Vision Correction

The mathematical side of 20/20 vision

Everyone has heard the term 20/20 at one time or another. What does that mean, though?

Joel Hunter, MD
Joel Hunter, MD
Refractive Surgeon, Hunter Vision Updated 03/22/21 11:03 AM

Vision is the only one of the five senses to have a measurement that people use outside of a lab. There are no common equivalents for 20/20 when people talk about their sense of smell or hearing. Instead, we use a generic word like “excellent” when describing those qualities. But with vision, it’s different. Everyone has heard the term 20/20 at one time or another. What does that mean, though?

If you ask someone who’s looked into it, 20/20 means you can see from 20 feet away what an ideal eye could see from 20 feet away. If you think about it, however, seeing something as well as an ideal eye sees isn’t much more specific than when we describe hearing with the word “excellent.” But 20/20 has become a common enough phrase for the essentially super “folksy” nature of it to not stand out as odd. “My eyes see things from 20 feet away as good as good eyes should.” This is exactly what 20/20 is short for. It sounds like something you’d hear from an old country farmer leaning on a shovel. But there’s more to it, of course. It is somewhat of a loss to the fun, old-timey feeling of 20/20 as an unquestioned way to say someone’s got good eyes. But the math behind 20/20 has the virtue of helping us understand why good eyes are ...well, good.

The eye works by having two natural lenses focus images onto a retina inside the back of it. There's the cornea, nicknamed the “window of the eye." Then there's the lens, nicknamed “the one that got named first,” since we just call it the lens. The retina lines the back of the eye. It’s tremendously more complicated than the lenses. With 10 layers of highly-specialized cells that are so complex we’re lucky only one of them matters for figuring out what 20/20 means. It is the photosensory layer, which is made of photoreceptors. Those photoreceptor cells are either “on” (light is hitting me) or “off” (no light here,).

The accuracy (defined as acuity) of those photoreceptors depends on two things. One is how perfect those lenses at the front can focus. The other is how close together those photoreceptors are. Since the second one of these is the less variable, it is where we get our definition of 20/20. Knowing that those photoreceptor cells are either on or off helps us here. Because of this, we can measure how tiny a stretch of retina can distinguish dark-light-dark by how small of an object those cells can identify. You can imagine why that’s the case if you consider the distinction of an image comes only from contrast (i.e. lines instead of uniform light or dark).

In case you’re ready to punch your screen, just wait because we’re almost there! One step further and we’re at the goal of defining 20/20. The retina lines the back of the eye, but it’s an eyeball, and a ball is round. The retina curves along the inner surface of that round sphere. We’re measuring, “How small is this stretch of retina that can distinguish light and dark lines?” So we’ve got to measure with units made for round surfaces, called degrees. Or, to be more specific, small units of 1/60th of a degree, which are called “minutes of arc.” Each minute of arc of your retina’s photoreceptors should be able to be on or off independent of the others. 


Imagine a letter E. Better yet, look at the one I typed right there. You can see it has three horizontal lines. That E projects onto your retina as you look at it. When this happens, you should be able to see it at a size where each horizontal line is separated by one minute of arc. This is the size of about 25 thousandths of a millimeter on your retina. And that’s what it means to be 20/20. Seeing an E when it is that small on your retina equals 20/20.

No one can actually measure that, but with some algebra we can say what size E that would be at different distances. Let’s pick 20 feet since it will let us know what 20/20 means. At 20 feet, a 20/20 eye will be able to see an E that is 0.35 inches tall. Why? Well, in a futile attempt to make all this less boring, I skipped the algebra involved to determine this. That algebra shows that at 20 feet, a 0.35 inch tall E projects onto your retina as an E where each horizontal line (dark) is separated (light) by one minute of arc. When you can see that as an E, instead of a black smudge on the chart, you are 20/20. What if that E is a smudge to you and you need the E to be twice as big to see it? That means you’re 20/40. An easier way to say this would be: 20/40 is when you can see from 20 feet away things a good eye could see from 40 feet away.

In general, we can count on people to have retinas that are pretty similar in ability. So all this 20/20 talk boils down to how focused is the image produced by the lenses at the front of the eye. If your cornea isn’t quite right because of astigmatism or it's overpowered or underpowered when it comes to focusing, you'll need that E to be pretty big. The reason for this is, in those cases, a retina needs a larger image to get enough clarity to decipher it. And for that clear image you can do one of two things. You can make it big enough by increasing the size of it (that’s the big E on the eye chart). Or you make it bigger by walking up to the eye chart and getting closer to it. When it’s a street sign, the option of making it bigger is off the table. You’ve got to wait till you’ve gotten close enough to see it.

The reason 20/20 works so well to describe vision is you don’t have to read this blog, wishing by now you’d stopped back at the old-timey farmer, for it to work. It comes down to the only vision test we have in the real world. How far away can you see something like a street sign compared to your friend with good vision, or to yourself with glasses? There’s a lot of exact science behind what determines those numbers, but you don’t need it to tell you how well you see. Hopefully, understanding the science in the folksy description of good vision makes the time you spent reading this worth it. Looking back, if you find it wasn’t, then that’s why they say hindsight is the ability to see dark/light contrast separated by one minute of arc.

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