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Can I run Qwen2.5-3B-Instruct on an RTX 4060?

Yes, just

Its published weights (6.17 GB) fit in the 7.20 GB an RTX 4060 can use, with room for ≈ 27K tokens of context.

Full analysis of Qwen2.5-3B-Instruct Everything that runs on RTX 4060 Get the weights on Hugging Face
hf download Qwen/Qwen2.5-3B-Instruct

Files and context on RTX 4060

Each file of Qwen2.5-3B-Instruct (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 4060 Context (16-bit)Context (8-bit)
As published6.17 GBTight27K32K
4-bit (estimate)1.74 GBFits32K32K

Qwen2.5-3B-Instruct on other hardware

Popular models that run on RTX 4060

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.