Bollinger Bands show price relative to an average and the dispersion of prices in a selected window. The upper line is not a ceiling and the lower one is not a floor. Two traders can assign opposite trading rules to the same chart, but neither interpretation establishes an outcome. This lesson starts with a calculation you can reproduce before studying possible applications.

What Bollinger Bands are made of

In the traditional construction, the middle line is SMA of n closing prices. Compute standard deviation σ from the same window; upper = SMA + k × σ and lower = SMA − k × σ. Each side is k × σ from the mean, while the entire channel is 2 × k × σ wide. The common (20, 2) settings are defaults, not universal optimum parameters. The period means bars of the selected timeframe, and a platform may allow another price source or basis type.

Components of the bands in standard settings (20, 2)
Middle lineTwenty-period simple moving average (SMA 20)
Upper bandSMA 20 plus two standard deviations taken from the same twenty candles
Lower bandSMA 20 minus two standard deviations
Band widthThe distance between the upper and the lower band — a rough measure of volatility

With k = 2, each band is two standard deviations from the mean and the full width is four. That arithmetic does not imply a 5% probability of a future outside close. John Bollinger warns against coverage assumptions; the calculation uses rolling price levels, not an independently estimated distribution of future returns. A tag alone does not define a complete buy or sell rule.

Two paths to the same band reading

Reorder the same four closes. Mean and standard deviation stay identical even though the charts look different.

Scroll sideways to see the full diagram

Two paths to the same band readingWindow A is 98, 98, 102, 102; B is 98, 102, 98, 102. Both have SMA=100 and population standard deviation=2, so with k=2 the final bands are 96 and 104. Band lines show one final reading, not the full indicator history.Identical bands do not recover price orderA · 98, 98, 102, 102U 104M 100L 96B · 98, 102, 98, 102U 104M 100L 96Both windows: SMA = 100 · σ = 2n = 4, k = 2 → L = 96, U = 104Same dispersion; different order.

Hypothetical model: arbitrary units, four closes, n = 4 and k = 2 only for the calculation. Horizontal lines show the whole-window reading, not bands computed at every candle. Population formula: MetaTrader 5 — Bollinger Bands.

Final band width does not reveal price order inside the window.

Compute one complete reading

Use hypothetical closed EUR/USD candles with n = 4 and k = 2, solely to make the arithmetic visible. The closes are 1.0990, 1.0990, 1.1010 and 1.1010 USD per EUR. SMA = 1.1000. Deviations are −0.0010, −0.0010, +0.0010 and +0.0010; each squared deviation is 0.000001. This is a teaching window, not a recommendation to trade four-period bands.

  1. The squared deviations sum to 0.000004. Divide by n = 4 for the population variance: 0.000001.
  2. Take its square root: σ = 0.0010. This is dispersion of the closing-price levels around one current-window mean, not dispersion of returns or of separate moving averages.
  3. Upper = 1.1000 + 2 × 0.0010 = 1.1020; lower = 1.1000 − 2 × 0.0010 = 1.0980.
  4. At pip 0.0001, each band is 20 pips from the mean and the full width is 40 pips.
  5. The last close 1.1010 is above the mean and below the upper band. That location does not supply entry, stop, size or exit rules.

Population and sample standard deviation

The MT5 formula divides the sum of squared deviations by n. A spreadsheet’s sample-standard-deviation function may divide by n − 1 instead. In the same four-price example, sample σ = √(0.000004/3) ≈ 0.00115470. With k = 2, its bands would be about 1.10230940 and 1.09769060. A wider spreadsheet result can therefore come from the denominator alone; the word “sample” does not make it the correct implementation to reproduce.

Checks when two band readings differ
InputsUse the same closed bars and price source.
Window and basisRecord n, the moving-average type and initialization where relevant.
DispersionCheck division by n or n − 1 and whether the same current-window mean is used.
MultiplierRecord k and distinguish one-sided distance from full channel width.
Time and offsetRecord chart and indicator timeframes and any line shift.
PrecisionKeep unrounded intermediate values until the final display.

An ADX reading can be an additional recorded input, but crossing 25 does not prove that a band-bounce rule starts or stops paying. Bollinger describes band tags and walking the bands without a guaranteed result. Similarly, the candlestick-pattern descriptions can define observations; they do not independently certify a turn or a profitable fill.

Changing the window or multiplier

Each new bar moves a rolling window: the oldest observation leaves and the newest enters. Recompute both mean and dispersion. Width can change because an earlier extreme leaves the window, even without a new large move. Current-bar inputs can also change before close; label that state when comparing it with a confirmed historical reading.

  1. Keep the four EUR/USD closes unchanged, so SMA stays 1.1000 and population σ stays 0.0010.
  2. Change only k from 2 to 1.5.
  3. The upper line becomes 1.1015 and the lower 1.0985.
  4. Full width becomes 0.0030, or 30 pips at pip 0.0001.
  5. The narrower channel came from the setting, not changed price behaviour. Record the parameter before comparing screenshots or counting events.

Price can remain near one band during a trend, as Bollinger notes. The observation alone does not fix how long the trend lasts or where it ends. A narrow window also does not specify the timing, direction or size of a subsequent move. Define any proposed condition and its information time before testing it.

The most common mistakes in reading the bands

  1. Confusing a tag with an outcome. A tag describes location, not guaranteed reversal or continuation.
  2. Assuming a required timeframe. Bollinger allows bars of different lengths; no universal H4 boundary certifies effectiveness.
  3. Assuming expansion must follow a close outside. Both the mean and dispersion change with the window. A band calculation does not determine which broker stop executes.
  4. Counting unavailable information. A completed close and its final bands were not known throughout the open bar.
  5. Selecting settings after seeing results. Separate parameter development from later unused data and retain failed tests as well as favourable examples.

Band width, the underrated companion

BandWidth normalizes upper-minus-lower width by the middle line; multiply by 100 when expressing it as a percentage. With a positive middle line, this distinguishes relative width from a raw price distance. It does not include trading costs or notional exposure. The ATR calculation instead uses high, low and previous close; raw ATR is not already a percentage or the same dispersion statistic.

A squeeze rule may compare BandWidth with an explicitly chosen reference window. That is a definition to record, not an automatic forecast or a universal threshold. Check the platform’s scaling before using a decimal or percentage cutoff. A low historical width does not establish an outside close’s probability or the time available to execute an order.

Practical takeaway: The same mean and dispersion can come from different price sequences; identical bands do not recover that missing order.

What to do tomorrow

  1. Reproduce a reading. Compute one mean, population variance and both bands from a frozen set of closed prices.
  2. Compare the denominator. Calculate the sample-standard-deviation alternative without changing the data and note the difference.
  3. Change one parameter. Keep the prices fixed and change only k; distinguish an indicator-setting effect from a market change.
  4. Record the next question. The advanced use of Bollinger Bands lesson separates price location, BandWidth and squeeze definitions. Any trading use still needs complete rules, costs and testing.