Visual acuity converter
Snellen 20/x, 6/x, decimal, logMAR, MAR and ETDRS letters: type one, read all the others.
For general information only — not medical advice. This page converts numbers between notations; it does not measure your vision or diagnose anything. Questions about your eyesight belong with an eye-care professional.
For Snellen type only the bottom number: 40 for 20/40, 12 for 6/12. Use a negative logMAR for better than 20/20, such as −0.1 for 20/16.
What visual acuity numbers mean
Visual acuity is the smallest detail an eye can resolve. Every notation starts from the same quantity, the minimum angle of resolution (MAR), measured in minutes of arc, where one minute is 1/60 of a degree. A person who reads the 20/20 line resolves a detail of one minute of arc, so MAR is 1. Someone who needs letters twice as large, the 20/40 line, has MAR 2. Snellen fractions, decimals, logMAR and letter counts are just different ways of writing that one number.
Formulas used
- MAR = Snellen denominator ÷ 20 (feet) or ÷ 6 (meters), and decimal acuity = 1 ÷ MAR.
- logMAR = log10(MAR), so MAR = 10logMAR (Holladay, 2004).
- Snellen denominator in feet = 20 × MAR; in meters = 6 × MAR.
- ETDRS letters read at 1 meter = 85 − 50 × logMAR, because each letter is worth 0.02 logMAR (Beck et al., 2003). At 4 meters the relation is logMAR = 1.1 − 0.02 × letters (Ferris et al., 1982), 30 letters lower.
Worked example
Take 20/40. MAR = 40 ÷ 20 = 2. logMAR = log10(2) = 0.30. Decimal = 1 ÷ 2 = 0.50. The metric twin is 6/12. The ETDRS letter score at 1 meter is 85 − 50 × 0.301 = 69.9, about 70 letters. Going the other way, 70 letters means logMAR 0.30, which is Snellen 20/39.9, the 20/40 line to within rounding. At the legal-blindness line, 20/200, MAR is 10, logMAR is 1.00 and the score is 35 letters.
A metric example and what a line is worth
A report in meters, 6/9, works the same way. MAR = 9 ÷ 6 = 1.5, so logMAR is 0.18, decimal acuity is 0.67, the feet-based equivalent is 20/30 and the letter score is about 76. On a 0.1 logMAR chart each line is five letters (5 × 0.02 = 0.1), so a change of three lines is 0.3 logMAR, or 15 letters, a size of change often quoted in clinical trials. Because the scale is logarithmic, a gain from 20/200 to 20/100 (logMAR 1.00 to 0.70, 15 letters) is the same size on the chart as a gain from 20/40 to 20/20 (0.30 to 0.00, 15 letters), even though the decimal acuity moves by 0.1 in the first case and 0.5 in the second.
Chart lines at a glance
| Snellen | Metric | logMAR | Decimal | Letters (1 m) |
|---|---|---|---|---|
| 20/10 | 6/3 | −0.30 | 2.00 | 100 |
| 20/12.5 | 6/3.8 | −0.20 | 1.58 | 95 |
| 20/16 | 6/4.8 | −0.10 | 1.26 | 90 |
| 20/20 | 6/6 | 0.00 | 1.00 | 85 |
| 20/25 | 6/7.6 | 0.10 | 0.79 | 80 |
| 20/32 | 6/9.5 | 0.20 | 0.63 | 75 |
| 20/40 | 6/12 | 0.30 | 0.50 | 70 |
| 20/50 | 6/15.1 | 0.40 | 0.40 | 65 |
| 20/63 | 6/19 | 0.50 | 0.32 | 60 |
| 20/80 | 6/23.9 | 0.60 | 0.25 | 55 |
| 20/100 | 6/30.1 | 0.70 | 0.20 | 50 |
| 20/125 | 6/37.9 | 0.80 | 0.16 | 45 |
| 20/160 | 6/47.7 | 0.90 | 0.13 | 40 |
| 20/200 | 6/60 | 1.00 | 0.10 | 35 |
The rows are the lines of a 0.1 logMAR chart, each 26% larger than the one before (100.1 ≈ 1.26). The Snellen labels are the conventional rounded names for those steps, so 20/12.5 is really 20/12.6 and 20/32 is 20/31.7.
Limits and common mistakes
- Averaging. Do not take the arithmetic mean of decimals or Snellen denominators. Holladay (2004) shows that acuities should be converted to logMAR, averaged there, and converted back; the result is a geometric mean.
- Mixing chart distances. A letter score only makes sense with its test distance. The 4 meter and 1 meter scales differ by 30 letters, and a traditional Snellen chart has no letter score at all, so a conversion from Snellen to letters is an approximation.
- Uneven Snellen steps. Neighbouring lines on a traditional chart (20/20, 20/25, 20/30, 20/40, 20/50, 20/70, 20/100, 20/200) are not equal steps in log terms; an ETDRS chart makes them equal. Treat a converted value as the line the person reached, not a finer measurement.
- Best correction. The legal-blindness definition applies to the better eye with correcting lenses, not to unaided vision. Driving vision standards differ by state and are not covered here.
Common questions
How do I convert 20/40 to logMAR?
Divide the bottom number by the top: 40 ÷ 20 = 2. That is the minimum angle of resolution (MAR), the size of the smallest detail you can resolve, in minutes of arc. logMAR is the base-10 logarithm of MAR, so 20/40 is logMAR 0.30. The decimal acuity is 1 ÷ MAR = 0.50, and the same line on a metric chart is 6/12. On a standard ETDRS chart read at 1 meter it corresponds to about 70 letters.
What is the difference between Snellen, decimal and logMAR?
They describe the same measurement. Snellen (20/x or 6/x) compares the distance you stood at with the distance at which a person with typical sight would read the same line. Decimal is that fraction worked out as one number (20/40 is 0.5). logMAR is the logarithm of the angle of the smallest letter detail, so every line of an ETDRS-style chart is 0.1 logMAR, every letter 0.02, and a better eye has a lower, or even negative, number.
How many ETDRS letters is 20/20?
On the 1-meter scale used here (Beck and colleagues, 2003) the letter score is 85 − 50 × logMAR, which makes 20/20 equal to 85 letters. A chart read at 4 meters is scored differently: logMAR = 1.1 − 0.02 × letters, so the same 20/20 eye reads 55 letters there. The two scales differ by a constant 30, so always check which distance a letter score belongs to before you compare studies.
What counts as legally blind in the United States?
The tax code (26 U.S.C. § 63(f)(4)) calls a person blind only if central visual acuity does not exceed 20/200 in the better eye with correcting lenses, or if acuity is better than 20/200 but the widest diameter of the visual field subtends an angle no greater than 20 degrees. That is decimal 0.1, logMAR 1.00 or worse. The converter reports only the acuity part; it cannot judge a visual field. Other programs and agencies word their definitions separately, so the statute quoted here is not a ruling on any benefit or license.
Does the converter handle counting fingers, hand motion or light perception?
No. Those are categories for vision too poor to read a chart, not measurements on a scale. Holladay (2004) proposed numeric stand-ins and a later FrACT-based summary by Michael Bach uses different values, so published conversions disagree and the page leaves them out instead of choosing one.
Is 20/20 perfect vision?
No. 20/20 means the eye resolves a detail of one minute of arc (MAR 1), which is the typical reference level, not a ceiling. Many eyes read smaller lines: 20/16 is logMAR −0.10, and 20/10 is −0.30. Acuity also says nothing about visual field, contrast, color, depth or eye health.
For optics beyond acuity, see the spherical equivalent calculator for a glasses prescription, the reading add calculator for presbyopia, the vertex distance calculator for contact lenses, or the thin lens calculator for the underlying physics.
For general information only — not medical advice. Conversions here are educational; they are not a prescription or an eye examination, and any decision about your vision must come from an eye-care professional. Sources: J.T. Holladay, “Visual acuity measurements,” J Cataract Refract Surg 30:287–290 (2004); R.W. Beck et al., Am J Ophthalmol 135:194–205 (2003); F.L. Ferris et al. (1982); the conversion relations as summarized by Michael Bach at michaelbach.de/sci/acuity.html; 26 U.S.C. § 63(f)(4) at law.cornell.edu/uscode/text/26/63. How we check our calculators.