Return Volatility Calculator
Compare arithmetic and geometric periodic returns with sample and conventionally annualized volatility.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Calculate the arithmetic mean, sample standard deviation with n−1 denominator, and compounded growth. Annualize standard deviation with the square root of the entered frequency.
Sample variance=Σ(r−mean)²/(n−1); annualized SD=sample SD×√frequency
Worked example
Returns +10%, −10%, +5%, −5% average 0%, with sample SD 9.12870929% per period and geometric mean about −0.313345%.
Assumptions and input details
2–500 equally spaced simple returns from −100% to 1000%. A −100% observation makes compounded growth −100%. Annualized volatility assumes independent, similarly distributed periods; autocorrelation can invalidate this scaling. This is historical sample dispersion, not a loss limit or forecast. Returns must use a consistent fee and distribution basis. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: CFA Institute: risk-adjusted performance measures
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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