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:

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

Response:

{
  "result": {
    "result": 1.5707963267948966
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

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

HTTP (no key)

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.

CLI

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

Get the client at /clients/cli/.

Related tools

• Vector lerp: Linearly interpolate (or extrapolate) between two equal-length finite-number vectors.
• Vector add: Add two equal-length finite-number vectors elementwise.
• Vector approx equal: Compare two equal-length finite-number vectors for approximate equality within an absolute tolerance.
• Vector dot: Compute the dot (scalar) product of two equal-length finite-number vectors.
• Vector outer product: Compute the outer product of two finite-number vectors, producing a matrix.
• Matrix vector multiply: Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.