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Can I run Qwen3-14B-AWQ on an RTX 5070?

Yes, just

Its published weights (9.98 GB) fit in the 10.8 GB an RTX 5070 can use, with room for ≈ 5K tokens of context.

Full analysis of Qwen3-14B-AWQ Everything that runs on RTX 5070 Get the weights on Hugging Face
hf download Qwen/Qwen3-14B-AWQ

Files and context on RTX 5070

Each file of Qwen3-14B-AWQ (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 5070 Context (16-bit)Context (8-bit)
As published9.98 GBTight5K10K
4-bit (estimate)8.31 GBFits15K30K

Qwen3-14B-AWQ on other hardware

Popular models that run on RTX 5070

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.