Embedding Dimension Tradeoff
An embedding storage calculator. Enter how many vectors you have and compare the memory footprint across common embedding dimensions and quantization levels (float32, float16, int8) — so you can weigh retrieval quality against the RAM and cost of your vector index, and see what dimension reduction or quantization buys you.
| Dimensions | float32 (4B) | float16 (2B) | int8 (1B) |
|---|---|---|---|
| 256 | 14.3 GB | 7.2 GB | 3.6 GB |
| 384 | 21.5 GB | 10.7 GB | 5.4 GB |
| 512 | 28.6 GB | 14.3 GB | 7.2 GB |
| 768 | 42.9 GB | 21.5 GB | 10.7 GB |
| 1024 | 57.2 GB | 28.6 GB | 14.3 GB |
| 1536 | 85.8 GB | 42.9 GB | 21.5 GB |
| 3072 | 172 GB | 85.8 GB | 42.9 GB |
Memory ≈ vectors × dimensions × bytes/component × (1 + overhead). Dropping precision (int8 = ¼ of float32) or dimensions cuts memory linearly, usually for only a small recall loss — often recovered by re-ranking the top hits with full-precision vectors.
A vector index’s size is set by three numbers, and the text you embedded is not one of them. Memory is roughly vectors × dimensions × bytes-per-component, plus the overhead of the approximate-nearest-neighbour structure on top. Ten million 1536-dimension float32 vectors is about 61 GB of raw data before HNSW’s graph adds its 20–100%. That is why, in a RAG system, the embedding dimension and the number of chunks — not the document sizes — dominate what your vector database costs to run.
Once you see the formula, the levers are obvious. Quantization shrinks the bytes-per-component: float16 halves the index, int8 quarters it, for only a small precision loss that usually barely dents recall — so a common pattern is to search over int8 vectors and re-rank the top hits with full-precision ones to claw the accuracy back. Dimension is the other lever, and more is not free: it costs linearly in memory, in compute per comparison, and in index size, with diminishing quality returns past a point.
The right choice is the smallest dimension and lowest precision that still clears your retrieval-quality bar, and this tool lays those options side by side so the tradeoff is a number instead of a guess. One modern shortcut worth knowing: models trained with Matryoshka Representation Learning pack the important signal into the leading dimensions, so you can truncate a 1536-vector to 512 or 256 and keep most of the quality — a cheap way to trade a little accuracy for a large memory win without re-embedding anything.
How it works
- Memory ≈ vectors × dimensions × bytes/component + index overhead.
- Compares float32 / float16 / int8 side by side.
- Higher dimensions cost linearly in RAM, compute and index size.
- Notes MRL truncation and int8-then-rerank patterns.
Frequently asked questions
How much memory does a vector index take?
Roughly: number of vectors × dimensions × bytes per component, plus index overhead. A float32 component is 4 bytes, so 10 million 1536-dimension vectors is about 10M × 1536 × 4 ≈ 61 GB of raw vectors — before the graph or list structure an ANN index (like HNSW) adds on top, often another 20–100%. This is why embedding dimension and vector count, not the text size, dominate a vector database’s memory.
What does quantization trade away?
Storing each component in fewer bytes shrinks the index proportionally: float16 halves it versus float32, and int8 cuts it to a quarter. The cost is a small loss of precision, which usually causes only a minor drop in retrieval recall — often well worth a 4× memory saving. Many teams store int8 (or binary) vectors for the first-pass search and re-rank the top candidates with full-precision vectors to recover accuracy.
Are more dimensions always better for quality?
No. Higher dimensions can capture more nuance but with diminishing returns, and they cost linearly more memory, more compute per similarity comparison, and more index size. Beyond a point, extra dimensions add cost without meaningfully improving retrieval for your data. The right dimension is the smallest that hits your quality bar — which is exactly the tradeoff this tool makes visible.
What is Matryoshka (MRL) truncation?
Some modern embedding models are trained so that the most important information is packed into the leading dimensions (Matryoshka Representation Learning). That lets you truncate a, say, 1536-dimension vector down to 512 or 256 and keep most of the retrieval quality, shrinking memory and speeding search — without re-embedding. If your model supports it, truncation is a cheap dial to trade a little accuracy for a lot less memory.