BOLL (Bollinger Bands): calculation and reading

Bollinger Bands use a moving average as the midline and add and subtract a multiple of the standard deviation to draw the range of price fluctuation.

Updated：2026-11-08

Where the three lines come from

• Middle band: the N-day simple moving average (default 20 days).
• Upper band: middle band + K times the standard deviation (default 2).
• Lower band: middle band − K times the standard deviation.

The standard deviation measures how widely the last N closing prices are spread around the middle band. This site uses the population standard deviation by default, and you can switch to the sample standard deviation; the multiple can be adjusted between 0.5 and 5.

How to read it

• Price spends most of its time between the upper and lower bands; a wider band means larger fluctuation, and a narrower band means smaller fluctuation.
• %b = (close − lower band) ÷ (upper band − lower band): 1 means at the upper band, 0 means at the lower band, and 0.5 means at the middle band.
• Band width = (upper band − lower band) ÷ middle band, which lets you compare fluctuation across different periods.

Limits

Price touching the upper or lower band only means it is relatively far from the moving average; it does not mean a reversal must follow. In a clear trend, price can run along the upper or lower band for a long time. The bands are calculated from historical closing prices and do not predict the future.

Where the idea comes from

Bollinger Bands were introduced by John Bollinger. This article explains them in our own words.

This article only explains the calculation and how to read a chart. It is not investment advice.