ETDRS logMAR Letter Score Calculator

Every letter is 0.02 logMAR and every line is 0.1, so logMAR = 1.70 − 0.02 × the letter score. The 4-metre score carries a 30-letter credit; leaving it out costs six lines.

Last updated 8 Oct 2026

ETDRS letters ⇄ logMAR

Letter scoring

Letters read correctly at 4 metresOut of 70 — fourteen lines of five. The protocol tests every patient at four metres first, whatever their acuity.

Letters read correctly at 1 metreOnly used when fewer than four letters were read at four metres. The protocol repeats the test at one metre whenever fewer than twenty letters were read at four, and records both totals — but the score still comes from the four-metre result unless that result was under four letters. Leave it at 0 if the one-metre test was not done; the field cannot be blank, because the engine refuses to answer on a partially filled form.

0.32logMARExample

39 letters at 4 metres, 0 at 1 metre — the protocol document’s own worked example

The scoring rule, and the two routes to the same number

logMAR = 1.70 − 0.02 × N · N = letters at 4 m + 30, or letters at 1 m when fewer than 4 were read at 4 m

0.02 per letter: every ETDRS line carries five letters and every line is 0.1 logMAR from the next, so one letter is 0.02. The uniform per-letter value is an approximation the protocol document itself flags, because a letter near the top of the chart is not quite the same increment of angle as one near the bottom
the 30-letter credit: quoted from the protocol: “30 letters will be considered as having been read correctly prior to testing” at four metres. The four-metre chart’s top line is six lines below the one-metre chart’s, and the credit is those six lines of five letters. Omitting it understates the acuity by 0.60 logMAR
the 4-metre rule: quoted: “if four or more letters are read correctly at the four-meter test distance” then “the visual acuity score is equal to the number of letters read correctly at four meters plus 30”. Otherwise “the visual acuity score is equal to the number of letters read correctly at one meter”
the 1-metre rule: quoted: “if the number of letters read correctly at four meters is less than twenty, the test should be repeated at one meter”, with +0.75 D added to the trial frame for the shorter distance and the patient seated. Both totals are recorded. Note the two different numbers: twenty letters decides whether the one-metre test is DONE, four letters decides whether it is SCORED
a score of 0: the protocol records a score of zero when no letters are read at either distance. This page refuses to print a logMAR for it, because 1.70 − 0.02 × 0 = 1.70 would assert that the eye reads the one-metre chart’s top line, which is the line it just failed
the per-letter route: the chart’s own method: take the logMAR of the last line read in full and subtract 0.02 for each further letter, or take the logMAR of the line being read and add 0.02 for each letter missed. This is algebraically identical to 1.70 − 0.02N and is asserted identical for all fourteen lines and all five letter counts

Worked example

39 letters at 4 metres, 0 at 1 metre — the protocol document's own worked example
39 letters is four or more, so the score is 39 + 30 = 69 letters
logMAR = 1.70 − 0.02 × 69 = 1.70 − 1.38 = 0.32, which is the figure the protocol document prints for this case
That is a Snellen denominator of 6 × 10^0.32 = 6/12.5 and a decimal acuity of 0.479
The credit, costed. Score the same 39 letters without it: 1.70 − 0.02 × 39 = 0.92 logMAR, which is 6/49. That is 0.60 logMAR — six whole lines — of fabricated visual loss from one omitted constant, and it is the commonest way this arithmetic is got wrong
The two published routes agree. 39 letters is seven full lines (35 letters) plus four. Line 7 of the chart is logMAR 0.40, so the per-letter route gives 0.40 − 4 × 0.02 = 0.32. Same answer, different method
The chart's ends. All 70 letters at four metres is a score of 100 and logMAR −0.30; the first line alone is a score of 35 and logMAR 1.00 exactly; a score of 85 is logMAR 0.00, which is the 6/6 line
Where the one-metre test is used. Change the four-metre total to 3 and the one-metre total to 20: the score becomes 20 with no credit, and the logMAR is 1.30. Change the four-metre total to 4 and leave the one-metre total at 20: the score jumps to 34 and the logMAR to 1.02, because one extra letter at four metres moves the scoring from one rule to the other
And the refusal. Zero at both distances gives a score of 0, and no logMAR is printed. The protocol records the zero; it does not convert it

Letter score, logMAR and Snellen across the chart

Every logMAR here is 1.70 − 0.02 × the score and every Snellen denominator is this page’s own arithmetic. The fifth row is the protocol document’s worked example. The last two rows are the floor of the four-metre rule: at four letters the score is still the four-metre total plus 30, and at three it becomes the one-metre total instead.
Letters at 4 m	Score (+30)	logMAR	Snellen 6 m	Snellen 20 ft	Decimal
70	100	−0.30	6/3.0	20/10	2.00
60	90	−0.10	6/4.8	20/16	1.26
55	85	0.00	6/6	20/20	1.00
45	75	0.20	6/9.5	20/30	0.63
39	69	0.32	6/12.5	20/42	0.48
35	65	0.40	6/15	20/50	0.40
25	55	0.60	6/24	20/80	0.25
15	45	0.80	6/38	20/125	0.16
5	35	1.00	6/60	20/200	0.10
4	34	1.02	6/63	20/209	0.10

The two decision numbers in the protocol, which are not the same

Twenty letters decides whether the one-metre test is performed; four letters decides whether its result is scored. The middle row is where readers most often assume the one-metre letters count, and they do not: the protocol records them and scores the four-metre result. Both sentences are quoted on this page from the protocol document’s running text.
Letters at 4 m	Is the 1 m test done?	Which total is scored?	Credit applied?
20 or more	No	4 metres	Yes, +30
4 to 19	Yes, and both totals recorded	4 metres — the 1 m total is not used	Yes, +30
0 to 3	Yes	1 metre	No
0 at 4 m and 0 at 1 m	Yes	Neither — the score is 0	No

Why trial acuity is counted in letters, and the constant everybody drops

The ETDRS chart is the instrument almost every published acuity outcome is measured on, and its design is the reason. Five letters on every line, a constant 0.1 logMAR step between lines, and letter sets balanced for difficulty mean that one letter is worth the same 0.02 logMAR wherever on the chart it is read. That turns acuity from an ordinal line count into something a trial can average, difference and test — which is precisely what a standard Snellen chart cannot support, because its lines carry different numbers of letters and its size step between lines is irregular.

Two numbers come out of the test and they are the same thing. The letter score is how many letters the patient read, and the logMAR is 1.70 minus two hundredths of that score. The relation is exact and reversible: 85 letters is logMAR 0.00, every five letters is a line, and the chart’s full range at four metres runs from a score of 35 at logMAR 1.00 to a score of 100 at −0.30. Trials report change in letters rather than in logMAR for the same reason they use the chart at all — a 15-letter gain is three lines, and it is a whole number.

The constant that gets dropped is the 30-letter credit. The protocol’s words are that “30 letters will be considered as having been read correctly prior to testing” at four metres, and the credit is there because the four-metre chart’s top line sits six lines below the one-metre chart’s top line. Score a four-metre result without it and the arithmetic reports 0.60 logMAR of visual loss that does not exist. The companion trap is the pair of decision numbers: the one-metre test is performed when fewer than twenty letters were read at four metres, but the one-metre total is only scored when fewer than four were. A patient who read ten letters at four metres is tested at one metre and scored 40 regardless of what happens there.

Two honest limits. First, the uniform 0.02 per letter is an approximation, and the protocol document says so: a letter high on the chart is not quite the same increment of resolved angle as one low down. Second, a zero score is not an acuity. The protocol records it as zero letters, and this page refuses to convert it, because 1.70 − 0.02 × 0 would claim the eye reads the one-metre chart’s top line — the line it has just failed. Below the chart there is counting fingers, hand movements and perception of light, and those are not acuities: the nominal logMAR values published for them disagree by up to a full logarithmic unit. The chart itself comes from the Early Treatment Diabetic Retinopathy Study, whose letter scores were read against glycaemic exposure, which is this corpus’s own route into the subject.

Frequently asked questions

How do I convert an ETDRS letter score to logMAR?

logMAR = 1.70 − 0.02 × the letter score. A score of 69 is 0.32 logMAR; 85 is 0.00; 35 is 1.00 exactly; 100 is −0.30. The inverse is score = 85 − 50 × logMAR, which is the same relation rearranged.

What is the 30-letter credit and when does it apply?

It applies to any score taken at four metres, where the protocol treats 30 letters as already read before testing begins. The four-metre chart’s top line is six lines — 30 letters — below the one-metre chart’s top line, so the credit puts both distances on one scale. Letters read at one metre get no credit. Omitting it understates the acuity by 0.60 logMAR, which is six lines.

When is the test repeated at one metre?

When fewer than twenty letters were read at four metres, with +0.75 D added to the trial frame and the patient seated. But the one-metre total is only used for the score when fewer than four letters were read at four metres. Those are two different thresholds and conflating them is the commonest misreading of the protocol.

Is one letter really worth 0.02 logMAR everywhere on the chart?

Approximately, and the protocol document flags it as an approximation. Each line is five letters and 0.1 logMAR, so 0.02 per letter follows by division — but a letter read high on the chart is not quite the same increment of resolved angle as one read low down. The approximation is accepted because it makes the score linear, which is what lets trials average it.

What does a letter score of zero mean?

That no letters were read at either four metres or one metre. The protocol records the score as 0; it does not give it a logMAR, and neither does this page. Converting it would assert an acuity of 1.70 logMAR, which is the one-metre chart’s top line and the line the eye has just failed.

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References

PhenX Toolkit. Protocol 111101: Visual Acuity — ETDRS, web page and protocol PDF. RTI International for the National Institutes of Health. Accessed 9 October 2026. (The document’s two tables are JPEG images and were not read; every figure used here is from its running text.)
Good-Lite. What is ETDRS? ETDRS (LogMAR) Vision Test Charts. good-lite.com. Accessed 9 October 2026.
LogMAR chart. Wikipedia, citing Bailey IL, Lovie JE. New design principles for visual acuity letter charts. Am J Optom Physiol Opt. 1976;53(11):740-5.
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.
Bach M. Visual Acuity and its Notations [michaelbach.de/sci/acuity.html]. Freiburg: Eye Centre, University of Freiburg. 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/