Standard Deviation Calculator for Stocks
Calculate periodic return volatility from entered prices or returns, with optional annualization under a stated frequency assumption.
Enter historical closing prices in chronological order (oldest first)
Log returns add over time; simple returns express percentage price changes.
N−1 estimates variance under sampling assumptions; N describes this data set.
Match the actual sampling interval; 252 and 365 assume daily data.
Return dispersion per input period, not average absolute movement.
Arithmetic mean per input period
σ² (squared deviation)
Lowest observed periodic return
Highest observed periodic return
Additional Statistics
No universal risk grade is assigned. Annualization is an assumption-based scaling of this sample.
From Prices to Return Dispersion
Enter positive prices in chronological order or periodic percentage returns directly. Simple returns are (P₁/P₀ − 1) × 100; log returns are [ln(P₁) − ln(P₀)] × 100. Neither is universally superior: use the convention appropriate to your analysis and keep it consistent.
A Checkable Example
For monthly returns −1%, 0%, 1%, the mean is zero and squared deviations sum to 2. Sample variance is 1 percentage point squared, sample SD is 1%, and population SD is √(2/3)% ≈ 0.8165%. With 12 periods per year, annualized sample SD is √12% ≈ 3.4641%.
For that symmetric sample, unadjusted moment skewness is zero and excess kurtosis is −1.5. Relative SD is undefined because the mean is zero. Constant-return data similarly have undefined shape statistics.
Match Frequency and Estimator
The sample setting uses N−1 for variance; population uses N. The square-root estimator itself is not generally unbiased. Shape statistics use population central moments regardless of that selector. The default values are an illustrative series, not a named stock or evidence of market performance.
Annualized SD = periodic SD × √K, where K is the entered periods per year. Serial correlation and changing variance can invalidate this scaling. Standard deviation is not a forecast price interval or a complete risk assessment; adding a second asset also requires correlation information to assess diversification.
References: NIST Measures of Scale, Skewness and Kurtosis, and Relative SD limits; Sharpe's time-dependence discussion.
Frequently Asked Questions
What return frequency does this tool assume?
One input step is one return period. Use equally spaced observations and match periods per year: 252 is a common trading-day convention, 52 weekly, and 12 monthly. These are editable assumptions, not detected from your data.
Is annualized volatility a forecast?
No. The output multiplies observed per-period SD by the square root of periods per year. This scaling assumes stable variance and uncorrelated returns; it can mislead with serial dependence, volatility changes, or irregular sampling.
What happens with constant returns?
Standard deviation is zero. Skewness and excess kurtosis are undefined because their moment denominators are zero. Relative SD is also undefined if the mean is zero; the tool does not turn these into zero-valued evidence of safety.
Should prices be adjusted?
Use a consistent series for your question. Split adjustments avoid mechanical split jumps; a total-return series additionally requires the appropriate dividend/reinvestment treatment. Check the provider definition rather than assuming every adjusted close is total return. This form does not adjust prices itself.
Are these sample-adjusted skewness and kurtosis?
No. Shape statistics use population central moments: m3 / m2^(3/2) and m4 / m2^2 − 3. They remain unchanged when switching the SD denominator. Small samples make these estimates particularly unstable.
Can this identify a suitable investment?
No universal low, moderate, or high risk grade is applied. Historical return dispersion does not measure all liquidity, leverage, or tail risks. The calculator performs local arithmetic without fetching a ticker or connecting an account.
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