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How do you convert between 20/x and diopters?
#1
How do you convert between acuity (noted as 20/50, 20/100, etc.) and a glasses prescription in diopters (-2, -5, etc.) ?

You can probably find someone to suggest a conversion table or another way to convert it, but there is no such conversion. It's two different things that only correlate very roughly, and even then only sometimes.

Acuity is a subjective measurement of what sized letters you can read on an eye chart at 20ft. Other than your quality of vision, this will vary by lighting levels, the chart used, and how good of a guesser you are. A diopter is the unit of measurement used for prescribing glasses to "correct" your vision for either distance (20ft or farther) or reading distance (18in). It is determined by calculations involving the light rays not being focused properly by your eyes and how much of an angle is needed to correct it. There is also usually at least a small amount of astigmatism correction noted in the prescription. Various conditions or diseases will affect how well you actually see. Misusing your eyes by a greater or lesser amount than you habitually do will affect it as well.

Diopters should be of little or no concern to people improving their vision. You can't easily measure it yourself, and it doesn't correlate well to how well you actually see, whereas an eye chart is a much better representation of the changes in your vision over time.
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