How to calculate Bollinger Bands
Middle band = SMA(n)
Upper band = SMA + k × σ Lower band = SMA − k × σ
σ = population standard deviation of the last n closes
%B = (Close − Lower) ÷ (Upper − Lower)
Bandwidth = (Upper − Lower) ÷ Middle × 100
Paste prices oldest-first, one value or row per bar — straight from a spreadsheet or CSV export. Use “Sample data” to try it instantly.
Worked example
- 20-bar SMA = 100, standard deviation = 2.
- Upper = 100 + 2 × 2 = 104, lower = 96.
- Close at 103 → %B = (103 − 96) ÷ 8 = 0.875.
How to interpret Bollinger Bands
Bands widen when volatility rises and contract when it falls. A “squeeze” — bandwidth at its lowest in months — often precedes a big move. Closes outside the bands (%B above 1 or below 0) show strong momentum, not automatically a reversal. For a pure volatility measure see the ATR.
Limitations and common mistakes
- Statistically, prices are outside 2σ bands more often than the normal distribution suggests.
- In strong trends price can “walk the band” for a long time.