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Simplest case is you are farsighted. So your lenses are magnifiers. You move them away from a printed page til the magnification is at maximum. The distance to the page is the focal length. Diopter is 1/FL in meters, so eg. 50cm FL is 2.0 diopter. Negative diopters, astigmatism corrections etc are more complicated.
It looks like you can also test your own vision with a phone app and simple device:
https://www.cnet.com/tech/mobile/in-the-era-of-warby-parker-measure-your-own-eyeglass-prescription-at-home/
Idk anything about that though.
Seems neat I guess. I just wonder why the hell I can't just go in with my old prescription, tell them straight up that this is perfectly fine, I just need new lenses that ain't all scratched up..
That's easiest I guess. Just find out your prescription when you get tested. Yes a lot of the industry is bogus, but then a lot of the world in general is bogus. Part of being an independent and flexible person is being able to find ways around bogosity.