Quick answer
The geometric average return is (Π(1 + rᵢ))^(1/n) − 1, and the arithmetic average is the mean. Yearly returns of 10%, −5%, 8% and 12% have a geometric average of 6.0326%, an arithmetic average of 6.25% and a total return of 26.4032%.
Enter the return for each period as percentages separated by commas. The calculator returns both averages and the total return.
Related tools: Stock Average Calculator: Average cost per share across several purchases. Portfolio Return Calculator: Weighted return of a portfolio from asset weights and returns. Cash on Cash Return Calculator: Annual pre-tax cash flow relative to the cash you invested.
How to use the Average Return Calculator
- Type returns per period (%), for example 10, -5, 8, 12.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Returns per period (%) | Text, such as 10, -5, 8, 12 | — |
Formula and method
Formula
geometric = (Π(1 + rᵢ))^(1÷n) − 1; arithmetic = mean of rᵢ
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
The geometric average is the constant rate that gives the same total growth.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Returns per period (%) = 10, -5, 8, 12.
| Result | Value |
|---|---|
| Geometric average return | 6.0326% |
| Arithmetic average | 6.25% |
| Total return | 26.4032% |
Example 2
Inputs: Returns per period (%) = 20, -20.
| Result | Value |
|---|---|
| Geometric average return | -2.0204% |
| Arithmetic average | 0% |
| Total return | -4% |
The first line is the headline result (geometric average return). Below it the average Return Calculator lists arithmetic average and total return, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Why they differ
The arithmetic mean overstates what you actually earned when returns vary. The geometric average is the constant yearly rate that gives the same final result: 1.0603^4 = 1.264. A −50% year followed by +50% averages 0% arithmetically but loses 25%.
Which to use
Use geometric for the growth of an investment over time and arithmetic for the expected return in a single period. A return of −100% or lower is invalid, since it would wipe out the investment.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Returns per period (%): left empty shows "Enter returns per period (%)." beside that field and no result.
Choosing between the Average Return Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Stock Average Calculator](/finance/stock-average/) | shares per purchase and price per share for each purchase | Average cost per share |
| [Portfolio Return Calculator](/finance/portfolio-return-calculator/) | weights and return of each asset | Portfolio return |
| [Cash on Cash Return Calculator](/real-estate/cash-on-cash-return-calculator/) | annual pre-tax cash flow and total cash invested | Cash-on-cash return |
| [Investment Calculator](/finance/investment-calculator/) | initial amount, annual interest rate and years | Projected value |
| [Financial Calculator](/finance/financial-calculator/) | solve for, periods per year and payments | Future value (FV) |
Background: interest, saving and investing
A nominal rate (APR) does not include the effect of compounding; the annual percentage yield (APY) does: APY = (1 + r/n)^n − 1. A 5% nominal rate compounded annually is 5.000%, semi-annually about 5.063%, quarterly about 5.095% and monthly about 5.116%, so more frequent compounding helps, but with diminishing returns.
The rate you enter in a projection is an assumption, not a promise: real returns vary and can be negative. Fees and taxes are not modelled unless the page says so.
Assumptions and limitations
- A return of −100% or less is invalid
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for returns per period (%) to confirm this.
Frequently asked questions
What is volatility drag?
The gap between arithmetic and geometric averages.
Are returns percentages?
Enter them as percentages like 10 or -5.
How many periods can I enter?
As many as you like.
What does the Average Return Calculator calculate?
Arithmetic and geometric average of periodic returns. It returns Geometric average return, Arithmetic average and Total return.
What formula does the Average Return Calculator use?
geometric = (Π(1 + rᵢ))^(1÷n) − 1; arithmetic = mean of rᵢ. The geometric average is the constant rate that gives the same total growth.
What do I need to enter in the average Return Calculator?
You enter Returns per period (%).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. A return of −100% or less is invalid.
What is an example of a average Return result?
With returns per period (%) 10, -5, 8, 12, the geometric average return is 6.0326%.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: A return of −100% or less is invalid.
Related calculators
- Stock Average Calculator — Average cost per share across several purchases.
- Portfolio Return Calculator — Weighted return of a portfolio from asset weights and returns.
- Cash on Cash Return Calculator — Annual pre-tax cash flow relative to the cash you invested.
- Investment Calculator — Project investment growth from a rate of return you choose.
- Financial Calculator — Time-value-of-money solver for N, rate, present value, payment or future value.
- IRR Calculator — Internal rate of return of an investment from its yearly cash flows.
- Doubling Time Calculator — Years for money to double at a given rate.
- PVIFA Calculator — Present value interest factor of an annuity.
- WACC Calculator — Weighted average cost of capital.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.