Snellen to logMAR Converter
Snellen to logMAR Converter
Snellen 6/12 is logMAR 0.301, decimal 0.5 and MAR 2 — the same measurement in four notations. Exact conversions both ways, in the 6 m and 20 ft forms, with the direction of each scale stated.
Snellen ⇄ logMAR ⇄ decimal
Acuity notationSnellen denominator 6, metre notation — the 6/6 reference line
The four notations, and the one definition behind them
- MAR
- the minimum angle of resolution, in minutes of arc: the angle subtended by the smallest detail the eye resolved. 6/6 is a MAR of one minute of arc, which is the reference the whole system is built on
- logMAR
- the base-ten logarithm of the MAR. 6/6 is 0, 6/12 is log₁₀(2) = 0.301, 6/60 is log₁₀(10) = 1 exactly. A HIGHER logMAR is WORSE vision, because it is a logarithm of a loss
- decimal
- the Snellen fraction worked out: 6/12 is 0.5, 20/40 is 0.5. A HIGHER decimal is BETTER vision. Decimal and MAR are exact reciprocals, so their product is one at every acuity and neither can move without the other moving the opposite way
- 6/4.8 and the −0.10 line
- 6/4.8 is logMAR −0.0969, not −0.1000. It is printed as −0.10 on every chart and every conversion table, and both sources read for this page print it that way. The acuity that is exactly −0.1000 is 6/4.766. The chart line is a rounded label, not the value
- ETDRS letters
- 85 − 50 × logMAR, which is the same relation as the ETDRS protocol’s logMAR = 1.70 − 0.02N rearranged. Five letters is one line is 0.1 logMAR, so one letter is 0.02. See the letter-by-letter scoring page for the protocol the score comes from
- what has no logMAR at all
- counting fingers, hand movements and perception of light. Published nominal values disagree: one widely used set assigns 1.9 logMAR to counting fingers and 2.3 to hand movements, while an earlier estimate derived from finger size gives about 2.3 and about 3.3. Perception of light and its absence are imputations rather than measurements on either set
Worked example
Snellen denominator 6, metre notation — the 6/6 reference line
MAR = 6 ÷ 6 = 1 minute of arc, the angle the whole system is referenced to
logMAR = log₁₀(1) = 0.00
decimal = 6 ÷ 6 = 1.0, and ETDRS letters = 85 − 50 × 0 = 85
In the other notation the same acuity is 20/20. The logMAR, the decimal and the MAR are unchanged, because the notation is a unit and not a measurement
Change the denominator to 12: MAR 2, logMAR log₁₀(2) = 0.301, decimal 0.5, 70 ETDRS letters. The same acuity in feet is 20/40
Change it to 60: MAR 10, logMAR 1.00 exactly, decimal 0.1, 35 ETDRS letters
Change it to 4.8: MAR 0.8, logMAR −0.097, printed on charts as −0.10, decimal 1.25. Better than the reference line, and the logMAR has gone negative while the decimal has gone up — the inversion, in one step
The logMAR chart’s lines, in four notations
| logMAR | Snellen 6 m | Snellen 20 ft | Decimal | ETDRS letters |
|---|---|---|---|---|
| −0.10 | 6/4.8 | 20/16 | 1.26 | 90 |
| 0.00 | 6/6 | 20/20 | 1.00 | 85 |
| 0.10 | 6/7.5 | 20/25 | 0.79 | 80 |
| 0.20 | 6/9.5 | 20/30 | 0.63 | 75 |
| 0.30 | 6/12 | 20/40 | 0.50 | 70 |
| 0.40 | 6/15 | 20/50 | 0.40 | 65 |
| 0.50 | 6/19 | 20/60 | 0.32 | 60 |
| 0.60 | 6/24 | 20/80 | 0.25 | 55 |
| 0.70 | 6/30 | 20/100 | 0.20 | 50 |
| 0.80 | 6/38 | 20/125 | 0.16 | 45 |
| 0.90 | 6/48 | 20/160 | 0.13 | 40 |
| 1.00 | 6/60 | 20/200 | 0.10 | 35 |
| 1.10 | 6/75 | 20/250 | 0.08 | 30 |
| 1.20 | 6/95 | 20/300 | 0.06 | 25 |
| 1.30 | 6/120 | 20/400 | 0.05 | 20 |
Thresholds that are written in Snellen, and who writes them
| Authority and purpose | Published threshold | logMAR | Decimal |
|---|---|---|---|
| ICD-11 category 1, mild vision impairment | worse than 6/12, at or better than 6/18 | 0.301 to 0.477 | 0.5 to 0.3 |
| ICD-11 category 2, moderate | worse than 6/18, at or better than 6/60 | 0.477 to 1.000 | 0.3 to 0.1 |
| ICD-11 category 3, severe | worse than 6/60, at or better than 3/60 | 1.000 to 1.301 | 0.1 to 0.05 |
| ICD-11 category 4, blindness | worse than 3/60, at or better than 1/60 or counting fingers at one metre | 1.301 to 1.778 | 0.05 to 0.02 |
| DVLA Group 1, car and motorcycle (United Kingdom) | at least 6/12 with both eyes open, plus the number-plate test at 20 m | 0.301 or lower | 0.5 or higher |
| DVLA Group 2, bus and lorry, better eye | 6/7.5, which the authority also gives as decimal 0.8 | 0.097 | 0.8 |
| DVLA Group 2, bus and lorry, poorer eye | 6/60, which the authority also gives as decimal 0.1 | 1.000 | 0.1 |
Why there are four notations for one measurement, and which one inverts
Visual acuity is one measurement — the smallest angle the eye resolved — written four ways. The angle itself is the minimum angle of resolution, in minutes of arc, and everything else is derived from it. The Snellen fraction is the testing distance over the distance at which the same letter would subtend one minute of arc, so its denominator divided by its numerator is the MAR: 6/12 and 20/40 are both a MAR of two. Decimal acuity is that fraction worked out. logMAR is the base-ten logarithm of the MAR. No information is added or lost between them.
The trap is that two of the four run backwards relative to the other two. Decimal acuity and the ETDRS letter score go up as vision improves; logMAR and the Snellen denominator go up as it worsens. Because decimal and MAR are exact reciprocals, their product is one at every acuity, so the inversion is not an approximation that holds in the middle of the range — it is structural. A trial that reports a mean acuity of 0.5 has to say which scale that is: 0.5 decimal is 6/12 and 0.5 logMAR is 6/19. Averaging in the wrong one is worse still, because the mean of several decimals is not the decimal of their mean logMAR.
logMAR exists because the Snellen chart’s geometry makes it a poor measuring instrument. Its lines carry different numbers of letters, and the size step between lines is irregular — one published account puts the range at 14% between the 20/70 and 20/80 lines and 100% between 20/100, 20/200 and 20/400. A patient who reads three letters on a line of four has done something different from one who reads three of eight, and a patient who drops one line near the top of the chart has lost a different amount of vision from one who drops a line near the bottom. The logMAR chart fixes both: five letters on every line and a constant ratio of 10^0.1 — about 26% — between lines, which is deliberately close to the 25% logarithmic progression proposed for the design. That is the whole reason research acuity is measured in logMAR and why the letter score is meaningful at all.
Three things this page will not do. It will not convert counting fingers, hand movements or perception of light, because those are not acuities: studies that need a number impute one, and the published imputations differ by as much as a full logMAR unit, so printing one would be inventing a measurement. It will not tell anybody whether they meet a driving standard or qualify for a registration — the thresholds in the table above are quoted as the named authority publishes them and are jurisdiction-specific. And it will not correct for a reduced testing distance, a crowded chart or a different optotype set, all of which change the number a chart produces. The one place this corpus already touches the eye is diabetes, because the chart these conversions rest on was designed for a diabetic retinopathy trial; HbA1c and estimated average glucose is the exposure those trials measured letter scores against.
Frequently asked questions
How do I convert Snellen to logMAR?
Divide the denominator by the numerator to get the MAR, then take the base-ten logarithm. 6/12 gives a MAR of 2 and log₁₀(2) = 0.301. 20/40 gives the same MAR of 2 and the same 0.301, because the two notations are the same ratio in different units. 6/60 gives a MAR of 10 and logMAR 1.00 exactly.
Is a higher logMAR better or worse?
Worse. logMAR is the logarithm of the angle the eye needed, so it is a measure of loss: 0.00 is 6/6 and 1.00 is 6/60. Decimal acuity and the ETDRS letter count run the other way, and higher is better on both. Decimal and MAR are exact reciprocals, so one cannot rise without the other falling.
Is 6/6 the same as 20/20?
Yes — identically. Both are a minimum angle of resolution of one minute of arc, logMAR 0.00 and decimal 1.0. The 6 and the 20 are the testing distance in metres and in feet, and 6 m is 19.7 ft, so the two charts are not quite the same physical distance but the ratio they define is the same number. 6/12 and 20/40 are likewise one acuity.
What is the logMAR of counting fingers or hand movements?
There isn’t one. Neither is an acuity measurement, and published studies that need a number for analysis assign different ones: one widely used set gives 1.9 logMAR for counting fingers and 2.3 for hand movements, while an earlier estimate derived from the angular size of a finger gives roughly 2.3 and roughly 3.3. Perception of light and its absence are imputed rather than measured on either. The gap between the two sets is about a full logMAR unit, so which one a study used changes its result.
Why are the logMAR chart’s Snellen equivalents not round numbers?
Because the logMAR lines are round and the Snellen labels are derived from them. Each line is 0.1 logMAR from the next, a constant ratio of 10^0.1 or about 1.26, so the denominators come out as 4.8, 6, 7.5, 9.5, 12, 15, 19, 24, 30, 38, 48, 60. The standard Snellen chart does the opposite — round denominators and an irregular size step, reported as varying from 14% to 100% between adjacent lines — which is why it is the worse instrument for measuring a change.
Related calculators
References
- Bach M. Visual Acuity and its Notations [michaelbach.de/sci/acuity.html]. Freiburg: Eye Centre, University of Freiburg. Accessed 9 October 2026.
- Royal College of Ophthalmologists. logMAR vs Snellen. RCOphth Curriculum, curriculum.rcophth.ac.uk. Accessed 9 October 2026.
- eye: Analysis of Eye Data — va(): Visual acuity conversion. CRAN reference manual, search.r-project.org. Conversions documented as logMAR = -log10(Snellen fraction) and ETDRS = 85 + 50 x log10(Snellen fraction), citing Holladay 2004, Beck 2003 and Schulze-Bonsel 2006.
- World Health Organization. ICD-11 for Mortality and Morbidity Statistics: 9D90 Vision impairment including blindness, as tabulated in the ICD-11 block listing at findacode.com. Accessed 9 October 2026.
- Driver and Vehicle Licensing Agency. Visual disorders: assessing fitness to drive. GOV.UK guidance. Accessed 9 October 2026.
- Precision Vision. Snellen Eye Chart: A Description and Explanation. precision-vision.com. Accessed 9 October 2026.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/