What Are Bollinger Bands? How the 20-Period, Two Standard Deviation Bands Work

Bollinger Bands are three lines on a price chart: a 20-period simple moving average, with an upper and a lower band set two standard deviations from it.

The bands are one of the most recognisable overlays on a chart: an envelope that widens when prices swing and narrows when they settle. This page covers who devised them and the exact recipe, a worked example done by hand, what the width of the bands measures and what it does not, how often S&P 500 closes have actually sat inside them, the readings people name, and how Kresmion's charts draw them. It is descriptive throughout.

Where the bands come from

John Bollinger developed the bands after he began working in the markets full time in 1980, starting from the fixed percentage bands then in use. On his own site he describes the formulation as an n-period moving average with bands drawn above and below it at a multiple of the standard deviation, and he states that the population calculation is used for the standard deviation. The defaults are 20 periods for the average and plus and minus two standard deviations for the bands. His published rules call those numbers "just that, defaults", meaning a given market or bar interval can need different ones.

Bollinger Bands is a registered trademark of John Bollinger, which is why some platforms print the name with a registered sign.

How they are calculated

With the default settings, on every bar:

1. Middle band. The simple average of the last 20 closes, the same simple moving average described in what a moving average is. 2. Standard deviation. How far those same 20 closes sit from their average: take each close minus the average, square it, add the squares, divide by 20 and take the square root. Dividing by the number of values, 20, is the population formula Bollinger specifies. Dividing by 19, the sample formula, gives a standard deviation about 2.6 percent wider, which is one reason two charts can draw slightly different bands for the same prices. 3. Upper band. The middle band plus two standard deviations. 4. Lower band. The middle band minus two standard deviations.

Bollinger's rules also say the middle band is a simple average because a simple average is what the standard deviation calculation itself uses, so the two are consistent.

A worked example

Twenty rows make a long table, so this example uses a 5-period window to keep the arithmetic short. The steps are identical at 20.

A hypothetical stock closes at 100, 102, 101, 104 and 103.

• Middle band: (100 + 102 + 101 + 104 + 103) / 5 = 102.00
• Deviations from 102: minus 2, 0, minus 1, plus 2, plus 1. Squared: 4, 0, 1, 4, 1, which sum to 10.
• Standard deviation: the square root of 10 / 5, which is the square root of 2, about 1.414
• Bands: 102.00 plus and minus 2 x 1.414 gives an upper band of 104.83 and a lower band of 99.17

The next day the stock closes at 110, a jump of 7 points. The window drops the 100 and becomes 102, 101, 104, 103, 110.

• Middle band: 520 / 5 = 104.00
• Squared deviations: 4, 9, 0, 1 and 36, which sum to 50. Standard deviation: the square root of 50 / 5, about 3.162
• Bands: an upper band of 110.32 and a lower band of 97.68

The close of 110 is well above the previous day's upper band of 104.83, yet it sits inside the new one, because the jump itself entered the window and more than doubled the standard deviation. The bands are recomputed from the price they are drawn around, so a large move widens the envelope on the same bar.

There is also a hard limit at short windows. With the population standard deviation, no value in a window of n values can sit more than the square root of (n minus 1) standard deviations from their mean. With five values that limit is exactly 2, so a close can at most touch a 5-period band at two standard deviations, and only when the other four closes are equal; it can never cross it. At 20 periods the limit is about 4.36, and closes outside the bands do occur.

What the width measures, and what it does not

The distance between the bands is four standard deviations of recent closing prices. It is a measure of how spread out the last 20 price levels were, in the same currency units as the price. Two features follow from that.

First, it is the dispersion of price levels, not of returns. A steady climb with no day-to-day swings still produces wide bands, because the 20 closes in the window sit at different levels. Return volatility, the measure implied volatility is quoted as and the one risk statistics use, is built from percentage changes instead, so the two can disagree.

Second, the two-standard-deviation rule of thumb from statistics, that about 95 percent of values fall within two standard deviations of the mean, holds for a single draw from a normal distribution whose mean and standard deviation are known. Here both are estimated from 20 consecutive, often trending price levels that include the close being tested, so the share of closes inside the bands is an empirical question. Bollinger's own rules say that in practice about 90 percent, not 95 percent, of the data falls inside the bands at the default settings.

How often closes sit inside the bands: the S&P 500

Computed with the default settings on the S&P 500's daily closes as published by the Federal Reserve Bank of St. Louis (FRED series SP500), from the first full 20-close window on 28 October 2016 to 30 September 2026:

About 89 percent of closes were inside, not 95, and more closes finished above the upper band than below the lower one over this decade. The figures describe one index over one period; another market, interval or decade gives different shares.

The readings people name

Several readings come up with the bands, and each is a description of where prices have been.

• A tag of a band. A close at or beyond the upper or lower band. Bollinger's own rules say a tag is just that, a tag, and that a tag of a band is not in and of itself a reason to act either way. They also note that in a trending market prices can walk up the upper band or down the lower band for a long stretch.
• %b. Where the close sits within the bands, from 0 at the lower band to 1 at the upper band. In the worked example the close of 110 had a %b of about 0.97.
• BandWidth. The distance between the bands divided by the middle band. In the example it is 12.65 / 104.00, about 0.12, or 12 percent of price.
• The squeeze. A stretch when BandWidth falls to a low level relative to its own history, meaning the last 20 closes have been unusually close together. It describes a quiet period and says nothing about which direction the next move takes.

%b and BandWidth are Bollinger's own companion measures, described on his site. %b is (close minus lower band) divided by (upper band minus lower band), so it reads above 1 when the close is above the upper band and below 0 when it is under the lower band.

Bollinger Bands in Kresmion's charts

Kresmion's charting workspace lists Bollinger Bands in the volatility group of its Indicators menu, drawn on the price pane over the candles for any stock, index, crypto pair or other market the charts cover. The defaults are 20 periods, two standard deviations and the close, matching Bollinger's. The length can be set from 2 to 500, the multiple from 0.5 to 5 in steps of 0.5, and the input switched from the close to the open, high, low or one of three price averages. The standard deviation uses the population formula, as Bollinger specifies, and the middle band is drawn dashed between the two solid outer bands. The same menu carries a Keltner Channel, an envelope built on an exponential average and the average true range, and a Standard Deviation indicator for the raw dispersion in its own pane. %b and BandWidth are not built-in indicators. The charts open with a free Kresmion account.

Honest limitations

The bands are built only from past prices. They describe how spread out recent closes were and where today's close sits against them; they carry no forward-looking term. The share of closes inside them depends on the market, the interval and the period, as the S&P 500 table shows. They can differ between platforms because of the standard deviation formula, the price input, and adjusted versus unadjusted history. The worked example uses invented prices, and the S&P 500 figures are a price index that excludes dividends.

Key takeaways

Frequently asked questions

What are the default Bollinger Band settings?

A 20-period simple moving average with bands two standard deviations above and below it, computed on closing prices. Bollinger's own rules describe these as defaults and suggest raising the multiple to about 2.1 for a 50-period average and lowering it to about 1.9 for a 10-period one, so the bands keep containing a similar share of prices.

What does it mean when the price touches the upper Bollinger Band?

It means the close is about two standard deviations above the average of the last 20 closes. Bollinger's rules say that a tag of a band is not in itself a reason to act, and that prices can walk along a band during a trend.

Do Bollinger Bands contain 95 percent of prices?

Not as a rule. That figure comes from the normal distribution, and consecutive closing prices do not follow it. On the S&P 500's daily closes from late 2016 to September 2026, about 89 percent closed inside the default bands.

What is a Bollinger Band squeeze?

A period when the bands narrow to an unusually small width relative to their own history, measured by BandWidth. It records that recent closes have been tightly grouped. It does not indicate the direction or timing of the next move.

Why do my Bollinger Bands look different on another platform?

The most common reasons are the standard deviation formula (population or sample), the price input, a different length or multiple, and whether the history is adjusted for splits and dividends. A sample standard deviation over 20 closes is about 2.6 percent wider than the population one.

This page is information, not investment advice.

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Source: John Bollinger, Bollinger Bands, https://www.bollingerbands.com/bollinger-bands ; John Bollinger, Bollinger Band Rules, https://www.bollingerbands.com/bollinger-band-rules ; StockCharts ChartSchool, Bollinger Bands, https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/technical-overlays/bollinger-bands ; StockCharts ChartSchool, %B Indicator, https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/technical-indicators/b-indicator ; StockCharts ChartSchool, Bollinger BandWidth, https://chartschool.stockcharts.com/table-of-contents/technical-indicators-and-overlays/technical-indicators/bollinger-bandwidth ; S&P Dow Jones Indices, S&P 500 daily close (FRED series SP500, downloaded 1 October 2026), https://fred.stlouisfed.org/series/SP500 ; band containment shares computed by Kresmion from that series ; Kresmion chart engine (Bollinger Bands indicator, defaults 20 and 2). Prices in the worked example are invented.

Kresmion Research.