# `cosineSimilarity()`

When you want to compare the similarity of embeddings, standard vector similarity metrics
like cosine similarity are often used.

`cosineSimilarity` calculates the cosine similarity between two vectors.
A high value (close to 1) indicates that the vectors are very similar, while a low value (close to -1) indicates that they are different.

```ts
import { openai } from '@ai-sdk/openai';
import { cosineSimilarity, embedMany } from 'ai';

const { embeddings } = await embedMany({
  model: openai.embedding('text-embedding-3-small'),
  values: ['sunny day at the beach', 'rainy afternoon in the city'],
});

console.log(
  `cosine similarity: ${cosineSimilarity(embeddings[0], embeddings[1])}`,
);
```

## Import

<Snippet text={`import { cosineSimilarity } from "ai"`} prompt={false} />

## API Signature

### Parameters

<PropertiesTable
  content={[
    {
      name: 'vector1',
      type: 'number[]',
      description: 'The first vector to compare',
    },
    {
      name: 'vector2',
      type: 'number[]',
      description: 'The second vector to compare',
    },
    {
      name: 'options',
      type: 'Object',
      isOptional: true,
      description: 'Optional configuration.',
      properties: [
        {
          type: 'Object',
          parameters: [
            {
              name: 'throwErrorForEmptyVectors',
              type: 'boolean',
              isOptional: true,
              description:
                'Set throwErrorForEmptyVectors to true to throw an error when vectors are empty (default: false)',
            },
          ],
        },
      ],
    },
  ]}
/>

### Returns

A number between -1 and 1 representing the cosine similarity between the two vectors.


## Navigation

- [generateText](/v4/docs/reference/ai-sdk-core/generate-text)
- [streamText](/v4/docs/reference/ai-sdk-core/stream-text)
- [generateObject](/v4/docs/reference/ai-sdk-core/generate-object)
- [streamObject](/v4/docs/reference/ai-sdk-core/stream-object)
- [embed](/v4/docs/reference/ai-sdk-core/embed)
- [embedMany](/v4/docs/reference/ai-sdk-core/embed-many)
- [generateImage](/v4/docs/reference/ai-sdk-core/generate-image)
- [transcribe](/v4/docs/reference/ai-sdk-core/transcribe)
- [generateSpeech](/v4/docs/reference/ai-sdk-core/generate-speech)
- [tool](/v4/docs/reference/ai-sdk-core/tool)
- [experimental_createMCPClient](/v4/docs/reference/ai-sdk-core/create-mcp-client)
- [Experimental_StdioMCPTransport](/v4/docs/reference/ai-sdk-core/mcp-stdio-transport)
- [jsonSchema](/v4/docs/reference/ai-sdk-core/json-schema)
- [zodSchema](/v4/docs/reference/ai-sdk-core/zod-schema)
- [valibotSchema](/v4/docs/reference/ai-sdk-core/valibot-schema)
- [CoreMessage](/v4/docs/reference/ai-sdk-core/core-message)
- [createProviderRegistry](/v4/docs/reference/ai-sdk-core/provider-registry)
- [customProvider](/v4/docs/reference/ai-sdk-core/custom-provider)
- [cosineSimilarity](/v4/docs/reference/ai-sdk-core/cosine-similarity)
- [wrapLanguageModel](/v4/docs/reference/ai-sdk-core/wrap-language-model)
- [LanguageModelV1Middleware](/v4/docs/reference/ai-sdk-core/language-model-v1-middleware)
- [extractReasoningMiddleware](/v4/docs/reference/ai-sdk-core/extract-reasoning-middleware)
- [simulateStreamingMiddleware](/v4/docs/reference/ai-sdk-core/simulate-streaming-middleware)
- [defaultSettingsMiddleware](/v4/docs/reference/ai-sdk-core/default-settings-middleware)
- [simulateReadableStream](/v4/docs/reference/ai-sdk-core/simulate-readable-stream)
- [smoothStream](/v4/docs/reference/ai-sdk-core/smooth-stream)
- [generateId](/v4/docs/reference/ai-sdk-core/generate-id)
- [createIdGenerator](/v4/docs/reference/ai-sdk-core/create-id-generator)


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