Average Return Calculator
Measure arithmetic, geometric, cumulative, and dated cash-flow returns.
Compare arithmetic average and geometric compounded returns.
Result
Calculation details
Scroll horizontally or vertically to see more. Download CSV for the complete schedule.
| Period | Return (%) |
|---|---|
| 1 | 10 |
| 2 | -5 |
| 3 | 15 |
How to use this calculator
Compare arithmetic average and geometric compounded returns. Enter amounts in the units shown, select the applicable options, and click Calculate. Use Reset to restore the starting values.
Calculation formula
Arithmetic = sum(r)/N; geometric = product(1+r)^(1/N)−1.
Assumptions and accuracy
Review timing, rates, fees and result notes when comparing scenarios. Future returns and rates are assumptions rather than guaranteed outcomes. Monetary display follows the currency’s precision; intermediate calculations retain additional digits.
Choose what to calculate
Annualized return calculator with dated cash flows
Use actual cash-flow dates for a money-weighted annualized return. Arithmetic average returns and compound returns answer different questions.
Related searches: Annualized return calculator
Open this calculationAverage return calculator
Use actual cash-flow dates for a money-weighted annualized return. Arithmetic average returns and compound returns answer different questions.
Open this calculationUnderstanding this calculation
Compare arithmetic and geometric returns, or use dated cash-flow and variable-period modes when investment amounts or period lengths differ.
Worked examples
Why average return can hide a loss
Illustrative inputs are specified in the steps below; the example link loads the complete settings. Unmentioned settings use the linked defaults.
- The arithmetic average is (50% − 50%)/2 = 0%. But 100 grows to 150 then falls to 75; the compound result is a loss, despite the zero arithmetic average.
Arithmetic average: 0%.
Try these inputsCommon questions
Why can a zero average return still lose money?
Equal positive and negative percentage returns apply to different balances. The compound growth factor, not their arithmetic sum, determines ending wealth.
When should I use a dated cash-flow return?
Use it when deposits and withdrawals occur on particular dates. A simple average of percentage returns does not account for those cash-flow timings.
Scope and assumptions
A single average is not a risk measure. Dated numerical return estimates can be ambiguous for cash flows with repeated sign changes.
Sources
- Calculation methodology, rule versions and testing limitations
- Reference calculator for feature comparison (not a model-parity certification)
Calculation notes checked . Examples are mathematical checks under the stated assumptions.
Calculation methods and formulas
Average and Cumulative Return
Compare arithmetic average and geometric compounded returns.
Arithmetic = sum(r)/N; geometric = product(1+r)^(1/N)−1.
Dated Cash Flows
Find the annual money-weighted return using exact transaction dates.
Σ CFᵢ/(1+r)^((dateᵢ−date₀)/365) = 0.
Variable Period Returns
Calculate cumulative growth and an annualized return across unequal holding periods.
Growth = product(1 + period return); annualized return = growth^(1/total years) − 1.
See our calculation methodology and review status for data versions, rounding and validation limitations.