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Cosine Similarity Calculator
Compare two embedding vectors by cosine similarity, dot product and distance.
Paste JSON arrays, comma-separated or space-separated numbers — straight from an embeddings API response or a vector database row. Both vectors need the same number of dimensions.
Quick Tool Overview
The Cosine Similarity Calculator compares two vectors or embeddings and returns cosine similarity and distance, the angle between them, the dot product, Euclidean and Manhattan distance and each vector length, with notes on which metric vector databases use.
- What it does
- Measures similarity between two vectors
- You give it
- Two embedding vectors of the same length
- You get back
- Cosine similarity, dot product and distances
- Best for
- Debugging semantic search and embeddings
About the Cosine Similarity Calculator
Semantic search, recommendation and deduplication all come down to comparing vectors: embed two pieces of text, measure how closely the vectors point in the same direction, and treat that as how closely the meanings match. Cosine similarity is the measure almost everyone uses.
Paste two vectors as JSON arrays, comma-separated or space-separated numbers — straight from an embeddings API response or a vector database row — and get cosine similarity and cosine distance, the angle between the vectors, the dot product, Euclidean and Manhattan distances, the normalised Euclidean distance and the length of each vector, with a scale from opposite to identical.
When both vectors are normalised, the page points out that dot product and cosine similarity are the same number, which is why vector databases can use the cheaper operation. A reference card shows which operator pgvector, Pinecone, Qdrant, FAISS and Chroma use for each metric.
Key features of the Cosine Similarity Calculator
Every common metric
Cosine similarity and distance, angle, dot product, L2, normalised L2 and L1.
Paste any vector format
JSON arrays, comma-separated or space-separated numbers from an API or database.
Dimension check
Vectors of different lengths are rejected with a clear explanation.
Normalisation detection
Notes when both vectors are unit length, so dot product equals cosine.
Vector database reference
pgvector, Pinecone, Qdrant, FAISS and Chroma metric names side by side.
How to use the Cosine Similarity Calculator
-
1
Paste vector A
A JSON array or a list of numbers separated by commas or spaces.
-
2
Paste vector B
It must have the same number of dimensions and come from the same model.
-
3
Read the similarity
Cosine similarity runs from -1 for opposite, through 0 for unrelated, to 1 for identical direction.
-
4
Compare other measures
Dot product and distances are listed for the metric your database uses.
Frequently asked questions
The cosine of the angle between two vectors: their dot product divided by the product of their lengths. It measures direction and ignores magnitude, which suits text embeddings.
It depends on the model. Some embedding models score unrelated text around 0.7 and related text above 0.85, while others spread scores much wider. Compare scores from the same model rather than using a universal threshold.
Cosine distance is one minus cosine similarity. Vector databases often sort by distance, where smaller means more similar.
When both vectors are normalised to length 1. Many embedding APIs return normalised vectors, so the faster dot product gives the same ranking.
Similarity is only defined between vectors in the same space. Different lengths almost always mean the vectors came from different models, and would not be comparable anyway.
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