# Vector angle

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

Compute the angle in radians between two equal-length finite-number vectors.

**Use when you need to: angle between vectors · vector angle radians.**

## Supported

- angle between vectors
- vector angle radians

## Not supported

- angle in degrees (convert the radian result separately)
- angle for a zero-magnitude vector

## Behavior

- Inputs a and b are arrays of finite JSON numbers with the same length, from 1 to 64 entries, magnitude bounded to at most 1000000.
- The angle is acos((a . b) / (|a| * |b|)), computed in IEEE-754 double precision and returned in radians in the closed range [0, pi].
- The cosine argument is clamped to [-1, 1] before acos to compensate for floating-point rounding that could otherwise push it slightly outside that range.
- Either vector having Euclidean norm 0 makes the angle undefined and is rejected.

## Input

- `a` (array of number, required): min items 1; max items 64
- `b` (array of number, required): min items 1; max items 64

## Output

- `result` (number, required)

## Limits

- max dim: 64
- max abs value: 1000000

## Example

Request input:

```json
{
  "a": [
    1,
    0
  ],
  "b": [
    0,
    1
  ]
}
```

Response:

```json
{
  "result": {
    "result": 1.5707963267948966
  }
}
```

## How to call it

### MCP

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

```json
{
  "id": "vector-angle",
  "version": "1.0.0",
  "input": {
    "a": [
      1,
      0
    ],
    "b": [
      0,
      1
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/vector-angle/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[1,0],"b":[0,1]}'
```

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

### CLI

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

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

## Related tools

- [Vector lerp](/tools/vector-lerp): Linearly interpolate (or extrapolate) between two equal-length finite-number vectors.
- [Vector add](/tools/vector-add): Add two equal-length finite-number vectors elementwise.
- [Vector approx equal](/tools/vector-approx-equal): Compare two equal-length finite-number vectors for approximate equality within an absolute tolerance.
- [Vector dot](/tools/vector-dot): Compute the dot (scalar) product of two equal-length finite-number vectors.
- [Vector outer product](/tools/vector-outer-product): Compute the outer product of two finite-number vectors, producing a matrix.
- [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.