Average Return Calculator

Average return calculator with two methods

This calculator measures investment performance in two distinct situations. Use dated cash-flow mode when an account had deposits or withdrawals between its starting and ending values. Use holding-period mode when you already know several separate investment returns and want their combined cumulative and annualized result. Keeping these methods separate avoids treating investor contributions as investment gains.

Money-weighted return from dated cash flows

Cash-flow mode solves a money-weighted annual return, often called an annualized internal rate of return or XIRR. The starting balance and deposits are treated as money invested, while withdrawals and the ending balance are treated as money received. Each amount is discounted according to its exact number of days from the starting date. The solved rate makes the present value of all entered cash flows equal to zero.

0 = sum of cash flow / (1 + annual return)^(days from start / 365)

Cash-flow example

Suppose an account starts at $10,000 on January 1, 2021, receives a $1,000 deposit on January 1, 2023, and ends at $16,000 on January 1, 2026. Simply comparing $16,000 with $10,000 would count the added $1,000 as investment performance. The money-weighted calculation instead recognizes both the size and timing of that deposit before solving the annual rate.

Multiple holding-period returns

Period mode compounds the entered returns in sequence. A 10% gain followed by a 10% loss does not return to the starting value: 1.10 multiplied by 0.90 equals 0.99, a cumulative loss of 1%. The annualized result converts the combined growth factor into one equivalent yearly compound rate over the total holding time.

cumulative growth factor = product of (1 + each holding-period return)

annualized return = cumulative growth factor^(1 / total years) - 1

Arithmetic average versus geometric return

An arithmetic average adds the entered percentages and divides by the number of periods. It describes the average observation but does not reproduce the investment's compounded ending value when returns vary. The geometric annualized return incorporates compounding and is therefore better suited to comparing realized growth across different holding lengths. The results show both figures and label them separately.

Total return, annualized return, and net gain

Total or cumulative return measures the full gain or loss over the complete interval. Annualized return expresses that performance as an equivalent compound rate per year. Net gain is a dollar amount after adjusting the ending value for entered deposits and withdrawals. These measures answer different questions, so a high cumulative return over many years should not be compared directly with a one-year return.

Why contribution timing matters

A deposit made near the beginning has more time to experience investment performance than one made shortly before the ending date. Money-weighted return accounts for this difference. It also reflects the investor's timing decisions, which means it can differ from a fund's published time-weighted return even when both calculations are correct.

Compounding and comparison

Compound growth earns a return on both the original amount and prior gains. The Investor.gov introduction to investing explains this compounding effect. Annualizing can make holding periods easier to compare, but it does not remove differences in volatility, risk, taxes, fees, liquidity, or asset type.

Accuracy and assumptions

The cash-flow solver uses a 365-day year and searches for a real annual rate above -100%. Some unusual cash-flow patterns can have multiple mathematical solutions or no practical solution. This page reports one detected solution and warns when no bracketed solution is found. Enter account values after fees only if you want a return that reflects those fees, and use consistent treatment of dividends, taxes, and distributions.

Average rate of return versus accounting ARR

In capital budgeting, “average rate of return” can also mean accounting rate of return: average annual accounting profit divided by average investment. That metric uses accounting income and does not discount cash flows for timing. This calculator measures investment performance instead; it does not calculate project accounting ARR, net present value, or a business investment's depreciation-based book return.

Frequently asked questions

Is annualized return the same as CAGR?

For one beginning value, one ending value, and no intermediate cash flows, the annualized compound return is mathematically the same as CAGR. Dated deposits and withdrawals require a money-weighted calculation.

Should deposits be entered as positive numbers?

Yes. Select Deposit and enter a positive amount; the calculator applies the necessary cash-flow sign internally. Do the same for withdrawals.

Can the annual return be negative?

Yes. If the ending value and withdrawals do not compensate for invested amounts, the solved or compounded result can be below zero, but never below -100% for a standard real annual growth rate.

Does this predict future returns?

No. It measures the scenario entered. Historical or hypothetical performance does not guarantee a future result.