To find the absolute minimum you just multiply the number of parameters by the bits per parameter, divide by 8 if you want bytes. In case 8 billion parameters of 4 bits each means "at least 4 billion bytes". For back of the napkin add ~20% overhead to that (it really depends on your context setup and a few other things but that's a good swag to start with) and then add whatever memory the base operating system is going to be using in the background.

Extra tidbits to keep in mind:

- A bits-per-parameter higher than the model was trained adds nothing (other than compatibility on certain accelerators) but a bits-per-parameter lower than the model was trained degrades the quality.

- Different models may be trained at different bits-per-parameter. E.g. 671 billion parameter Deepseek R1 (full) was trained at fp8 while llama 3.1 405 billion parameter was trained and released at a higher parameter width so "full quality" benchmark results for Deepseek R1 require less memory than Llama 3.1 even though R1 has more total parameters.

- Lower quantinizations will tend to run proportionally faster if you were memory bandwidth bound and that can be a reason to lower the quality even if you can fit the larger version of a model into memory (such as in this demonstration).

q4=4bits per weight

So Q4 8B would be ~4GB.