Average Return Calculator

Which Type of Return Should You Use?

Six measures, six different questions. Picking the wrong one is the most common way an investment return gets misstated, so start here and the rest of this page follows from your answer.

How to Calculate Average Return

Add every period return together and divide by how many periods there are. That is the arithmetic average, and it answers one specific question: what did a typical period look like? It is the right figure for describing the spread of a set of periods, and the right input for a forward-looking model that treats each period as an independent draw.

It is not the figure that tells you what you ended up with. Money compounds, so a set of returns has a second average - the geometric one - that reproduces your actual ending balance. Both are computed above, side by side, because quoting either without the other leaves the reader guessing which question was answered.

The periods have to be the same length. Twelve monthly returns and three annual returns cannot go into the same average; pick the frequency that matches your data and enter one row per period.

Arithmetic Average Return Formula

The arithmetic average return is the sum of the period returns divided by the number of periods:

Each rᵢ is the return of one period, expressed as a decimal - 8% enters the formula as 0.08 and −4% as −0.04. The calculator above takes them as whole percentages and converts them for you. n is the number of periods, not the number of years: twelve monthly returns give n = 12 even though they span a single year.

Average Return Example

Take three years of returns: +20%, then −10%, then +15%.

The arithmetic average adds them and divides by three: (20% − 10% + 15%) / 3 = 8.33% a year.

The cumulative return multiplies the growth factors and subtracts one: (1.20 × 0.90 × 1.15) − 1 = 24.20%.

The geometric average takes the cube root of that same product: (1.20 × 0.90 × 1.15)^(1/3) − 1 ≈ 7.50%.

Three numbers, three different questions. 8.33% describes a typical year. 24.20% is the whole three-year journey. 7.49% is the steady yearly rate that would have produced exactly that journey - and it is the only one of the three that reproduces your ending balance. Load these returns into the calculator above and the wealth path shows why: 10,000 becomes 12,000, then 10,800, then 12,420.

Arithmetic Average vs. Geometric Average Return

The arithmetic average treats each period as a separate draw and asks what a typical one looked like. The geometric average asks what single constant return, repeated every period, would have left you with exactly the balance you actually have.

Because money compounds, the geometric average is always lower than the arithmetic one unless every period return was identical. The two are equal only when the returns never vary, and the gap widens with every point of variation.

Which to report depends on the direction you are facing. Looking backwards at what an investment delivered, the geometric average is the honest figure. Looking forwards, building an expectation from a set of independent yearly outcomes, the arithmetic average is the correct input - which is exactly why published expected returns and published historical returns are often different numbers describing the same series.

Why Average Return Can Overstate Investment Growth

A loss is taken against a bigger base than the gain that preceded it. Up 50% turns 100 into 150; the following 50% loss is then applied to 150, not to 100, so it removes 75 rather than 50. The two moves are equal in percentage terms and unequal in money, which is why they do not cancel.

The consequence is that an arithmetic average can be positive - or zero - while the investment lost money. It is not a rounding error or a trick of presentation: it is what compounding does to an uneven series, and it gets worse as the series gets rougher.

The distance between the two averages has a name, volatility drag, and the calculator reports it directly so the cause and the cost sit next to each other.

Volatility Drag Example

Gain 50%, then lose 50%.

The arithmetic average is (50% − 50%) / 2 = 0%.

The wealth path is $100 → $150 → $75.

The cumulative return is (1.50 × 0.50) − 1 = −25%, and the geometric average is (0.75)^(1/2) − 1 ≈ −13.40%.

A 0% arithmetic average does not mean the investment broke even. It lost a quarter of its value, and the compound average that describes that outcome is −13.40% a year. Volatility drag here is the whole 13.40 points between the two averages - the entire arithmetic figure is drag.

The table below holds the arithmetic average fixed at 8% and widens the spread between two years. The arithmetic column never moves; the ending balance falls all the way down it.

The arithmetic average is identical on every row. What changes is the ending balance — which is the only one of the two averages you can spend. The standard deviation calculator measures the dispersion that causes it.

How to Calculate Cumulative Return

Turn each period return into a growth factor by adding one to it, multiply the factors together, then subtract one:

Cumulative return is the whole journey in a single number. It carries no time unit, which is both its strength and its limit: it states exactly what happened, and it cannot be compared between an investment held for two years and one held for twelve without being annualized first.

This is why a headline such as “up 240% since launch” says almost nothing on its own. Across three years it is remarkable; across thirty it is about 4.1% a year.

One period of −100% takes the product to zero and the cumulative return to −100%. No later percentage return can lift a balance of zero, which is why the calculator accepts −100% and refuses anything below it.

How to Calculate Annualized Return

Annualizing converts a result that covers some span of time into a rate per year, so investments held for different lengths of time become comparable. It is the same compounding restated, not a different measurement.

Two routes reach it. From a list of period returns, raise the cumulative growth factor to the power of one over the number of years those periods cover. From a starting and an ending value, raise the ratio of the two to the power of one over the number of years. Both are in the calculator above - the first in Returns mode, the second in Start & End Value mode - and both produce the same figure when given the same underlying series.

Annualized Return Formula

years is the elapsed time the return covers, not the number of periods. Twelve monthly returns cover one year, so compounding them gives an annual figure directly. Four quarterly returns also cover one year. Thirty-six monthly returns cover three, and the exponent becomes 1/3.

When you give the calculator two dates rather than a duration, elapsed time is calendar days divided by 365.2425, the mean length of a Gregorian year. That handles leap years without a special case and keeps the answer reproducible.

CAGR vs. Average Return

CAGR is the geometric average applied to annual periods. It is not a different formula - it is the same nth root of the same growth product, with the periods happening to be years and the inputs happening to be a starting and an ending value rather than a list.

So CAGR is not the arithmetic average, and the arithmetic average is what most people mean by “average return”. That is the whole source of the confusion. If somebody tells you an investment averaged 10% a year, the follow-up question is which average, because the two can be several points apart.

Take $10,000 growing to $15,000 over five years. The total return is 50%. The CAGR is (15,000 / 10,000)^(1/5) − 1 ≈ 8.45% a year.

Dividing 50% by 5 to get 10% is the mistake this page exists to prevent. That arithmetic assumes the gain is added each year rather than compounded on a growing balance. Compound 10% for five years and $10,000 reaches $16,105, not $15,000 - the shortcut overstates the annual rate by more than a point and a half.

A holding worth $10,000 that grows to $15,000 over 5 years has a total return of 50.00% and a CAGR of 8.45%. Dividing the total return by five instead would give 10.00% — the shortcut this section exists to prevent. Start & End Value mode above computes both, and adds dates, distributions and the inflation and fee restatements.

Both figures are computed by the same engine as the calculator, and re-verified against it on every build.

Rate of Return Formula

“Rate of return” is a family, not a single formula. Every member measures the gain relative to what was put in; they differ in what counts as “put in” and over what span the answer is expressed.

That is total return over the holding period, with no time attached. Annualize it, and it becomes CAGR. Feed it a series of periods instead of two endpoints, and it becomes the cumulative return with an arithmetic and a geometric average sitting behind it. Add dated deposits and withdrawals, and it becomes the money-weighted return, because a single starting figure no longer describes what you invested.

Income belongs in the numerator. If dividends, interest, coupons or rent were received and not already reflected in the ending value, add them - otherwise the rate of return you calculate is a price change wearing the wrong name.

How to Calculate Investment Return

Start by writing down three things: what went in, what came out, and when each of those happened. The third is the one people skip, and it is what decides which formula is valid.

One amount in and one amount out, nothing in between: total return and CAGR describe it completely. Use Start & End Value mode.

A run of periodic returns from a statement or a factsheet: use Returns mode, and read the geometric average rather than the arithmetic one if you want to know what actually happened.

Money added or taken out along the way: neither of the above is valid, because the amount at risk changed. Use Cash Flows mode for your own return, or Time-Weighted Return mode to judge the investments without your timing counting for or against them.

Whatever you choose, keep the basis consistent. A gross-of-fee return compared against a net-of-fee benchmark, or a price return compared against a total return index, produces a difference that has nothing to do with performance.

How to Calculate Stock Returns

A share position earns in two ways, and a stock return is complete only when both are counted.

Price appreciation is the change in the share price over the holding period: (selling price − purchase price) / purchase price. On its own this is the price return, and it is what a bare index level such as a headline stock index quote usually reflects.

Dividends and distributions are the cash paid out while you held the shares. If you took them as cash, add them to the numerator. If you reinvested them, they bought more shares and are already inside your ending value - adding them again double-counts, which is the single most common error in a stock-return calculation.

Total return is the sum of the two components and the figure worth comparing. Published “total return” index series assume dividends are reinvested; published price index series do not, and the gap between them over long periods is large. Include your brokerage commission in the purchase cost and net it out of the proceeds, or the return will flatter the trade.

Bought in several tranches, or sold part of the position? That is a cash-flow problem, not a two-point one. Use Cash Flows mode with each purchase and sale dated.

For a single buy-and-sell trade with no interim purchases, Start & End Value mode above is the shorter route: enter what you paid, what it was worth, and any dividends you took as cash. Use Cash Flows mode when there were several tranches or a partial sale.

Returns With Deposits and Withdrawals

The moment money moves in or out, a single starting value stops describing what you had invested, and total return divided by years stops meaning anything.

Consider $10,000 invested at the start of a year and another $10,000 added one month before the end, finishing at $21,000. Simple arithmetic says $20,000 became $21,000, a 5% return. But the second $10,000 was only invested for a month; the money that was actually at risk for the year is much closer to $10,800, and the return the first $10,000 earned is far higher than 5%. Two different measures exist precisely to resolve this, and they answer different questions.

Run that case through the calculator. $10,000 invested on 1 January, another $10,000 added on 1 December, $21,000 at the year end: total contributions $20,000.00, a gain of $1,000.00, and a money-weighted return of 9.22% a year — not the 5.00% that dividing the gain by the total contributions suggests. The second deposit was invested for one month, and the money-weighted calculation is the one that knows it.

Money-Weighted Return (MWR / XIRR)

The money-weighted return is your personal return. It weights every dollar by how long it was invested, so a deposit made just before a strong stretch raises it and one made just before a weak stretch lowers it.

Mathematically it is the internal rate of return of your dated cash flows: the single rate that makes the present value of everything you put in equal to the present value of everything you got back, including what the account is worth today. In a spreadsheet it is the XIRR function, and the calculator above solves the same equation.

Deposits are money out of your pocket and count as negative; withdrawals and the closing value are money back in and count as positive. In Cash Flows mode you enter every amount as a positive number and pick its type, so no minus sign is ever needed. A set of cash flows that never changes direction has no rate of return at all, and the calculator says so rather than producing a number.

A longer history works the same way. Take $10,000 invested on 2021-01-01, two further deposits of $5,000, a $3,000 withdrawal, and $24,000 left on 2025-01-01. Contributions total $20,000.00, withdrawals $3,000.00, and net invested capital $17,000.00. The money-weighted return is 9.93% a year.

Time-Weighted Return (TWR)

The time-weighted return removes the effect of your deposits and withdrawals entirely. It cuts the history into sub-periods at every external cash flow, measures the return of each one on its own, and chains them together.

Each sub-period return sᵢ is the ending value measured immediately before the cash flow at that boundary, divided by the value it opened with. Because every sub-period is measured on its own base, the size and the timing of the flows cancel out of the chain.

This is the standard for reporting investment performance, and the reason a fund's published return is time-weighted: a manager controls the investments but not when clients pay money in. To use it you need a valuation at each cash-flow date, which is the practical cost of the method.

The same portfolio, measured the other way: $100,000 rises to $112,000 before a $20,000 deposit, then falls from $132,000 to $125,400. The two sub-period returns are 12.00% and -5.00%; chained, that is a cumulative time-weighted return of 6.40%. The deposit is invisible to the result, which is exactly the point.

MWR vs. TWR

Neither is more correct. They answer different questions, and the gap between them is itself information: it measures how much of your outcome came from timing rather than from the investments.

Use the money-weighted return to answer “how did my money do?”. It is the right figure for your own account, and it is what most brokerage statements show.

Use the time-weighted return to answer “how did this strategy, fund or manager do?”. It is what published performance uses, and it is what makes two funds comparable when their investors behaved differently.

When your money-weighted return beats the time-weighted one, more of your capital happened to be invested during the stronger stretches. When it trails, the opposite. Enter a portfolio value immediately before each transaction in Cash Flows mode and the calculator reports both figures and the gap between them from the same data.

Run the deposits-and-withdrawals sample above and the calculator reports both from one set of entries: a money-weighted return of 9.93% a year against a time-weighted return of 10.23% a year — a gap of -0.29 pts. That gap is the effect of when the money went in, and nothing else.

Nominal vs. Real Return

A nominal return is what the account statement says. A real return is what it bought. Prices rise while your money grows, so the two are different, and only the second one tells you whether you are better off.

Adjusting is a division, not a subtraction:

A 10% nominal return with 3% inflation leaves 6.7961% real, not 7%. The shortcut looks harmless over one year and compounds into a serious overstatement across a working lifetime, because inflation applies to the whole balance rather than to the gain alone.

The Advanced panel in the calculator applies this to your own result. Inflation is measured by a published price index; the calculator does not supply one, so use the rate that matches your currency and period rather than a remembered figure.

To convert a single amount between two points in time rather than adjusting a return, use the inflation calculator. To apply an inflation rate to the result above, open the Advanced panel in the calculator.

How Fees Affect Investment Returns

A percentage charged on the balance every year is deducted from a base that is supposed to be compounding, so its cost compounds too. That is why a fee that looks small next to a return is not small next to the outcome.

The arithmetic is the same ratio form as inflation: a 10% gross return with a 1% annual charge leaves 1.10 × 0.99 − 1 = 8.9%, not 9%. Over one year the difference is a rounding detail. Over decades, the fee is applied to a balance that should have been growing, and the shortfall grows with it.

Three checks are worth making before comparing any two return figures. Is each one gross or net of the fund's ongoing charge? Does either include platform, advice or transaction costs, which usually sit outside the fund's own figure? And is the comparison benchmark quoted on the same basis, since an index carries no costs at all?

The Advanced panel applies one illustrative annual charge to your result. It is a single percentage on the balance, not a model of a real fee schedule.

This page measures what a fee already cost. To see what one costs a balance you are still building, the compound interest calculator projects the same charge forward.

What Is a Good Average Investment Return?

There is no universal number, and any page that gives you one has left out the question it depends on. A return is good or bad only relative to what you were exposed to in order to earn it.

Asset class sets the range. Cash, bonds, listed equity and property have structurally different return and risk profiles; comparing a figure from one against a figure from another says nothing.

Risk taken is the price of the return. A higher return earned by accepting far more variability is not obviously better, which is why volatility and volatility drag appear alongside the averages in this calculator.

Time horizon changes both the range of outcomes and which average is meaningful. A single year says very little; a long series says considerably more.

Benchmark is what makes a figure interpretable at all. The relevant question is almost never “is 7% good?” but “is 7% good against the appropriate index, over this period, after costs?”

Fees are subtracted from whatever the investments earned, and the comparison is only fair if both sides are on the same gross or net basis.

Inflation decides whether a positive nominal return is a real gain or a real loss.

Tax depends on your jurisdiction, your account type and your holding period, and can change the ranking of two investments that look identical before it.

Geography and currency affect the return you actually receive, because a return earned in another currency is also a currency position.

This calculator measures what happened. Judging whether that is good is a decision about your own circumstances, and nothing on this page is advice about it.

Average Stock Market Returns

This page quotes no market average, and the reason is methodological rather than cautious: the phrase “the average stock market return” is ambiguous until four choices are stated, and different published figures for the same market and the same era differ because they made those choices differently.

Arithmetic or geometric. The arithmetic mean of annual returns is higher than the compound annual growth rate of the same series - often by more than a percentage point for a volatile index. Both get published, and they are not interchangeable.

Nominal or real. An inflation-adjusted series is materially lower than a nominal one, and which is quoted is often left implicit.

Price or total return. A price index excludes dividends. A total-return index reinvests them. Over long periods the difference between the two is one of the largest sources of disagreement between quoted figures.

The period chosen. A long-run average is highly sensitive to its start and end dates, because both fall somewhere in a market cycle. Moving the window a few years moves the answer.

If you want a figure for a specific index, take it from the index provider or a regulator's investor-education material, note all four choices above, and treat it as a description of a past period rather than a forecast. Then enter it here as one input among several rather than as a result.

Average Returns for Common Investments

What differs between asset classes is not only the return but what the word means. This table gives the convention that applies to each, so the number you calculate is the number you meant to calculate. It deliberately quotes no rates: a return figure is only meaningful with its period, its basis and its source attached, and this page holds no market dataset to supply them.

Use the calculator above with figures from your own statement, fund factsheet or broker export. Where a published figure is involved, check whether it is price or total return, arithmetic or geometric, nominal or real, and gross or net of fees before comparing it with anything.

Common Return Calculation Mistakes

Ten errors account for most misstated returns. Each one has a specific fix, and the calculator above is built to make the fix the default.

1. Using the arithmetic average as compound growththe arithmetic average describes a typical period, not what you ended up with. Read the geometric average whenever the question is about the outcome.
2. Dividing total return by the number of years50% over five years is not 10% a year. Compound growth needs the fifth root, which gives about 8.45%. Simple division always overstates.
3. Ignoring dividends and distributionsa price change is not a total return. Add income that is not already inside the ending value, and do not add it if you reinvested it.
4. Ignoring deposits and withdrawalsonce money moves in or out, total return over a single starting value is invalid. Switch to a money-weighted or time-weighted calculation.
5. Confusing nominal and reala 6% nominal return with 4% inflation is not a 2% real return, and it is not a comfortable one either. Divide the growth factors.
6. Ignoring feesan annual charge on the balance compounds against you. Compare gross with gross and net with net, and check what the benchmark includes.
7. Comparing periods that are not comparablea three-year figure and a ten-year figure are different quantities until both are annualized, and even then the windows matter.
8. Treating ROI as an annualized returnreturn on investment is a total, with no time in it. Two investments with the same ROI over three and thirty years are not remotely alike.
9. Using money-weighted return to judge a managerthe manager did not choose when you deposited. Time-weighted return is the measure that holds them responsible only for the investments.
10. Treating a historical average as a forecasta past average describes a period that has finished. It is an input to a projection, never a prediction, and this calculator does not project.

What a −100% return means, and why below it is refused

A period return of −100% means the position lost everything. The calculator accepts it, and the wealth path correctly goes to zero and stays there, because no later percentage return can lift a balance of zero.

A return below −100% is refused rather than computed. For an ordinary unleveraged holding it describes something that cannot happen, and letting it through would produce a negative growth factor whose geometric mean has no meaning. Positions that can lose more than their value — margin, short sales, some derivatives — are not period returns in this sense and need a different treatment.