are treated, which is the income this page counts alongside the price change — Internal Revenue Service (United States)

Related calculators

CAGR CalculatorCompound annual growth rate between two values.Annualized Return CalculatorAnnualized return from a total return over a holding period.ROI CalculatorReturn on investment, as a percentage and a multiple.Investment CalculatorGrowth of regular contributions over time.