Direct answer
A worked example of Bollinger Range shows how you turn a price series and Bollinger Band calculations into a single, interpretable distance measure. Because “Bollinger Range” is used in different ways, you must state the exact definition you are using—typically based on the upper band, lower band, and (sometimes) the middle band.
In this article, a worked example means: you choose explicit numbers for inputs, calculate the Bollinger Band levels from those assumptions, and then compute Bollinger Range from the computed bands. No live prices are used.
Mechanism or definition
First, define the core building blocks.
Bollinger Bands usually consist of three lines computed from a moving average (the middle band) plus or minus a multiple of standard deviation (a volatility measure). The most common convention uses a 20-period simple moving average and 2 standard deviations, but parameter choices can vary.
Next, define Bollinger Range. Because definitions vary, the example here uses a clear distance measure:
Bollinger Range (example definition):
- Compute Upper Band = Middle Band + k · SD
- Compute Lower Band = Middle Band − k · SD
- Then define Bollinger Range = Upper Band − Lower Band
With this definition, the range simplifies to:
- Bollinger Range = (Middle + k·SD) − (Middle − k·SD) = 2k·SD
So, under this specific definition, Bollinger Range is directly proportional to the standard deviation (volatility). That separation is important: the “worked example” is about math, not about predicting outcomes.
Evidence or example (fully numeric)
Assume you are working on one bar at the current time, and you will compute bands from the following assumed inputs:
Assumptions (stated):
- Middle Band (20-period moving average, value in price units) = 1.2000
- Standard deviation over the same lookback window (SD, in price units) = 0.0100
- Band width multiplier k = 2.0
Now calculate:
- Upper Band = 1.2000 + 2.0 · 0.0100 = 1.2000 + 0.0200 = 1.2200
- Lower Band = 1.2000 − 2.0 · 0.0100 = 1.2000 − 0.0200 = 1.1800
Finally, compute Bollinger Range with the chosen definition:
- Bollinger Range = Upper Band − Lower Band = 1.2200 − 1.1800 = 0.0400
Check the shortcut:
- 2k·SD = 2 · 2.0 · 0.0100 = 0.0400, which matches.
What this numerical example tells you: under these assumptions, Bollinger Range quantifies how wide the bands are in absolute price units. If SD increases, the computed range increases proportionally.
Optional comparison (still using assumptions): if you keep Middle Band = 1.2000 and k = 2.0 but the SD rises to 0.0125, then:
- Bollinger Range = 2k·SD = 4 · 0.0125 = 0.0500 This shows sensitivity to volatility.
Limitations and risks
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Definition mismatch risk. Some sources compute Bollinger Range differently (for example, as a percent of the middle band, or using only the distance to one band). Your calculations only match the intended meaning if you use the same formula.
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Parameter sensitivity. Lookback length and k change the band width and standard deviation estimate. Even with identical math, different inputs produce different ranges.
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Market and condition uncertainty. Bollinger Bands rely on historical dispersion. The fact that a band width was wide or narrow in the past does not establish what will happen next.
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Failure mode: treating a range as a standalone rule. A range value can help describe volatility, but it does not guarantee that prices will behave in any particular way. Execution costs, slippage, and regime changes can all break simple interpretations.
Verification or next question
To independently verify the example, you can recompute the bands from the stated assumptions (Middle Band, SD, and k) and confirm that Bollinger Range equals Upper Band minus Lower Band. If you use a different definition (for example, dividing by the middle band to get a percent), redo the final step and document the exact formula.
A good next question is: Which Bollinger Range definition are you using—absolute width (Upper − Lower), or a normalized width (for example, (Upper − Lower) / Middle)? The worked calculation will change only in the last formula, but the meaning can change too.