Volume Weighted Moving Average (VWMA)

Summary

Volume Weighted Moving Average: the mean price over a trailing window of optInTimePeriod bars, each bar weighted by its own volume. Heavily traded bars pull the average toward their price; quiet bars barely move it.

Read like any moving average — price above is strength, below is weakness. Against a plain SMA of the same window it leads on high-volume moves and lags on low-volume drift, so the gap between the two lines measures how volume-confirmed a move is.

It has no attributable inventor — charting-package folklore — and every published definition agrees, so there is no competing variant.

Formula

VWMA = ( sum_{k=t-N+1..t} P[k] * V[k] ) / ( sum_{k=t-N+1..t} V[k] ), N = optInTimePeriod

Equivalently, and bit-identically so in TA-Lib for N of 2 or more, SMA(P * V, N) / SMA(V, N) — the composition TradingView documents for ta.vwma. There is no seeding and no recursion, hence no unstable period.

Notes

A period of 1 performs no smoothing: the output is a copy of the input, whatever the volume.
Volume is expected to be non-negative. Individual zero-volume bars are fine: a bar that did not trade simply carries no weight, and the average stays well defined as long as some bar in the window has volume. At a period of 2 or more, a window in which every volume is zero has no weights at all; the weighted mean is then undefined and that element is NaN, as it is in every other implementation. Series carrying no volume on any bar, such as cash-index feeds, are outside what a volume-weighted average can describe — use SMA or WMA there.

Inputs

inReal — Source price series, close by convention
inVolume — Volume of each bar

Outputs

outReal — Volume weighted moving average of the input

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	30	1–100000	Number of bars in the weighting window

Properties

Numerical Stability: Start-Independent


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

Implementation

TA-Lib Definition: vwma.c · vwma.yaml

Native	File
C	`ta_VWMA.c`
Rust	`vwma.rs`
Java	`Core_VWMA.java`

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

Aliases

Volume Weighted Moving Average

References

VWMA has no separately documented originator; its definition is uniform across charting packages.
MotiveWave, Volume Weighted Moving Average study documentation — the closest thing to a primary definition.
TradingView, Volume Weighted Moving Average (VWMA) — documents the equivalence with SMA(price * volume) / SMA(volume).