Crypto volatility calculator with real Bitcoin data
Turn two Bitcoin price readings into a daily return, an annualized volatility estimate, and a one sigma daily move band. Runs on real BTC daily data from September 2026.
Volatility is the number that decides position size, stop distance, and how loud a drawdown will get. This page measures it from two real Bitcoin price readings and annualizes it the way practitioners do: daily return scaled by the square root of 365.
Your readings
Inputs and results stay in this browser. Values are capped to keep calculations finite and responsive.
Calculated result
- Daily return
- +8.62%
- Annualized volatility
- 30.06%
- One sigma daily band
- -1.57% to 1.57%
Price moved up from the first reading to the second, on a log basis.
Standard deviation proxy from a single daily return scaled by the square root of 365.
One standard deviation band around the middle reading, roughly a 8.62% move either way on an average day.
What the numbers say
A 30.06% annualized volatility fits one day at roughly an 8.62%% swing in either direction at one standard deviation. On roughly two thirds of days you would expect the move to land inside that band if the same rhythm held. A wide band means a jumpier market; a narrow band means a calmer one.
How the model turns two prices into a risk number
Enter two Bitcoin price readings and the number of calendar days between them. The model takes the log return between the readings, scales it to a daily figure, and then annualizes it by multiplying by the square root of 365. That annualized number is directly comparable to the volatility figures quoted for stocks and volatility indices.
The one sigma band answers the practical question: on a normal day, how far should price travel before it is merely routine? A band of 2% to 4% means a 3% day is noise. A band of 0.5% to 1% means the same move is an event worth checking against your stops.
Bitcoin's realized volatility has ranged from under 20% annualized in quiet stretches to over 100% in stressed ones. Whatever the market does next, the honest way to size exposure is to measure the current regime rather than assume yesterday's number still holds.
Worked example on real data
Enter a first reading of 111,532 and a second of 114,213, 30 days apart. The model turns the gap between the two into a daily return and an annualized volatility estimate. It also gives the one standard deviation daily move band you would expect around the middle reading.
Reading one is $111,532, reading two is $114,213, and the readings are 30 days apart. The daily log return is about 0.079%. Annualized, that is roughly 1.5%, which would be an extraordinarily calm regime. Insert the prices you actually care about and the same arithmetic produces the number that fits your window.
Where this model is honest and where it is thin
A single pair of readings produces one return observation, so the annualized figure is a scaling of that one observation, not a statistical estimate from a sample. Treat it as a sanity check on regime, not as a precise forecast. Multi-window studies need a full price series, which is what the site's backtest pages run on.
A two price point sample is a rough volatility gauge, not a full statistical estimate. Real daily returns cluster and jump, so one pair of readings cannot capture the true shape of the distribution. Annualizing assumes a move repeats evenly all year, which prices rarely do. Crypto can move far beyond any single standard deviation band. Treat the numbers as a planning sketch and confirm against a fuller dataset before acting.
The formulas this page runs
- daily return = ln(price2 / price1)
- annualized volatility = |daily return| x sqrt(365)
- one sigma band = price x (1 ± annualized volatility / sqrt(365))
Questions traders actually ask
Why annualize with the square root of 365?
Independent daily shocks add in variance, not in return. Variance scales linearly with time, so the standard deviation scales with the square root of time. Bitcoin trades every day of the year, so 365 rather than 252.
Is annualized volatility the same as implied volatility?
No. This page computes realized volatility from prices that already happened. Implied volatility is the market's forward-looking estimate embedded in option prices. The two often diverge, and the gap itself is tradable signal.
Can I use prices from different assets?
The arithmetic works on any two prices, but the interpretation only holds when both readings come from the same asset in the same currency. Mixing BTC and ETH readings produces a relative-return number, not a volatility estimate.
How should volatility change my position size?
A common rule keeps dollar risk constant: divide your risk budget by the expected move. If the daily band is 3% wide, a position sized for a 1% band is three times too large. Recompute when the regime shifts, not every day.
References
- Investopedia: volatility definition Defines volatility as the dispersion of returns and distinguishes realized from implied measures.
- CBOE VIX white paper methodology The reference methodology for annualizing and quoting a volatility index, used here as the scaling convention.