# Vector normalize

`vector-normalize` · version 1.0.0 · Vectors & matrices · free, no key needed

Scale a finite-number vector to unit Euclidean length.

**Use when you need to: vector normalization · unit vector · make vector unit length.**

## Supported

- vector normalization
- unit vector
- make vector unit length

## Not supported

- normalizing the zero vector (undefined direction)
- normalization by a norm other than L2

## Behavior

- Input vector is an array of 1 to 64 finite JSON numbers, each bounded to at most 1000000 in magnitude.
- The Euclidean (L2) norm is computed with IEEE-754 double-precision Math.sqrt over the sum of squares.
- Optional input tolerance (default 1e-9, range 0 to 1) is the minimum norm accepted; vectors whose norm is at or below tolerance are rejected as having no well-defined direction.
- The result is result[i] = vector[i] / norm, computed in IEEE-754 double precision; -0 is normalized to 0.
- Every result entry is checked to be a finite number before it is returned; a non-finite intermediate is rejected as invalid input rather than silently serialized.

## Input

- `vector` (array of number, required): min items 1; max items 64
- `tolerance` (number, optional): min 0; max 1

## Output

- `result` (array of number, required)

## Limits

- max dim: 64
- max abs value: 1000000

## Example

Request input:

```json
{
  "vector": [
    3,
    4
  ]
}
```

Response:

```json
{
  "result": {
    "result": [
      0.6,
      0.8
    ]
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "vector-normalize",
  "version": "1.0.0",
  "input": {
    "vector": [
      3,
      4
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/vector-normalize/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"vector":[3,4]}'
```

The machine-readable contract is at [/v1/tools/vector-normalize/versions/1.0.0](/v1/tools/vector-normalize/versions/1.0.0).

### CLI

```sh
node cli.mjs run vector-normalize 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Vector norm](/tools/vector-norm): Compute the L1, L2 (Euclidean), or L-infinity (Chebyshev) norm of a finite-number vector.
- [Matrix vector multiply](/tools/matrix-vector-multiply): Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.
- [Vector add](/tools/vector-add): Add two equal-length finite-number vectors elementwise.
- [Vector angle](/tools/vector-angle): Compute the angle in radians between two equal-length finite-number vectors.
- [Vector approx equal](/tools/vector-approx-equal): Compare two equal-length finite-number vectors for approximate equality within an absolute tolerance.
- [Vector cross](/tools/vector-cross): Compute the 3-dimensional cross product of two finite-number vectors.