logMAR, Snellen and decimal acuity
Four notations for a single quantity — the smallest angle your eye can resolve. Each is a rescaling of the same number, so converting between them is arithmetic rather than approximation.
The short answer. 20/20 feet = 6/6 metres = 1.0 decimal = 0.00 logMAR. They are the same result. To convert any Snellen fraction to decimal, divide the top by the bottom; to get logMAR, take the base-10 logarithm of the bottom divided by the top.
The question this page answers: how do I convert between 20/20, 6/6, 1.0 and logMAR?
They are all the same number
Visual acuity measures one thing: the smallest angle, in minutes of arc, at which your eye can distinguish two separate points. That quantity is called the minimum angle of resolution, or MAR, and every notation on this page is a rescaling of it.
An average healthy adult resolves about one minute of arc. One minute is the reference, and every notation expresses it differently:
20/20 feet = 6/6 metres = 1.0 decimal = 0.00 logMAR = one minute of arc.
Snellen notation is a fraction: the distance you were tested at, over the distance at which an average eye could read the same line. 20/40 means you needed to be at 20 feet to read what an average eye reads at 40. The numerator is a testing convention — 20 feet in the United States, 6 metres almost everywhere else — which is why 20/20 and 6/6 are the same result written in different units, and why neither says anything about perfection.
Decimal acuity is that fraction worked out: 20/40 becomes 0.5. logMAR is the base-10 logarithm of the MAR, so 1.0 minute becomes log10(1) = 0.00 and larger angles give positive values. Better-than-average vision produces logMAR values below zero, which is the one feature of the scale that catches people out.
The conversion table
| Feet | Metres | Decimal | logMAR | What it means |
|---|---|---|---|---|
| 20/10 | 6/3 | 2.00 | −0.30 | Better than the reference standard — common in healthy young eyes |
| 20/15 | 6/4.5 | 1.33 | −0.12 | Better than the reference standard — common in healthy young eyes |
| 20/20 | 6/6 | 1.00 | 0.00 | The reference standard |
| 20/25 | 6/7.5 | 0.80 | 0.10 | Mild reduction; around the usual driving threshold |
| 20/30 | 6/9 | 0.67 | 0.18 | Mild reduction; around the usual driving threshold |
| 20/40 | 6/12 | 0.50 | 0.30 | Mild reduction; around the usual driving threshold |
| 20/50 | 6/15 | 0.40 | 0.40 | Moderate reduction |
| 20/60 | 6/18 | 0.33 | 0.48 | Moderate reduction |
| 20/70 | 6/21 | 0.29 | 0.54 | Substantial reduction |
| 20/80 | 6/24 | 0.25 | 0.60 | Substantial reduction |
| 20/100 | 6/30 | 0.20 | 0.70 | Substantial reduction |
| 20/200 | 6/60 | 0.10 | 1.00 | Substantial reduction |
| 20/400 | 6/120 | 0.05 | 1.30 | Severe reduction |
Doing it yourself
To convert any Snellen fraction:
- To decimal: divide the numerator by the denominator. 20/40 becomes 0.5.
- To logMAR: take the base-10 logarithm of the denominator divided by the numerator. 20/40 gives log10(2), which is 0.30.
- Feet to metres: multiply the denominator by 6/20, or 0.3. 20/40 becomes 6/12.
- logMAR to decimal: decimal = 10−logMAR. A logMAR of 0.30 gives 10−0.3, which is 0.5.
Note that decimal and logMAR run in opposite directions. Higher decimal is better vision; higher logMAR is worse. Reading a logMAR value as though higher were better is the single commonest error in interpreting these results.
Why research uses logMAR
Snellen charts have a structural problem that matters as soon as you want to do arithmetic with the results. The lines are not evenly spaced — the gap from 20/20 to 20/25 is a different amount of vision from the gap between 20/100 and 20/200 — and each line has a different number of letters, so the top lines are measured far less precisely than the bottom ones.
That makes ordinary operations invalid. You cannot average two Snellen results, you cannot say a treatment improved vision "by two lines" and have it mean the same thing for two patients, and you cannot compare a change at the top of the chart with one at the bottom.
A logMAR chart fixes all of it by construction: five letters on every line, a constant 0.1 logMAR step between lines, and letters chosen to be of equal difficulty. Each letter is worth 0.02 logMAR, so partial lines count. The result is a genuinely linear scale on which averaging and subtraction mean what they appear to mean — which is why every clinical trial reports logMAR, whatever the clinic down the road puts on your card.
The practical consequence for a patient: a logMAR result from a research study and a Snellen result from a routine test are not equally precise, even after conversion. The conversion is exact arithmetic on an inexact input.
What acuity does not measure
Acuity is high-contrast resolution at distance, in good light, with one eye at a time. That is a narrow slice of vision, and a great deal of real visual function sits outside it.
- Contrast sensitivity. The ability to distinguish shades close together, as in fog or at dusk. It can be badly reduced with 20/20 acuity intact, and it is often the first thing to go with early cataract.
- Field of vision. Glaucoma can take peripheral field while central acuity stays normal for years.
- Colour vision, which is tested separately and bears no relation to acuity.
- Binocular function — depth perception and eye coordination.
- Near vision. Acuity charts are read at distance. Reading difficulty in your forties is presbyopia and will not show on a distance chart at all.
This is why "my vision is 20/20" and "my eyes are fine" are different statements, and why a sight test takes twenty minutes rather than two.
Legal thresholds, which are not conversions
Several commonly quoted figures look like acuity values but are legal or administrative definitions that vary by jurisdiction and usually include conditions beyond acuity.
- Driving. Most jurisdictions set a standard around 20/40, often with a visual field requirement attached. The exact figure and the field requirement differ by country and sometimes by licence class.
- Legal blindness in the United States is 20/200 or worse in the better eye with best correction, or a visual field of 20 degrees or less. Someone can meet the definition with acuity far better than 20/200.
- WHO impairment categories use metric Snellen and are a separate scheme again, designed for international statistics rather than for individual entitlement.
Converting your acuity into one of these notations tells you where you sit on a scale. It does not tell you whether you meet a threshold, because the thresholds have conditions attached that a number cannot carry.
Convert your own
The acuity converter takes a value in any of the four notations and gives you the other three, snaps it to the nearest line that actually exists on a chart, and places it in the WHO impairment category. It runs in your browser.
This page explains notation and arithmetic. It is not a vision test, cannot assess your eyesight, and is not medical advice. Acuity measured on a screen at an unknown distance is not a clinical result. If your vision has changed, see an optometrist.
Questions people ask
- Is 6/6 the same as 20/20?
- Yes, exactly. They are the same measurement in different units — 6 metres and 20 feet are the same testing distance. Neither means perfect vision; both mean you resolved the line an average healthy adult resolves at that distance. Plenty of eyes do better.
- What is logMAR 0.0?
- The logarithm of the minimum angle of resolution, where 0.0 means an angle of one minute of arc — the same thing 20/20, 6/6 and 1.0 decimal all mean. Negative logMAR values are better than average: −0.1 is roughly 20/16.
- Why do researchers use logMAR instead of Snellen?
- Because Snellen lines are unevenly spaced and have different numbers of letters, so the difference between two adjacent lines is not a constant amount of vision. logMAR charts have five letters per line and a constant 0.1 step, which makes the scale linear and the arithmetic — averaging, comparing, measuring change — actually valid.
- What does 20/40 vision mean?
- You read at 20 feet what someone with average vision reads at 40. It is the common legal threshold for driving without correction in many jurisdictions, and it is about 0.5 decimal or 0.30 logMAR.
- Is decimal acuity the same as a percentage of vision?
- No, and the confusion is widespread. Decimal 0.5 is not 50% of normal vision in any meaningful sense — it is a ratio of resolvable angles. Percentage-of-vision figures used in disability assessments come from separate scales and do not convert directly.