Calculate a money-weighted average annual return from dated cash flows, or chain-link a series of period returns into one blended annual rate
Calculation History
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Enter a starting balance and an ending balance (each with its date), plus any deposits or withdrawals that occurred in between. We solve for the single annual rate of return that reconciles all of these dated cash flows (a money-weighted / XIRR-style calculation).
$
$
Deposits & withdrawals (optional)
Each row is a deposit or withdrawal that occurred between the starting and ending balance dates. Enter a positive amount; the type selector determines the sign.
Inflation (optional)
Average Annual Return
0.00%
—
Investment Period
0.000 yrs
Net Deposits
$0.00
Real Return (Infl.-Adj.)
—
Transaction Breakdown
Date
Type
Amount
Enter each period's return (%) and how long that period lasted (years + months). We chain-link the periods geometrically into one blended average annual return and a total cumulative return.
Inflation (optional)
Average Annual Return (Geometric)
0.00%
—
Cumulative Return
0.00%
Total Time Span
0.000 yrs
Real Return (Infl.-Adj.)
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Return by Period
Period Breakdown
Period #
Return %
Holding Length
Growth Factor
All figures are theoretical calculations based on the amounts, dates, and returns you enter — actual investment returns vary and are not guaranteed. The Cash Flow tab solves a money-weighted (XIRR-style) annual rate via numerical bisection; if your balances and transactions are inconsistent (e.g. no sign change is possible across the cash flow series) no solution can be found and this is reported explicitly rather than showing an incorrect number. The Average & Cumulative Return tab chain-links period returns geometrically; it assumes each period's return compounds directly into the next with no intervening cash flows. Not financial advice. Currency selection changes the displayed symbol/format only; no live exchange-rate conversion is performed.
There are two very different ways to ask “what was my average return?” One accounts for money added or withdrawn along the way; the other simply chains a series of known period returns into one blended rate. This average return calculator handles both, and adjusts for inflation on request, so you can see your return in real, purchasing-power terms, not just nominal percentages.
How to use this average return calculator
Select your Currency, or add a custom one.
Choose a tab: Return Based on Cash Flow, or Average & Cumulative Return.
Return Based on Cash Flow: enter a Starting balance with its date, an Ending balance with its date, and any Deposits & Withdrawals that occurred in between, each as its own dated row.
Average & Cumulative Return: add each period’s return percentage along with how long that period lasted (years + months).
Optionally enter an Inflation rate on either tab to see your Real Return alongside the nominal figure.
Click Calculate to see your Average Annual Return, supporting stats, and a full breakdown table.
Export your results as PDF, Excel, or PNG, and check View History for past calculations.
What this average return calculator does
The two tabs answer genuinely different questions. Return Based on Cash Flow solves for a money-weighted annual rate that reconciles every dated cash flow you enter, your starting balance, ending balance, and any deposits or withdrawals in between, into one consistent XIRR-style figure. Average & Cumulative Return instead takes a series of already-known period returns and chain-links them geometrically into one blended annual rate and a total cumulative return, without needing any dollar amounts or dates at all, just the percentages themselves.
Return Based on Cash Flow: the money-weighted approach
Solves for r such that:
Σ [Cash Flowi ÷ (1 + r)(daysi ÷ 365)] = 0
using your starting balance, ending balance, and every dated deposit/withdrawal as the cash flow series
This is a money-weighted calculation, meaning periods where your account held a larger balance count more heavily toward the final rate than periods with a smaller balance. This makes it the right choice when you’ve actually added or withdrawn money over time and want a single rate that reflects your real, dollar-weighted experience, not just an average of percentage changes.
Average & Cumulative Return: chain-linking known percentages
This tab is built for the case where you already know each period’s return (perhaps from account statements or a fund’s published yearly figures) and want to combine them into one number, without needing to reconstruct dollar amounts or dates. Because each period return compounds on the previous one, this uses geometric chaining rather than a simple average, which correctly reflects the actual multiplicative effect of consecutive gains and losses.
Why geometric chaining matters
A simple arithmetic average of period returns overstates actual growth whenever returns vary, since it doesn’t account for compounding, a loss reduces the base that a following gain compounds from. This calculator’s Average Annual Return is explicitly geometric, meaning it correctly reflects your actual realized growth across the full time span, not an inflated figure a plain average would produce.
Adjusting for inflation: the Real Return figure
Both tabs let you enter an inflation rate (0% to disable), and when set, the results include a Real Return (Infl.-Adj.) figure alongside the nominal Average Annual Return. A nominal return that looks solid can represent much thinner, or even negative, real purchasing-power growth once inflation over the same period is accounted for, and this calculator makes that distinction explicit rather than leaving you to work it out separately.
Starting and ending balances, with dated deposits/withdrawals in between
Return Based on Cash Flow
A list of already-known period returns (e.g. yearly percentages from a statement)
Average & Cumulative Return
A note on accuracy
These are theoretical calculations based on the amounts, dates, and returns you enter, actual investment returns are never guaranteed. The cash-flow-based calculation solves numerically for the rate that reconciles your entered transactions; if your data is genuinely inconsistent, no valid rate exists and this is reported explicitly rather than showing an incorrect number. This tool is not financial advice, and currency selection changes only the displayed symbol and formatting.
Frequently asked questions
What’s the difference between the two tabs on this calculator?
Return Based on Cash Flow solves for a money-weighted return from actual dollar amounts and dates, including any deposits or withdrawals along the way. Average & Cumulative Return instead chain-links a series of already-known period return percentages into one blended rate, without needing any dollar figures at all.
Why is the Average Annual Return geometric, not a simple average?
A simple arithmetic average overstates actual growth whenever returns vary period to period, since it ignores compounding. Geometric chaining correctly accounts for how a loss in one period reduces the base a later gain compounds from, making it the more accurate reflection of your real realized growth.
What does the Real Return figure show me that the nominal return doesn’t?
Real Return adjusts your nominal average return for the inflation rate you entered, showing your actual purchasing-power growth rather than the raw percentage. A nominal return that looks positive can represent flat or even negative real growth once inflation over the same period is factored in.
Why might the cash-flow calculation report that no rate could be found?
The underlying calculation requires a sign change across your cash flow series (money going in at some point, coming out at another) for a valid rate to exist mathematically. If your entered balances and transactions don’t allow for that, no solution genuinely exists, and the calculator reports this rather than displaying an incorrect number.
