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Can I run gpt-oss-20b on an RTX 4090?

Yes

Its published weights (13.8 GB) fit in the 21.6 GB an RTX 4090 can use, with room for ≈ 128K tokens of context.

Full analysis of gpt-oss-20b Everything that runs on RTX 4090 Get the weights on Hugging Face
hf download openai/gpt-oss-20b

Files and context on RTX 4090

Each file of gpt-oss-20b (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 4090 Context (16-bit)Context (8-bit)
As published13.8 GBFits128K128K
4-bit (estimate)11.8 GBFits128K128K

gpt-oss-20b on other hardware

Popular models that run on RTX 4090

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.