Historical Volatility Calculator
Historical volatility tells you how much an asset's price has actually moved over a past window. It is the annualised standard deviation of the asset's log returns, and it is a key input to option pricing and risk models. Paste a list of closing prices (oldest to newest), set the periods per year that match your data, and this calculator returns the per-period and annualised volatility.
Historical volatility formula
Log return r_t = ln(price_t / price_t-1)
Mean r-bar = sum(r_t) / n
Sample variance = sum((r_t - r-bar)^2) / (n - 1)
Per-period vol = sqrt(variance)
Annualised vol = per-period vol * sqrt(periods per year)
n is the number of returns (one fewer than the number of prices). The sample standard deviation uses the n-1 (Bessel) correction. Volatility is shown as a percentage.
Worked example
Prices 100, 102, 101, 103. Log returns: ln(102/100) = 0.019803, ln(101/102) = -0.009852, ln(103/101) = 0.019608. Mean = 0.009853. Deviations squared sum to about 0.000582; sample variance = 0.000582 / 2 = 0.000291; per-period vol = 0.017066 (1.71%). Annualised over 252 days: 0.017066 * sqrt(252) = 0.2709, or 27.09%.
Historical volatility: frequently asked questions
What is historical volatility?
Historical (realised) volatility measures how much an asset's price has actually fluctuated over a past period. It is the standard deviation of the asset's log returns, annualised by multiplying by the square root of the number of periods per year (typically 252 trading days for daily data).
Why use log returns?
Log returns, ln(price_t / price_t-1), are time-additive and symmetric, which makes them the standard choice for volatility estimation. The sample standard deviation of these log returns, using n-1 in the denominator, gives the per-period volatility before annualisation.
What annualisation factor should I use?
For daily closing prices, 252 trading days per year is the convention; the annual volatility is the daily figure times sqrt(252). For weekly data use 52, for monthly use 12. Enter the periods-per-year that matches your price series.
Sources and method
- U.S. Securities and Exchange Commission investor education: Investor.gov.
- Method: the sample standard deviation of log returns, annualised by the square root of time; a standard public statistical estimator. No proprietary data is used.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.