Based on Cash Flow
This tab finds the single annualized rate that explains how a starting balance grew (or shrank) into an ending balance, given every deposit and withdrawal that happened in between and exactly when each one occurred. This is a money-weighted return — the same underlying calculation used for XIRR — and it accounts for the time value of money: a deposit made early in the period has more time to compound than one made near the end, and the calculator correctly weights it that way.
Ending Balance is the account value at the end of the calculation period, including any remaining money after deposits, withdrawals, and investment gains or losses. The annualized return is the performance measure that accounts for the timing of those cash flows.
There's no simple formula for this — it requires solving for the rate that makes the whole cash-flow timeline balance, which the calculator does internally.
Average & Cumulative Return
This tab is for a series of already-known percentage returns, each with its own holding period — for example, three separate investments held for different lengths of time. It reports two different numbers:
Cumulative = [(1 + R₁) × (1 + R₂) × ... × (1 + Rₙ)] − 1 Example: +10% then +20% → (1.10 × 1.20) − 1 = +32.00% Average = (1 + Cumulative)1 / Total Years Held − 1 Example: +32% cumulative over 0.5 + 1.0 = 1.5 years → +20.33% per year Cumulative return ignores time entirely — it's just the combined growth, whether that took a month or a decade. Average return spreads that same total growth across the combined holding period to give a single annualized rate, so investments held for different lengths of time can be compared on equal footing.
A note on "ARR"
"Average rate of return" is sometimes used interchangeably with a different, unrelated metric: the accounting rate of return, which divides average annual accounting profit by the cost of an investment and specifically ignores the time value of money and the timing of cash flows entirely. Both calculators on this page are the opposite of that — they're built specifically to account for when money moves, not just how much.
Frequently asked questions
What's the difference between money-weighted and time-weighted return?
Money-weighted return (what the "Based on Cash Flow" tab calculates) is sensitive to the size and timing of deposits and withdrawals — a large deposit right before a strong period boosts the result more than the same deposit during a weak one. Time-weighted return strips that effect out entirely, measuring only the investment's own performance regardless of when money was added or removed. Money-weighted is generally the right choice for judging how well your own account actually did, given your own deposit and withdrawal decisions.
Why are cumulative return and average return so different?
Cumulative return is the total combined growth with no reference to how long it took. Average return takes that same total growth and spreads it evenly across the combined holding period as an annualized rate. A large cumulative return achieved quickly implies a much higher average annual rate than the same cumulative return achieved slowly.
What if a deposit or withdrawal date falls outside my start and end dates?
Every deposit and withdrawal has to fall strictly between the account's start and end dates, since the calculation is measuring what happened to the balance during that specific window. Adjust the start or end date, or remove the row, if you see this error.