[KennyBlanken]

Aside from this being a really simple calculation for which there are lots of online calculators and articles...there is no reason to buy a prime lens for streaming.

Modern kit zoom lenses are more than sufficient for even raw 1080p...and by the time your stream has been compressed twice (the first time likely by a hardware encoder on your video card, which is not exactly stellar encoding quality in the first place), there is exactly zero point to the very minute difference in quality, particularly since in a studio you can provide enough light that the lens can be stopped down to its ideal aperture.

If the goal is "head and shoulders shot", you probably want an 85mm (35-mm-equivalent) focal length, or thereabouts. 85mm is the classic portraiture focal length for 35mm format, because it yields a very natural look. 50mm might be more conducive to smaller spaces, however.

If by "Sony" you mean one of the a7 series mirrorless cameras...unless you're planning on streaming in candle-light conditions, that's also a massive waste of money. Any micro four thirds camera made in the last ten years will output gorgeous video quality for streaming even if you don't go to great lengths lighting-wise.

[fleventynine]

It depends on your camera's low light sensitivity and how much noise you can tolerate. A cheap prime lens will let in an order of magnitude more light than a cheap kit lens. And some folks want that creamy bokeh effect behind them.