Crypto Volatility Calculator
Historical volatility quantifies how much a cryptocurrency's price has varied over a past period. It is the annualized standard deviation of the natural logarithm of daily price ratios. This is the same method used in the Black-Scholes option pricing model and by financial institutions for risk measurement. Enter a series of daily closing prices (oldest to newest) separated by commas.
Historical volatility formula
Daily Log Return(t) = ln(Price(t) / Price(t-1))
Mean Return = Sum of all Log Returns / N
Daily Variance = Sum of (Return(t) - Mean)^2 / (N - 1)
Daily Volatility = sqrt(Daily Variance)
Annualized Volatility = Daily Volatility x sqrt(Trading Days Per Year)
Source: Black, F. and Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy. The sample standard deviation (dividing by N-1) is used per standard statistical practice.
Interpreting volatility figures
- Annualized volatility of 0-10%: very low (typical of stablecoins or near-stable assets).
- 10-30%: moderate (comparable to large-cap equities like the S&P 500 at approximately 15-20%).
- 30-80%: high volatility (typical for Bitcoin and Ethereum in calmer periods).
- 80-150%+: very high (typical during bull markets or altcoin speculative phases).
- Higher volatility means both larger potential gains and larger potential losses over any given period.
Crypto volatility: frequently asked questions
What is historical volatility in crypto?
Historical volatility (HV) measures how much an asset's price has fluctuated over a past period, expressed as an annualized standard deviation of daily logarithmic returns. A higher HV means the price has moved more dramatically. Bitcoin's 30-day historical volatility has typically ranged from 40% to over 100% annualized, compared to about 15-20% for the S&P 500.
How is historical volatility calculated?
Step 1: Calculate daily log returns: r(t) = ln(P(t) / P(t-1)). Step 2: Calculate the mean of log returns. Step 3: Calculate the standard deviation of log returns. Step 4: Annualize: HV = StdDev x sqrt(trading days per year). For crypto, 365 trading days per year is used (markets trade 24/7). For stocks, 252 trading days is standard.
What is the difference between historical and implied volatility?
Historical volatility (HV) is backward-looking: it measures past price movements. Implied volatility (IV) is forward-looking: it is derived from the market price of options and reflects the market's expectation of future volatility. Crypto options are available on some exchanges, providing IV data.
Why do we use log returns instead of simple returns?
Logarithmic returns (log returns) are preferred in financial statistics because they are symmetric (a 50% loss followed by a 100% gain returns to the starting point), additive over time, and more closely follow a normal distribution. Simple percentage returns do not have these properties. The use of log returns is standard in the Black-Scholes model and financial econometrics.
How many data points do I need to calculate volatility?
A minimum of 10-20 data points is recommended for any meaningful calculation. Common lookback periods are 30 days (short-term), 90 days, or 252 days (1 year). Shorter windows react faster to recent volatility; longer windows provide a more stable, long-term measure. Enter closing prices separated by commas, one per day.
Official sources
- Black, F. and Scholes, M. (1973), Journal of Political Economy (option pricing and volatility): jstor.org/stable/1831029.
- NIST Engineering Statistics Handbook, standard deviation: itl.nist.gov handbook.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.