What Is 20/20 in Decimal Visual Acuity? Conversion Table and Formulas for Decimal, 6/6 and logMAR
“20/20 vision” in American TV shows, “6/6” in the UK, “logMAR 0.1” in research papers and eye clinic records. They’re all ways of writing visual acuity, but they look nothing like the decimal values “1.0” and “0.5” used in Japan, Korea and parts of Europe, so it’s hard to tell how they compare. This article explains what 20/20 is in decimal acuity, gives a conversion table for Snellen fractions, logMAR and decimal acuity, shows the formulas for converting yourself, explains why each notation exists, and covers the often-confused difference between visual acuity and lens power (diopters, D).
20/20 equals 1.0 in decimal acuity
In short, both the American 20/20 and the British 6/6 are the same as 1.0 in decimal acuity. “20/20” means “from 20 feet (about 6 m) away, you can make out what a person with normal vision can make out at 20 feet”. The top number is the test distance, and the bottom number is the distance at which a person with normal vision could make out that size.
For example, 20/40 means “you have to come as close as 20 feet to make out a size that a normal person can see from 40 feet away”, which equals 0.5. The bigger the bottom number, the lower the acuity: 20/200 is 0.1. Conversely, if the bottom number is smaller than 20, as in 20/15 or 20/10, the acuity is better than 1.0 (about 1.3 and 2.0).
Conversion table: decimal, Snellen fractions and logMAR
The table converts the lines from 0.1 to 2.0 on a Japanese acuity chart into US notation (20/◯ feet), UK notation (6/◯ metres) and logMAR. Values in brackets in the US column are the nearest lines that actually appear on charts used abroad.
| Decimal | US (20/◯) | UK (6/◯) | logMAR | Japanese school grade |
|---|---|---|---|---|
| 2.0 | 20/10 | 6/3 | -0.30 | A |
| 1.5 | 20/13 | 6/4 | -0.18 | A |
| 1.2 | 20/17 (20/15–20/20) | 6/5 | -0.08 | A |
| 1.0 | 20/20 | 6/6 | 0.00 | A |
| 0.9 | 20/22 | 6/6.7 | 0.05 | B |
| 0.8 | 20/25 | 6/7.5 | 0.10 | B |
| 0.7 | 20/29 (20/30) | 6/8.6 | 0.15 | B |
| 0.6 | 20/33 (20/30–20/40) | 6/10 | 0.22 | C |
| 0.5 | 20/40 | 6/12 | 0.30 | C |
| 0.4 | 20/50 | 6/15 | 0.40 | C |
| 0.3 | 20/67 (20/70) | 6/20 | 0.52 | C |
| 0.2 | 20/100 | 6/30 | 0.70 | D |
| 0.1 | 20/200 | 6/60 | 1.00 | D |
Values not in the table can be worked out with the formula above or the logMAR formula below. The Visual Acuity Test (Landolt Ring) shows your result as decimal acuity, logMAR, US notation and the Japanese school A–D grade side by side, and you can see the same table in the “Conversion table & standards” tab. What the school grades mean is explained in what the A, B, C and D grades in Japanese school eye tests mean.
What logMAR is: acuity in a form you can add and average
logMAR is the base-10 logarithm of the minimum angle of resolution (MAR: the smallest visual angle you can resolve, in minutes of arc). Acuity 1.0 corresponds to 1 minute of arc, so log10(1) = 0.0; acuity 0.1 corresponds to 10 minutes, so log10(10) = 1.0. From decimal acuity, logMAR = −log10(decimal acuity), and to convert back, decimal acuity = 10 to the power of (−logMAR).
- Smaller is better: 0.0 equals 1.0, negative values are better than 1.0 and positive values are worse. This runs the opposite way to decimal acuity, so be careful.
- Each step is the same size: in 0.1 steps, the size you can resolve always changes by a factor of about 1.26. There’s none of the unevenness of decimal acuity, where 0.1 to 0.2 is a doubling but 1.0 to 1.1 is only 1.1 times.
- Averages make sense: adding decimal 0.1 and 1.0 and dividing by 2 gives “0.55”, which is meaningless, but the average of logMAR 1.0 and 0.0 is 0.5, about 0.32 in decimal, which correctly represents the middle of the two.
For these reasons, clinical studies and papers that compare the effects of treatment normally report acuity in logMAR. The ETDRS chart used in research abroad has 5 letters per line, and each letter read improves logMAR by 0.02. A letter score, “85 − 50 × logMAR”, is also widely used to express acuity as a number of letters (logMAR 0.0 is 85 letters).
Why countries write visual acuity differently
| Notation | Main countries and settings | Idea behind it |
|---|---|---|
| Decimal (1.0, 0.5) | Japan, Korea, parts of Europe | The reciprocal of the visual angle you can resolve. Bigger is better |
| Snellen fraction in feet (20/20) | United States | Test distance of 20 feet ÷ the distance at which a normal person could see it |
| Snellen fraction in metres (6/6) | UK, Australia and others | Test distance of 6 m ÷ the distance at which a normal person could see it |
| logMAR (0.0, 0.3) | Clinical research and papers | Base-10 logarithm of the minimum angle of resolution. Smaller is better |
The fraction notation spread from the Snellen chart, devised by the Dutch ophthalmologist Snellen in the 19th century. In Japan the test distance is 5 m, so you could write a fraction such as “5/10”, but normally only the calculated decimal (0.5) is written. All of these share the same underlying idea, that a visual angle of 1 minute equals 1.0, so you can always convert with the formulas above. The relationship between a 1-minute angle and the size of the ring is explained in detail in calculating Landolt ring size and distance.
Visual acuity and lens power (D) are different things
Numbers on a glasses or contact lens prescription such as “−2.00” or “S−1.50 C−0.75 Ax180” are not visual acuity but lens power (diopters, D). Lens power describes how far out of focus your eye is, while visual acuity describes how fine a detail you can make out.
| Item | Visual acuity | Lens power (D) |
|---|---|---|
| What it describes | How fine a detail you can resolve | How far out of focus the eye is (the strength of the lens) |
| Examples | 1.0, 0.3, 20/40 | S−2.00 (short-sighted), S+1.50 (long-sighted), C−0.75 (astigmatism) |
| Which way is better | Bigger means you see better | Closer to 0 means less focusing error |
| How it’s measured | Acuity charts and acuity testers | Refraction machines and tests that swap lenses |
The stronger the short-sightedness, the lower the unaided acuity tends to be, but even at the same −1.00D, unaided acuity varies a lot with astigmatism, age and pupil size. You can’t convert one-to-one, as in “acuity 0.3 means a power of −◯”, so have your glasses or contact lens power measured by an eye doctor or optician.
FAQ
- What is 20/20 vision in decimal acuity?
- 1.0. 20/20 means that at 20 feet (about 6 m) you can make out what a person with normal vision can make out at 20 feet, which corresponds to 1.0 in decimal acuity. You can convert with decimal acuity = 20 ÷ bottom number.
- What are 20/40 and 20/200 in decimal acuity?
- 20/40 is 0.5 and 20/200 is 0.1. The bigger the bottom number, the lower the acuity. In the United States, corrected acuity of 20/200 or worse is one of the criteria for legal blindness.
- What does 6/6 mean?
- It’s the Snellen fraction written in metres, used in the UK, Australia and elsewhere. It means that at 6 m you can make out what a normal person can make out at 6 m, and like 20/20 it equals 1.0 in decimal acuity. 6/12 is 0.5 and 6/60 is 0.1.
- How do I convert logMAR to decimal acuity?
- Calculate decimal acuity = 10 to the power of (−logMAR). logMAR 0.0 is 1.0, 0.1 is about 0.8, 0.3 is about 0.5, 0.5 is about 0.32 and 1.0 is 0.1. To go from decimal acuity to logMAR, use −log10(decimal acuity).
- Can I work out my short-sighted lens power (D) from my acuity?
- Not one-to-one. The stronger the short-sightedness, the lower the unaided acuity tends to be, but it varies a lot with astigmatism, age and other factors. Have your lens power measured with a refraction test by an eye doctor or optician.
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