Embedding Storage Cost Calculator

The storage footprint of a vector index is arithmetic before it is economics. An embedding is an array of single-precision floats, so each dimension occupies 4 bytes: a 1,536-dimensional vector from text-embedding-3-small is 6,144 bytes of raw payload, and a 3,072-dimensional vector from the large variant is 12,288. Add roughly 500 bytes of metadata per record for source identifiers, offsets, and filter fields, then multiply by an index overhead factor of about 1.5 for the graph structure that an HNSW index maintains alongside the vectors, and finally by the replica count. One million 1,536-dimensional vectors therefore lands near 10 GB provisioned, of which about 9 GB should be resident in memory for approximate nearest-neighbour search to hit its latency targets. Dimensionality is the lever with the widest range, because it sets both storage and per-query distance computation. Higher dimensions capture finer semantic distinctions but with diminishing returns, and embedding families that support Matryoshka-style truncation let a vector be shortened to a fraction of its native width with only marginal loss in recall. Scalar or binary quantization gives another 4x to 32x reduction at a measurable accuracy cost. The main caveat is that vector storage is rarely the dominant line item in a retrieval system: generation typically costs an order of magnitude more per query than embedding and lookup combined, and the one-time embedding of a corpus is cheap relative to the recurring database bill. Re-embedding after a model change resets that one-time cost in full.

Representing meaning as coordinates in a numeric space goes back to the vector space model that Gerard Salton and colleagues developed for the SMART retrieval system at Cornell in the 1960s and 1970s, where documents became sparse term-weight vectors compared by cosine similarity. Latent semantic indexing, published in 1990 by Scott Deerwester, Susan Dumais, and co-authors, compressed those sparse vectors into a dense low-dimensional space via singular value decomposition, establishing the idea that a few hundred learned dimensions could carry semantic relatedness. Dense neural embeddings made the approach practical at scale. Word2vec, released by Tomas Mikolov and colleagues at Google in 2013, and GloVe from Jeffrey Pennington, Richard Socher, and Christopher Manning at Stanford in 2014, produced word vectors cheaply; Sentence-BERT, published by Nils Reimers and Iryna Gurevych in 2019, extended this to whole sentences and passages. Searching billions of such vectors required new index structures: Yury Malkov and Dmitry Yashunin described Hierarchical Navigable Small World graphs in work published from 2016, and Facebook released the FAISS library in 2017. Purpose-built vector databases followed, with Pinecone founded in 2019 and Weaviate, Qdrant, and Chroma appearing in the early 2020s. The launch of OpenAI text-embedding-ada-002 in December 2022 dropped embedding costs far enough that indexing entire document collections became routine, which is when storage sizing became a budgeting problem rather than a research detail.