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Can I run Qwen3-4B on an RTX 3060 12 GB?

Yes

Its published weights (8.04 GB) fit in the 10.8 GB an RTX 3060 12 GB can use, with room for ≈ 18K tokens of context.

Full analysis of Qwen3-4B Everything that runs on RTX 3060 12 GB Get the weights on Hugging Face
hf download Qwen/Qwen3-4B

Files and context on RTX 3060 12 GB

Each file of Qwen3-4B (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

FileSizeOn RTX 3060 12 GB Context (16-bit)Context (8-bit)
As published8.04 GBFits18K36K
4-bit (estimate)2.26 GBFits40K40K

Qwen3-4B on other hardware

Popular models that run on RTX 3060 12 GB

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.