Bollinger Bands %B (PERCENTB)

Summary

Bollinger Bands %B: where the input sits relative to its Bollinger Bands, 0 at the lower band and 1 at the upper band. Values below 0 or above 1 mean the input is outside the bands.

Formula

$$\%B_t = \frac{X_t - \mathrm{lower}_t}{\mathrm{upper}_t - \mathrm{lower}_t}, \text{ or } 0.5 \text{ when } \mathrm{upper}_t = \mathrm{lower}_t$$

where $\mathrm{upper}_t$ and $\mathrm{lower}_t$ are the BBANDS bands of $X$ with period $n$, moving-average type $\text{matype}$ and deviation multipliers $k_{\text{up}}$, $k_{\text{dn}}$.

Notes

• An input on the middle band reads optInNbDevDn / (optInNbDevUp + optInNbDevDn): 0.5 with equal multipliers.
• With a simple moving average and both multipliers equal to k, %B = 0.5 + z / (2k), where z is the z-score of the input in its window.
• The result is a ratio; multiply by 100 to read it as a percentage.
• Any optInMAType other than SMA is a TA-Lib generalisation, as it is for BBANDS: the deviation stays the population standard deviation about the simple mean.
• PERCENTB is bit for bit (inReal - lower) / (upper - lower) computed from BBANDS' own outputs, and 0.5 wherever those two bands are equal.

Inputs

• inReal — Input data series

Outputs

• outReal — Position of the input between the lower band (0) and the upper band (1)

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	20	2–100000	Periods for the MA and standard deviation
optInNbDevUp	real	2	any real	Standard-deviation multiplier for the upper band
optInNbDevDn	real	2	any real	Standard-deviation multiplier for the lower band
optInMAType	MAType	SMA (0)	any MAType	Moving-average type for the middle band

MAType values: 0 SMA · 1 EMA · 2 WMA · 3 DEMA · 4 TEMA · 5 TRIMA · 6 KAMA · 7 MAMA · 8 T3 · 9 HMA · 10 DISABLED · 11 DEFAULT · 12 ZLEMA · 13 RMA · 14 VIDYA · 15 ALMA

Properties

Numerical Stability: Depends on MA Type — This function's default, SMA, is start-independent.

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: percentb.c · percentb.yaml

Native	File
C	ta_PERCENTB.c
Rust	percentb.rs
Java	Core_PERCENTB.java
C#	Core_PERCENTB.cs

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Bollinger %b, %b, %B, Percent B, BB %B, BBP, Bollinger Bands %B

See Also

BBANDS · BBW · STOCHF

References

• John A. Bollinger, Bollinger on Bollinger Bands, McGraw-Hill 2001 (ISBN 0071373683)
• John Bollinger, Bollinger Band Rules, rules 15-17