Bollinger Bands, Keltner Channels and ATR: Measuring Volatility

Before you read: MACD Explained: Lines, Histogram and What Crosses Mean

What you will learn

• How Bollinger Bands use standard deviation to draw bands around an average.
• How average true range is calculated and how Keltner Channels use it.
• What a band “squeeze” describes, and why touching a band is not a signal.

Why measure volatility at all?

Would a $2 move mean the same thing in a quiet market and a wild one?

Volatility is how much price tends to move. A move that is large for a quiet market can be ordinary for a busy one. Volatility measures put moves in context, and many traders use them to size positions and set distances for stop orders. The position size lesson shows how the distance to a stop changes the size of a position for the same risk.

How are Bollinger Bands built?

If you drew lines a fixed number of standard deviations around an average, how would they behave when markets get busier?

Bollinger Bands, developed by John Bollinger, have three lines. The defaults are:

• Middle band: a 20-period simple moving average of closes.
• Upper band: the middle band plus 2 standard deviations of the same 20 closes.
• Lower band: the middle band minus 2 standard deviations.

When closes spread out, the standard deviation grows and the bands widen. When closes bunch together, the bands narrow. Two related measures are bandwidth (the distance between the bands divided by the middle band) and %B (where price sits between the bands, with 0 at the lower band and 1 at the upper).

You may have read that about 95% of values in a normal distribution fall within two standard deviations of the mean. That is not a forecast about these bands. Each band is built from a recent average of closes and the spread of those closes. The next price is not a random draw from a known, fixed distribution just because the formula uses standard deviation. Even if returns were normally distributed, price levels would not follow from that. Trends, dependence between bars, estimated inputs and fat tails all matter. John Bollinger’s own published rules say to make no statistical assumptions based on the standard deviation calculation. This lesson does not establish any next-bar coverage rate or confidence interval.

Fictional hand example, deliberately length 4 for calculation rather than changing the stated 20 default: closes 98, 100, 100, 102 price units have mean 100. Using population divisor 4, the squared deviations 4+0+0+4 sum 8, variance 2, SD √2≈1.414214. At multiplier 2, the band is 100±2√2, or 97.171573–102.828427. Its width≈5.656854; normalized bandwidth≈0.05656854 (5.656854% of the middle). The last 102 close has %B=(102−97.171573)/5.656854≈0.853553. An invented next close of 110 would sit outside these bands, which were calculated before that bar. Including 110 would create a new rolling window with a new mean and standard deviation. One example cannot confirm or refute any coverage rate; it only shows which quantity was calculated.

Volatility bands diagram

Illustrative diagram constructed for teaching. Not real market data.

The diagram shows a fictional price path with Bollinger Bands. The bands narrow during a quiet stretch and widen when moves get larger, while the ATR panel below rises at the same time. It is constructed for teaching and is not real market data.

How is ATR calculated?

What is the full distance price traveled in a bar, including any gap from the prior close?

True range for one bar is the largest of three distances:

1. high − low;
2. the distance from the high to the prior close;
3. the distance from the low to the prior close.

The second and third cover gaps: if a market opens well above yesterday’s close, the bar’s own high-low range understates how far price moved. Average true range (ATR), introduced by J. Welles Wilder, is a smoothed average of true range, usually over 14 bars. ATR is in price units and has no direction: it rises in busy markets whether prices are rising or falling.

Example. Prior close $50, today’s high $53, low $51. High − low is $2, high − prior close is $3, low − prior close is $1. True range is $3.

How are Keltner Channels different?

What changes if the band width comes from ATR instead of standard deviation?

A Keltner Channel draws bands a multiple of ATR around an exponential moving average, commonly a 20-period EMA with bands 1.5 or 2 ATRs away. Their width inputs differ: ATR uses bar ranges/gaps while close-based standard deviation uses dispersion of closes. Relative smoothness depends on lengths, smoothing and the price path; there is no universal guarantee that one channel is smoother under every configuration.

What is a squeeze?

What happens to the bands when a market goes quiet for a while?

A squeeze is a period when Bollinger Bands narrow. John Bollinger’s published rules use BandWidth to identify it. Some traders instead define it as the Bollinger Bands moving inside a Keltner Channel. These definitions need not agree, so state which one you use. A squeeze describes low recent volatility. It does not say when volatility will expand or in which direction, and this lesson measures no frequency of later expansion.

What this does not tell you about volatility bands

• A touch of a band is not a sign that price will reverse or continue. In strong trends, price can ride along a band for a long time.
• Volatility measures look backward. They do not tell you how much the next bar will move.
• A squeeze does not show the direction of any later move.
• Nothing here is a signal to buy or sell.

Check yourself

1. Prior close $30, high $31, low $28. What is the true range? Hint: compare all three distances.
2. Why do Bollinger Bands widen when markets get busier? Hint: what happens to standard deviation?
3. Why is “the next price has 95% probability of staying inside the current bands” not established merely by drawing 2 SD bands?
4. Recompute the four-close example’s mean and variance. Would a newly included 110 leave the same window unchanged?

Last reviewed November 8, 2026. Spotted a mistake? Report an error.