# Average True Range (ATR)

`D07-F04-A02` · Technical Indicators → Volatility and Channels · archetype `series-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/technical-indicators/volatility-and-channels/atr/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { averageTrueRange } from "fintech-algorithms/technical-indicators/volatility-and-channels/atr";
```

## Signature

```ts
averageTrueRange(high, low, close, p)
```

Wilder-smoothed true range. Most often used for position sizing and stop placement rather than as a signal — it says how far price typically moves, not which way.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `high` | `number[]` | yes | Per-bar high prices, chronological. |
| `low` | `number[]` | yes | Per-bar low prices, chronological. |
| `close` | `number[]` | yes | Per-bar closing prices, chronological. |
| `p` | `number` | yes | Wilder smoothing period. Note this is 1/p decay, not the 2/(p+1) of a standard EMA; substituting one changes every published ATR value. · min: 1, integer: true |

## Returns

`Record<string, (number | null)[]>` · length same-as-input

Parallel series: `true_range` and `atr`.

## Warm-up

The first `p - 1` positions are `null`. Applies to `atr` only; `true_range` is defined from the first bar. The first ATR is the mean of the first p true ranges, so it lands at index p - 1 and Wilder smoothing continues from there.

## Errors

- When p < 1 or is not an integer — throws RangeError
- When the input series are not all the same length — throws RangeError

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

### Input

`high`:

```json
[101.08, 101.6243955, 102.13058177, 102.56507653, 102.90321818, 103.1320792]
```

Showing 6 of 240 elements.

`low`:

```json
[98.92, 99.39457765, 99.83203556, 100.19996391, 100.47473988, 100.64442473]
```

Showing 6 of 240 elements.

`close`:

```json
[100, 100.50948657, 100.98130867, 101.38252022, 101.68897903, 101.88825197]
```

Showing 6 of 240 elements.

`p`:

```json
14
```

### Call

```ts
averageTrueRange(high, low, close, p)
```

### Returns

object with 2 fields: true_range, atr

```json
{
  "true_range": [
    2.1599999999999966,
    2.2298178500000034,
    2.298546210000012,
    2.365112620000005,
    2.4284782999999948,
    2.4876544700000096
  ],
  "atr": [null, null, null, null, null, null]
}
```

## Other exports

`trueRange`. Every module additionally exports `run` as an alias of its primary
function, and a `meta` object carrying its catalog id, domain, family, shape and article URL.

## Verification and provenance

Tier: **verified** (via scenario-fixture).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.1.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/technical-indicators/volatility-and-channels/atr/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/technical-indicators/volatility-and-channels/atr/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/technical-indicators/llms.txt