Yes — with 3.0 GB to spare
Qwen3 4B at Q4_K_M fits your GeForce RTX 3070 entirely on the GPU at 8K context, at an estimated 120 tokens per second. Past 29K the KV cache pushes it over — quantise the cache to q8_0, or step down a quantisation, to go longer.
Fully on GPU
8K context
Q4_K_M · 2.3 GB
Apache 2.0
Released Apr 2025
The 2025 sweet spot for 8 GB cards with reasoning traces. Qwen3.5 4B adds vision and 8× the context.
The VRAM budget
weights 2.3 GB
Weights 2.3 GB
KV cache @ 8K 1.13 GB
Runtime overhead 0.6 GB
Free 3.0 GB of 7.0 GB
Quantisation ladder
| Quant | Weights | Total @ 8K | Max context | Tok/s | Quality | Fit |
|---|---|---|---|---|---|---|
| F16 | 7.5 GB | 9.2 GB | — | ~12 | Reference | 2.2 GB over |
| Q8_0 | 4.0 GB | 5.7 GB | 17K | 68 | −0.1% ppl | Long context |
| Q6_K | 3.1 GB | 4.8 GB | 23K | 88 | −0.4% ppl | Long context |
| Q5_K_M | 2.7 GB | 4.4 GB | 26K | 102 | −0.8% ppl | Long context |
| Q4_K_M | 2.3 GB | 4.0 GB | 29K | 120 | −1.9% ppl | Recommended |
| Q3_K_M | 1.8 GB | 3.6 GB | 32K | 148 | −5.4% ppl | Long context |
| Q2_K | 1.6 GB | 3.3 GB | 32K | 173 | −15% ppl | Long context |
Quality is the published perplexity delta against f16 weights. Max context assumes an f16 KV cache; q8_0 roughly doubles it.
How to run it
$ ollama pull qwen3:4b $ OLLAMA_CONTEXT_LENGTH=8192 \ ollama run qwen3:4b
The default. One binary, a model registry, an OpenAI-compatible port. More on Ollama.
01Download is 2.3 GB. Keep it on an SSD — a first load off a spinning disk takes minutes.
02Close anything else holding VRAM. A browser with hardware acceleration can sit on 1–2 GB.
03There is room to go to 29K context on this card.