> ## Documentation Index
> Fetch the complete documentation index at: https://docs.darvas.app/llms.txt
> Use this file to discover all available pages before exploring further.

# Volatility

> ta.atr, ta.stdev, ta.variance, ta.dev, ta.bb, ta.keltner - volatility measurement functions.

## `ta.atr(high, low, close, length)` - Average True Range

Wilder-smoothed (RMA) average of the true range. Returns a positive scalar representing volatility in price units.

```js theme={null}
onBar(() => {
  const atr = ta.atr(ctx.high, ctx.low, ctx.close, 14);
  plot("ATR14", atr);
});
```

## `ta.stdev(source, length)` - Standard deviation

Population standard deviation of `source` over `length` bars.

```js theme={null}
onBar(() => {
  plot("StDev20", ta.stdev(ctx.close, 20));
});
```

## `ta.variance(source, length)` - Variance

Square of the standard deviation: `stdev^2`.

```js theme={null}
onBar(() => {
  plot("Variance", ta.variance(ctx.close, 20));
});
```

## `ta.dev(source, length)` - Mean absolute deviation

Average absolute distance from the mean. Less sensitive to outliers than standard deviation.

```js theme={null}
onBar(() => {
  plot("MAD", ta.dev(ctx.close, 20));
});
```

## `ta.bb(source, length, mult)` - Bollinger Bands

Returns `{ upper, middle, lower }`. `middle` is the SMA; `upper`/`lower` are `middle ± mult * stdev`.

```js theme={null}
const upper = plot("BB Upper", null, { color: "#3b82f6FF" });
const lower = plot("BB Lower", null, { color: "#3b82f6FF" });
plot("BB Middle", null, { color: "#3b82f680" });
fill(upper, lower, { color: "#3b82f615" });

onBar(() => {
  const bb = ta.bb(ctx.close, 20, 2);
  if (na(bb.upper)) return;
  plot("BB Upper",  bb.upper);
  plot("BB Middle", bb.middle);
  plot("BB Lower",  bb.lower);
});
```

## `ta.keltner(source, high, low, close, length, mult)` - Keltner Channel

Returns `{ upper, middle, lower }`. `middle` is the EMA of `source`; bands are `middle ± mult * ATR`.

```js theme={null}
plot("KC Upper",  null, { color: "#f59e0bFF" });
plot("KC Lower",  null, { color: "#f59e0bFF" });
plot("KC Middle", null, { color: "#f59e0b80" });

onBar(() => {
  const kc = ta.keltner(ctx.close, ctx.high, ctx.low, ctx.close, 20, 1.5);
  if (na(kc.upper)) return;
  plot("KC Upper",  kc.upper);
  plot("KC Middle", kc.middle);
  plot("KC Lower",  kc.lower);
});
```

## Squeeze momentum setup

Combining BB and Keltner to detect low-volatility "squeeze":

```js theme={null}
onBar(() => {
  const bb = ta.bb(ctx.close, 20, 2);
  const kc = ta.keltner(ctx.close, ctx.high, ctx.low, ctx.close, 20, 1.5);
  if (na(bb.upper) || na(kc.upper)) return;

  // Squeeze = BB inside KC
  const squeeze = bb.upper < kc.upper && bb.lower > kc.lower;
  bgcolor(squeeze ? "#a78bfa15" : null);
});
```

## Related pages

<CardGroup cols={2}>
  <Card title="Bollinger Bands example" href="/examples/bollinger-bands">
    Full working BB indicator with band shading.
  </Card>

  <Card title="Oscillators" href="/ta/oscillators">
    Momentum and oscillator functions.
  </Card>

  <Card title="Aggregators" href="/ta/aggregators">
    ta.highest and ta.lowest for range-based calculations.
  </Card>
</CardGroup>