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What it calculates: Volatility (Std Dev), Mean Return, Annualised Volatility, Variance.
Updated 5 June 2026 · Transparent assumptions
The typical distance of a return from the 6.33% average
The six returns entered — 12, −5, 8, 15, −2 and 10 percent — average 6.33%. Standard deviation measures how far they typically sit from that average, and here that is 8.02 points. Variance, at 64.27, is the same quantity before the square root, which is why it is stated in squared percentage units and rarely quoted directly.
Roughly two-thirds of observations fall within one standard deviation of the mean if returns are normally distributed, so this series suggests a typical year between −1.7% and 14.3%. That is the useful translation: volatility is not an abstract risk score, it is the width of the range you should expect.
Monthly volatility annualises by multiplying by the square root of 12, not by 12
Returns compound over time but their variance adds, so volatility grows with the square root of the number of periods. Monthly volatility of 4% annualises to 4 × √12 = 13.86%, not 48%. Daily volatility of 1% annualises to about 15.9% using √252 trading days.
The periods-per-year field applies exactly this conversion. Getting it wrong is one of the most common errors in risk reporting, and it goes in both directions: multiplying by the period count vastly overstates annual risk, while forgetting to annualise at all understates it.
The sample correction matters most exactly when you have least data
Population variance divides the squared deviations by n; sample variance divides by n − 1, correcting for the fact that the mean was itself estimated from the same data. On six observations that is a difference of 20% in the variance and about 10% in the standard deviation — not a rounding difference.
Because return series are always a sample of a longer process, the n − 1 form is generally correct. The gap shrinks as the series lengthens and is negligible past a hundred observations, but on the short series people usually type into a calculator, it is the difference between two materially different answers.
Direction, and whether the distribution is symmetric
Standard deviation is direction-blind. A series of steady gains with occasional larger gains produces the same figure as a series of steady losses with occasional larger losses. Two portfolios with identical volatility can have opposite return profiles, which is precisely why volatility is the denominator of a ratio and not a measure of quality on its own.
It also assumes stability. Volatility clusters in real markets — calm periods follow calm periods and turbulent ones follow turbulence — so a figure measured over a quiet stretch systematically understates what comes next. Measured volatility is a description of the period sampled, not a forecast of the one ahead.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Returns are assumptions, not guarantees. Actual results may vary because of market performance, taxes, fees, inflation, and timing. This is an educational projection, not investment advice.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified that annualisation scales with the square root of the period count rather than the count itself, and that variance is the square of the reported standard deviation.
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