Paste a list of closing prices and see how much they really moved. The calculator turns prices into daily, weekly or monthly log returns, takes their standard deviation and annualizes it, with a rolling volatility chart and a full returns table.
Last updated:
Chart
How it was calculated
Returns table
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How to use the Historical Volatility Calculator
Paste your prices, one per line, optionally with a date before each price. A full CSV export with a header row also works.
Check the price column and periods per year. Auto picks Adj Close or Close and detects daily, weekly or monthly data from the dates.
Choose log or simple returns and a rolling window for the chart.
Read the annualized volatility and the per-period standard deviation, then explore the returns, rolling volatility and price charts.
Copy the results or download the CSV with every return and the rolling volatility.
The historical volatility formula
Returns: rt = ln(Pt ÷ Pt−1) for log returns, or Pt ÷ Pt−1 − 1 for simple returns.
Mean: r̄ = (r1 + r2 + … + rn) ÷ n
Sample standard deviation: s = √( Σ (rt − r̄)² ÷ (n − 1) )
Annualized volatility: σannual = s × √N, where N is the number of return periods per year.
Volatility grows with the square root of time, not linearly. That is why a 1.5% daily standard deviation becomes about 1.5% × 15.87 ≈ 23.8% a year, not 1.5% × 252.
Annualization factors
Data frequency
Periods per year (N)
√N
1% per-period SD becomes
Daily, stocks (trading days)
252
15.87
15.9% a year
Daily, crypto (every day)
365
19.10
19.1% a year
Weekly
52
7.21
7.2% a year
Monthly
12
3.46
3.5% a year
Quarterly
4
2.00
2.0% a year
Tips for reliable volatility numbers
Use adjusted prices (Adj Close) so dividends and stock splits are not mistaken for price drops. A 2-for-1 split in raw prices shows up as a fake −50% day.
Keep the frequency consistent. Mixing daily and weekly prices, or leaving gaps, distorts the standard deviation.
Pick the window for your question. 20–30 days shows the current regime; one year or more gives a long-run baseline.
Volatility clusters. Calm and stormy periods tend to last, which is why the rolling chart often moves in waves rather than staying flat.
Volatility is not the whole risk story. Pair it with the maximum drawdown to see the worst loss, and with beta to see how much of the movement follows the market.
Frequently asked questions
How is historical volatility calculated?
Turn each pair of consecutive prices into a return, usually the log return ln(P today ÷ P yesterday). Take the sample standard deviation of those returns, then multiply by the square root of the number of periods in a year: √252 for daily stock prices, √52 for weekly and √12 for monthly data. The result is the annualized historical volatility.
Why use 252 instead of 365 for daily data?
US stock markets are open about 252 days a year, and prices do not move on weekends or holidays, so 252 trading days is the standard annualization factor for daily stock data. Crypto trades every day, so 365 is the usual choice for crypto prices.
Should I use log returns or simple returns?
Log returns are the standard for volatility because they add up over time and treat gains and losses symmetrically. For daily data the two give almost the same answer; the difference only becomes noticeable with large moves or long intervals.
What is a normal volatility for a stock?
Broad stock indexes have historically had annualized volatility in the mid-teens percent in calm periods and much higher in crises. Large, stable companies are often around 20–30%, while small caps, growth stocks and crypto can run well above 50%. These are rough ranges, not fixed rules; compare stocks over the same period.
What does annualized volatility tell me?
Volatility is one standard deviation of yearly returns. If returns were roughly normal, a stock with 25% volatility would end about two thirds of years within ±25% of its average return. It measures how much the price swings, not whether it goes up or down.
How many prices do I need?
The calculator works from 3 prices, but short samples are noisy. Common windows are 20 or 30 trading days for short-term volatility and 60, 90 or 252 days for a steadier estimate.
Is historical volatility the same as implied volatility?
No. Historical (realized) volatility is measured from past prices. Implied volatility is backed out of option prices and reflects what the market expects for the future. Traders often compare the two.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.