Sigma Price Bands Calculator
From spot, annual volatility and days, show symmetric ±1/2/3σ price bands for the horizon (log scale).
Results
Fill in the inputs and click Calculate.
- +1σ Upper
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- +2σ Upper
- –
- +3σ Upper
- –
- −1σ Lower
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- −2σ Lower
- –
- −3σ Lower
- –
- Horizon Volatility
- –
Risk disclaimer
The normal approximation understates tails; band width depends only on your volatility and days inputs.
What do the bands mean?
Under an approximately log-normal return, the price ends within ±1σ about 68% of the time, ±2σ about 95%, and ±3σ about 99.7%.
Those are end-of-period probabilities; paths can wander inside and briefly outside the band before ending.
How to use
- Enter the current price.
- Enter the annualized volatility %.
- Enter the horizon in days.
- Click Calculate for the 1/2/3σ upper and lower bounds.
Formula
- Horizon volatility = annual vol × √(days ÷ 365)
- kσ upper = spot × e^(k × horizon vol)
- kσ lower = spot × e^(−k × horizon vol)
Example
Spot 100, 60% annual vol, 30 days → ±1σ ≈ 118.77 / 84.20, ±3σ ≈ 167.54 / 59.69.
Longer horizons widen the bands as uncertainty accumulates.
FAQ
vs the volatility range tool?
That tool gives a single band for your chosen z; this page shows the 1/2/3σ ladder at once.
Why exponential, not linear?
Log scale keeps prices non-negative and makes up/down moves symmetric, matching geometric Brownian assumptions.