Money Weighted Return Calculator

Your fund reports one return, but your account usually earns another. The money-weighted return is the internal rate of return (IRR) of your actual cash flows: it takes your initial investment, every dated contribution and withdrawal, and your final value, then solves for the single annualized rate that ties them together. Timing is the whole point, because money added just before a rally counts more than money added just before a fall.

Quick Answer

How to use this money-weighted return calculator

Enter three fixed numbers and one row per cash flow, then read the solved rate at the top of the results. The steps below match the tool exactly, including the two quirks worth knowing before you trust the output.

1. Initial investment: what you put in at year 0. It has to be above zero.
2. Cash flow rows: one row for every later contribution or withdrawal. Pick the type, enter the amount, and enter when it happened in years. Fractions are fine: six months in is year 0.5. Use the Add cash flow button for more rows, and the x button to remove a row.
3. Final value and period: what the account is worth at the end, and the total period in years. Every flow year must sit between 0 and the total period, or the calculator stops with an error.
4. Read the results: the money-weighted return (the big number), the simple return for contrast, your total contributions and withdrawals, the net gain, and a table listing every flow with its sign and year so you can audit what the solver used.

Two entry quirks, stated plainly because they change answers. A row with a blank amount, or an amount of zero or less, is skipped silently. A row with an amount but a blank year is treated as a year 0 flow, as if the money moved on day one. If a skipped or day-one flow surprises you, the results table shows exactly which flows the solver counted.

The formula: one rate that makes the present value zero

The money-weighted return r is the rate that solves 0 = ∑ CF_t ÷ (1 + r)^t, summed over every cash flow. Contributions enter negative, withdrawals and the final value enter positive, and t is each flow’s timing in years.

There is no closed-form solution once flows land at irregular times, so the calculator solves numerically. It brackets the root between r = −99.99% and r = 1000%, widening the upper end (doubling it, up to 40 times) until the net present value changes sign across the bracket, then bisects the bracket 300 times. That is the same iterative logic spreadsheet functions use: Microsoft’s documentation for the IRR function describes cycling from a starting guess until the result is accurate, and its XIRR function applies the same idea to dated flows on a 365-day year. The professional standards agree on the definition: the 2020 GIPS Standards, summarized in PwC’s overview of the 2020 GIPS Standards, let firms present money-weighted returns (the since-inception IRR) where the firm controls the timing of external cash flows.

Worked example: the 13.29% hiding inside a 23.33% gain

The example is the one pre-filled above: $10,000 in at year 0, $5,000 more at year 1, $18,500 at year 2. Total gain is $3,500 on $15,000 invested, a 23.33% simple return that says nothing about when the money arrived.

The three present values sum to zero at the solved rate r = 13.2932% (shown as 13.29% in the results), which is the definition working as advertised: −$10,000 − $5,000 ÷ 1.132932 + $18,500 ÷ 1.132932² = 0. Run the same flows with the $5,000 arriving at year 0.5 instead of year 1 and the answer drops to 12.10%, because the extra money spent longer exposed to a return that, on the full $15,000, was never spectacular. Same deposits, same ending value, different timing, different personal return. That sensitivity is the feature, not a bug.

Money-weighted vs time-weighted: which one grades you?

Time-weighted return grades the investment; money-weighted return grades the investor. Funds report the time-weighted figure because it strips out flows the manager does not control, while your brokerage outcome is money-weighted whether anyone computes it or not.

The gap between the two is measurable in the real world, not just in textbooks. In Morningstar’s Mind the Gap research, fund investors earned about 6.3% a year dollar-weighted over the decade to the end of 2023 while their funds returned about 7.3% time-weighted: a 1.1 percentage point annual timing cost, repeated across every rolling decade Morningstar has measured. If you want the other side of the comparison for your own holdings, the time-weighted return calculator links sub-period returns the way funds report them, and the geometric mean return calculator covers the linking math underneath it. For a single stretch with no flows at all, a holding period return is the honest summary, and a money-weighted figure only earns its keep once money starts moving in and out, which is also where a portfolio performance review usually begins.

When the calculator says there is no valid return

That error is a real answer about your cash flows, and it appears in two distinct situations. Knowing which one you hit matters more than the error text itself.

No sign change. An IRR needs at least one negative and one positive flow. Money in at the start and a final value of zero, with no withdrawals, is negative at every possible rate, so no rate solves the equation. Microsoft’s XIRR documentation states the same requirement from the spreadsheet side: the series must contain at least one positive and one negative value or the function fails. The fix is in your data, not the solver: if you did take money out, enter it as a withdrawal.

More than one sign change. Flows that swing negative, positive, then negative again can have two different rates that both zero the present value. A stark case: −$100 at year 0, +$230 at year 1, −$132 at year 2 has a net present value of exactly zero at both 10% and at 20%. There is no single money-weighted return for that pattern, and this solver, which brackets one root between −99.99% and a widening upper bound, reports no valid return rather than silently picking one of the two. Spreadsheets have the same ambiguity and handle it with a guess argument; if your flows look like that example, the honest move is to split the timeline at the sign change and evaluate each stretch separately.

One cosmetic quirk to expect: an exactly break-even history can display as −0.00%, because the bisection settles a hair below zero. Read it as zero.

When the money-weighted return can mislead you

Two limits the number itself will not warn you about, carried over from the dollar-weighted return page this one replaces. First, it says nothing about risk: the same annual rate earned smoothly and the same rate earned on a roller coaster are one identical number here, so pair it with a risk measure such as standard deviation for the full picture. Second, it is yours alone: because it is built from your deposit and withdrawal schedule, you cannot fairly compare your money-weighted return with another investor’s, whose schedule differs. The only fair comparison is against a relevant benchmark over the same period.

What competing calculators miss

Money-weighted tools split into three camps, and two of them are not computing this number at all:

• Ratio tools dressed as MWR (Calculator Ultra’s page is the clearest case): the published formula is net cash flow divided by total invested capital. That is a simple return with a fancier name. Timing never enters it, so a deposit made the day before the end counts the same as one made a decade earlier.
• Modified Dietz tools (CalculatorsHub states this openly): Dietz is a respectable approximation that weights each flow by the fraction of the period it was invested, but an approximation is not the IRR. On lumpy flows the two can sit a full percentage point apart, and the page rarely tells you which one you got.
• True IRR solvers (BraveCalculator, Ryan O’Connell’s finance tools): the math is right, and O’Connell’s page adds a Newton-Raphson solver and an NPV check. The gaps are in the entry model: fixed or comma-listed flows instead of dated rows you can add, remove and audit, and no timing-blind simple return next to the answer to show what the timing actually cost.
• The gap this page fills: a real bisection IRR solver with unlimited dated rows (fractional years included), the per-flow table printed under the result so every sign and year can be checked, the simple return beside it, and the failure cases explained on the page instead of hidden behind a generic error.

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