Vector database sizing is one multiplication people skip: dimensions x 4 bytes x count.
768 dims x 4 bytes = 3,072 bytes per vector. A million of them: ~3 GB, raw, before the HNSW index adds its overhead (typically 1.5-2x with links and metadata). Use 1536-dim embeddings and double it.
That one line answers most "which free tier" questions. Managed free tiers capping you at 100K-1M vectors aren't being stingy — that's the RAM. And it tells you what self-hosting buys: a free 12 GB ARM VM comfortably holds a few million 768-dim vectors in Qdrant or Chroma, which is more corpus than most side projects ever embed.
It also explains the pro move: dimension-reduce before you shop. Matryoshka-style truncation to 256 dims cuts the memory 3x and often costs single-digit recall.
Free tiers and self-host options, sized in vectors-you-actually-get: https://toolfreebie.com/free-vector-database-rag/
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