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

# Embeddings — POST /v1/embeddings

> Generate vector embeddings for text using POST /v1/embeddings. Supports batch input and multiple embedding models for semantic search, clustering, and RAG.

The `/v1/embeddings` endpoint generates vector embeddings for text input. Embeddings represent the semantic meaning of text as a high-dimensional float array, enabling similarity search, clustering, and retrieval-augmented generation (RAG). The endpoint is compatible with the OpenAI Embeddings API.

## Endpoint

```
POST https://router.flatkey.ai/v1/embeddings
```

## Supported embedding models

| Model                    | Dimensions | Provider |
| ------------------------ | ---------- | -------- |
| `gemini-embedding-001`   | 3072       | Google   |
| `text-embedding-3-small` | 1536       | OpenAI   |
| `text-embedding-3-large` | 3072       | OpenAI   |

See the [Model Directory](/reference/model-list) for current availability and pricing.

## Request

### Headers

| Header          | Value                     |
| --------------- | ------------------------- |
| `Authorization` | `Bearer $FLATKEY_API_KEY` |
| `Content-Type`  | `application/json`        |

### Body parameters

<ParamField body="model" type="string" required>
  Embedding model ID. Example: `"gemini-embedding-001"`, `"text-embedding-3-small"`.
</ParamField>

<ParamField body="input" type="string | array" required>
  Text to embed. Can be a single string or an array of strings for batch embedding.
</ParamField>

<ParamField body="encoding_format" type="string">
  `"float"` (default) returns a float array. `"base64"` returns a base64-encoded string.
</ParamField>

<ParamField body="dimensions" type="integer">
  Number of dimensions for the output embedding. Not supported by all models.
</ParamField>

## Example requests

<CodeGroup>
  ```python python theme={null}
  import os
  from openai import OpenAI

  client = OpenAI(
      api_key=os.environ["FLATKEY_API_KEY"],
      base_url="https://router.flatkey.ai/v1",
  )

  # Single text
  response = client.embeddings.create(
      model="gemini-embedding-001",
      input="The quick brown fox jumps over the lazy dog",
  )

  embedding = response.data[0].embedding
  print(f"Embedding dimensions: {len(embedding)}")
  print(f"First 5 values: {embedding[:5]}")
  ```

  ```python python batch theme={null}
  import os
  from openai import OpenAI

  client = OpenAI(
      api_key=os.environ["FLATKEY_API_KEY"],
      base_url="https://router.flatkey.ai/v1",
  )

  # Batch embedding
  texts = [
      "What is machine learning?",
      "How does neural network training work?",
      "Explain gradient descent",
  ]

  response = client.embeddings.create(
      model="gemini-embedding-001",
      input=texts,
  )

  for i, item in enumerate(response.data):
      print(f"{texts[i]}: {len(item.embedding)} dimensions")
  ```

  ```bash curl theme={null}
  curl https://router.flatkey.ai/v1/embeddings \
    -H "Authorization: Bearer $FLATKEY_API_KEY" \
    -H "Content-Type: application/json" \
    -d '{
      "model": "gemini-embedding-001",
      "input": "The quick brown fox jumps over the lazy dog"
    }'
  ```
</CodeGroup>

## Response

```json theme={null}
{
  "object": "list",
  "data": [
    {
      "object": "embedding",
      "index": 0,
      "embedding": [0.0023064255, -0.009327292, ...]
    }
  ],
  "model": "gemini-embedding-001",
  "usage": {
    "prompt_tokens": 9,
    "total_tokens": 9
  }
}
```

### Response fields

<ResponseField name="data" type="array">
  Array of embedding objects, one per input string.

  <Expandable title="embedding object">
    <ResponseField name="index" type="integer">Position in the input array.</ResponseField>
    <ResponseField name="embedding" type="array">Float array of the embedding vector.</ResponseField>
  </Expandable>
</ResponseField>

<ResponseField name="usage.prompt_tokens" type="integer">
  Number of tokens processed.
</ResponseField>

## Cosine similarity example

```python python theme={null}
import os
import numpy as np
from openai import OpenAI

client = OpenAI(
    api_key=os.environ["FLATKEY_API_KEY"],
    base_url="https://router.flatkey.ai/v1",
)

def embed(text):
    return client.embeddings.create(
        model="gemini-embedding-001",
        input=text,
    ).data[0].embedding

def cosine_similarity(a, b):
    a, b = np.array(a), np.array(b)
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

q = embed("capital city of France")
doc1 = embed("Paris is the capital and most populous city of France.")
doc2 = embed("The Eiffel Tower is a famous landmark.")

print(cosine_similarity(q, doc1))  # higher — more relevant
print(cosine_similarity(q, doc2))  # lower
```