Bollinger Bands

Reviewed 12 August 2026 · Sourced from John Bollinger’s own published rules and construction notes, platform documentation, and two named papers on how prices are actually distributed

What the three lines are drawing

A stock you have been watching pokes above a curved line on the chart. Somebody in the replies says “overbought,” somebody else says take the profit while it lasts. Three weeks later the stock is higher than it was that day, and it has spent almost every session since pressed right up against that same line. Whoever sold the first touch has been watching from the sidelines the whole time.

That line is the upper Bollinger Band. The reason the replies got it wrong is not subtle and not a matter of opinion: the band was never a sell signal, and the man who invented it published a numbered rule saying so. That rule is quoted word for word below.

Bollinger Bands are three lines laid over a price chart. The middle one is a plain moving average — add up the last 20 closing prices, divide by 20, plot the dot, do it again tomorrow. The other two sit above and below that average, and the distance is set by how much the price has actually been moving around lately. Choppy stretch, the outer lines spread apart. Quiet stretch, they squeeze in toward the average. It is a channel that breathes with volatility.

John Bollinger developed them in the 1980s and still maintains bollingerbands.com, where he has published a list of 22 rules for using them. Rule 1 is the cleanest definition of purpose anybody has written: the bands “provide a relative definition of high and low. By definition price is high at the upper band and low at the lower band.”

Everything else on this page is either how that gets calculated, or a list of the things people load onto it that it cannot carry.

How the bands are built, with the arithmetic shown

You will never compute this by hand, but the formula is short and knowing its shape explains three separate things that confuse people later.

Two construction details are worth having. First, the middle band is a simple moving average, not an exponential one, and Bollinger’s Rule 12 gives the reason: “a simple average is used in the standard deviation calculation and we wish to be logically consistent.” Second, his site specifies the population calculation for standard deviation — divide the summed squared deviations by 20, not by 19. That sounds like pedantry until you check it against a spreadsheet, which defaults to the other one.

Now the divide-by-19 problem. A spreadsheet’s standard deviation function divides by 19 instead: 80.00 ÷ 19 = 4.2105, whose square root is $2.05, putting the bands at $54.10 and $45.90. Ten cents off in each direction, from nothing but the denominator. If you ever build this yourself and your numbers disagree with your platform by a hair, look there first.

The third thing the formula shows is that the outer bands have no independent existence. Nobody drew them, and no buyer or seller is watching a price there the way they might watch a round number or a prior high. They are the average plus a number computed from the last 20 bars. When those bars change, the bands move — including moving away from a price that just touched them.

Why it is not 95%, and why the creator says so himself

Here is the claim you will meet within ten minutes of learning what a standard deviation is: two standard deviations covers about 95% of observations, so about 95% of prices should sit inside Bollinger Bands, so a price outside them is a rare event worth acting on.

The intuition is appealing because the first half is genuinely true — for a normal distribution. In a bell-shaped normal distribution, roughly 95% of values do fall within two standard deviations of the mean. That is a real property of a real mathematical object. The problem is every step of getting from there to a stock chart.

Asset returns are not normally distributed. Eugene Fama measured this in 1965 in The Behavior of Stock-Market Prices and found daily stock returns had fatter tails and a taller peak than a normal distribution — too many tiny days and far too many enormous ones for the bell curve to describe. Extreme moves are not as rare as the normal distribution says. They are also the exact moves that push price outside a band, so the assumption breaks precisely where you were leaning on it.

Volatility clusters. Big moves arrive next to other big moves; quiet days next to other quiet days. Robert Engle formalized this in 1982 with ARCH models in Econometrica, and the 2003 Nobel Memorial Prize in Economic Sciences cited him “for methods of analyzing economic time series with time-varying volatility (ARCH).” If volatility is not constant, a single standard deviation figure is not describing a stable spread. It is describing one recent stretch, which the next stretch is under no obligation to match.

And the sample is 20 observations of a moving target. Twenty is a very small sample for saying anything about a distribution’s tails. Worse, the thing being averaged has no fixed center: over the 20 sessions above, price drifted from the mid-$46s to $53. The mean is walking, and a standard deviation measured around a walking mean is partly measuring the walk rather than the noise.

That is the single most useful sentence written about this indicator, and it comes from the person with the most to gain from you believing otherwise. The originator’s own instruction is to draw no statistical conclusion from the standard deviation in his own formula.

His parenthetical figure is around 90%. StockCharts’ documentation, describing the same defaults, says the bands “should contain 88-89% of price action.” Neither publishes the dataset, the securities or the period, and they do not agree with each other, so both sit under Unverified in the ledger below. What they agree on is the part that matters: it is not 95%, and the gap is not rounding error. Notice too that in the worked example, none of the 20 closes fell outside the bands. That is what small samples do, and it is evidence of nothing.

What Bollinger says his own bands are not

The most valuable page on bollingerbands.com is the rule list, because most of it is the author narrowing the claims other people make on his behalf. Four rules do the heavy lifting, and they are worth quoting rather than summarizing.

Rule 6 — tags are not signals. “Tags of the bands are just that, tags not signals. A tag of the upper Bollinger Band is NOT in-and-of-itself a sell signal. A tag of the lower Bollinger Band is NOT in-and-of-itself a buy signal.” The capital letters are his. When a chart tutorial teaches you to fade the upper band, it is teaching you something the tool’s author explicitly ruled out.

Rule 8 — a close outside the bands means the opposite of what people assume. “Closes outside the Bollinger Bands are initially continuation signals, not reversal signals.” The instinct on seeing price break out of the channel is that it has gone too far and must snap back. Bollinger’s stated reading is the reverse: the first thing a close outside the band suggests is more of the same.

Rule 2 — the bands are an input, not an output. “That relative definition can be used to compare price action and indicator action to arrive at rigorous buy and sell decisions.” The bands supply the relative context; the decision is supposed to come from combining that with something else. Rule 4 adds that if you use more than one indicator alongside them, they should measure genuinely different things — two momentum tools stacked together repeat one opinion in two fonts. Pair them with something reading volume rather than a second oscillator.

Rule 22 — the honest ceiling on the whole thing. “Bollinger Bands do not provide continuous advice; rather they help identify setups where the odds may be in your favor.” Note “may.” No number follows it, in his rules or on this page, because no named study establishes a hit rate for any Bollinger Band signal and anybody quoting you one got it from somewhere other than the source.

That is an unusual thing for an indicator’s creator to publish, and it is the reason this tool is worth learning while a lot of chart furniture is not. The claims are bounded and the boundaries are written down.

Walking the band

The specific way band-tag trading loses money has a name, and again the name comes from Bollinger. Rule 7: “In trending markets price can, and does, walk up the upper Bollinger Band and down the lower Bollinger Band.”

The arithmetic makes this inevitable rather than surprising. The bands are recomputed on every bar from the most recent 20 closes. In a persistent advance, each new close is higher, so the average rises, so the whole channel rises with it. Price does not have to fall back to the average for the tag to end — the average can come up to meet the price. Nothing in the construction limits how many sessions in a row that can happen. There is no counter, no cap, no accumulating pressure.

TradingView’s own documentation describes the same behavior and states plainly that during a strong trend these breakthroughs “are not actual reversal signals.”

The awkward part — and no honest page can resolve it for you — is that the tag which precedes a genuine turn and the tag which is session three of a two-month walk look identical when they print. TradingView’s documentation concedes the point directly: pinpointing which one you are in “can be a difficult event to pinpoint.” That ambiguity is not a gap in your chart setup. It is a property of the tool.

The squeeze, and the one thing it cannot tell you

The best-known pattern on these bands is the squeeze: the two outer lines drift close together because the standard deviation of the last 20 closes has fallen. Price has been going nowhere in a narrow range, and on the chart the channel looks pinched.

Bollinger measures it with his own derived indicator, BandWidth, described in Rule 19: “BandWidth has many uses. Its most popular use is to identify ‘The Squeeze’.” StockCharts’ reference gives the calculation and describes the squeeze as occurring “when volatility falls to a low level, as evidenced by the narrowing bands,” on the theory that “periods of low volatility are followed by periods of high volatility.”

Here is the honest reading, and it is narrower than almost anything written about it. A squeeze is a statement about volatility that already happened, plus one tendency about volatility to come. Low realized volatility now; volatility historically does not stay compressed forever. That is the whole claim. There is nothing in it about direction. Narrow bands are equally consistent with the next big move going up and with it going down, because the calculation has no directional term at all — squaring the deviations throws the sign away before the number exists.

You will see the squeeze written up as though it resolves that. StockCharts phrases it as “a new advance starts with a Squeeze and subsequent break above the upper band. A new decline starts with a Squeeze and subsequent break below the lower band.” Read the structure carefully: the direction arrives with the break, not with the squeeze. The squeeze sets up a move whose direction you learn at the moment it happens — which is the moment you no longer needed the squeeze to tell you.

Two more limits. There is no universal BandWidth number that counts as a squeeze: StockCharts says explicitly that BandWidth must be “gauged relative to prior BandWidth values” for that specific security over eight to twelve months, and the figure of 10 that circulates online is an example from one airline chart, not a threshold. And the first break out of a squeeze can be a breakout that fails; the same reference warns that “initial breaks can sometimes fail.” How often, nobody credible has published, so this page will not tell you.

%b and BandWidth — comparing across stocks

Bollinger added two derived measures to solve a problem the bands create. The bands are drawn in dollars, so “price is $1.40 below the upper band” means something completely different on a $12 stock than on a $600 one, and you cannot line up two charts and compare. The fix is to convert position and width into plain numbers.

%b answers “where is price inside the channel.” Rule 15: “%b tells us where we are in relation to the Bollinger Bands. The position within the bands is calculated using an adaptation of the formula for Stochastics.”

BandWidth, from the previous section, answers “how wide is the channel” on the same footing. Together they are the two facts about a chart that survive being moved to another ticker: 0.88 and 16.0 tells another reader that price is high in its channel and the channel is moderately wide, without either of you knowing the share price.

Rule 17 pushes this further and is the cleverest item on his list: “Indicators can be normalized with %b, eliminating fixed thresholds in the process. To do this plot 50-period or longer Bollinger Bands on an indicator and then calculate %b of the indicator.” Wrap the bands around something that is not price — RSI, MACD, volume — and you get a reading of whether that indicator is high or low for itself, instead of arguing over whether the fixed line belongs at 70 or 75. Whether it improves anything is not established by any study this page could find. The idea is his, and it is worth knowing.

What is confirmed, what is not, and what is only convention

This page mixes claims of three very different strengths. Sorted, so you can see which is which instead of taking the whole page at one confidence level.

The pattern there is worth naming. The mechanics are solid and the interpretations are not. How the lines get drawn can be sourced to the author and checked against two platforms. What a drawn line predicts is either explicitly disclaimed by the author or unsourced entirely.

What trips people up

• Treating the upper band as a sell and the lower as a buy. Rule 6 exists specifically to rule this out, in capital letters, and it is still the most common use of the tool.
• Believing the 95% figure. Two standard deviations covers 95% of a normal distribution. Prices are not normally distributed, volatility is not constant, and 20 observations is not a sample you can make tail claims from. Bollinger’s own rule says to make no statistical assumptions at all here.
• Expecting a tag to resolve quickly. The bands are recomputed every bar. In a trend the average rises to meet the price, so a stock can sit on the upper band for weeks — the same way RSI can hold above 70 for months.
• Reading direction into a squeeze. Narrowing bands say volatility has been low. The calculation squares the deviations, which discards the sign before the number exists. There is no directional information in there to find.
• Turning the knobs until the chart looks profitable. Shortening the average or narrowing the deviation multiplier produces more tags of the bands. That is arithmetic, not a better signal, and every additional tag is one more thing to be wrong about.
• Stacking bands with three more momentum tools. Rule 4 asks for indicators that measure different things. Bands plus MACD plus RSI plus a stochastic is one opinion wearing four costumes, and it feels like confirmation.
• Forgetting the bands are drawn from the same prices you are trying to judge. They contain no information about the company, the sector or the news — that work happens on the fundamentals side, and the reason a tag feels significant is usually a bias worth checking on the behavior side.
• Using any of this with money that has a job. No overlay changes what a loss does to a household with no cushion under it. The emergency fund calculator is a more consequential tool than any chart on this site.

The figures on this page are checked against the source that publishes them, and dated. Published rates move after the release named above — the linked source always carries the current number. This page explains a term; it does not recommend a product.