How do I convert Snellen to logMAR?

Divide the denominator by the numerator to get the minimum angle of resolution (MAR), then take log10. 20/40 → MAR 2 → logMAR 0.30; 6/18 → MAR 3 → logMAR 0.48; 20/200 → MAR 10 → logMAR 1.00. Decimal acuity is the reciprocal of MAR (20/40 = 0.5).

What is 20/40-2 in logMAR?

On a logMAR-style chart with 5 letters per line, each letter is worth 0.02 logMAR. 20/40-2 means the 20/40 line was read with 2 letters missed, so logMAR = 0.30 + 0.04 = 0.34. 20/40+2 (two letters read on the next smaller line) is 0.30 − 0.04 = 0.26.

What logMAR value is used for counting fingers and hand motion?

Measurements with the Freiburg acuity test (Schulze-Bonsel et al. 2006) put counting fingers at about logMAR 1.9 (decimal 0.013) and hand motion at about 2.3 (decimal 0.005). Light perception (2.7) and no light perception (3.0) are imputed conventions, not measurements; some trial protocols use CF 2.0, LP 2.6 and NLP 2.9 instead. State which convention you used.

What is the relationship between LogMAR and MAR?

MAR is the Minimum Angle of Resolution in arcminutes. LogMAR is log10(MAR). For standard 20/20 (6/6) vision, MAR = 1.0 arcminute and LogMAR = 0.00.

How is the ETDRS letter score estimated?

On standard ETDRS charts, 20/20 vision corresponds to 85 letters and each 0.1 LogMAR line contains 5 letters (0.02 LogMAR per letter). The score is approximated by 85 − (50 × LogMAR), clamped between 0 and 100. At 4 m this equals 30 plus the number of letters read when 20 or more are read.

How many letters is a 3-line gain?

One line is 0.1 logMAR or 5 ETDRS letters, so a 3-line gain is −0.30 logMAR or +15 letters, a doubling of the visual angle (for example 20/80 to 20/40). Lower logMAR means better vision.

Is decimal acuity × 100 equal to percentage of visual function?

No. Decimal × 100 represents a scaled notation index, not legal visual efficiency, disability percentage, or overall visual function. AMA visual efficiency curves are non-linear.

Are Snellen and LogMAR chart tests interchangeable?

Clinical studies (DRCR.net, AOS) demonstrate that mathematical conversions do not account for differences in optotype design, crowding, line spacing, and termination rules between charts.

LogMAR Visual Acuity Converter

Convert between LogMAR, Snellen (20/x or 6/x, with +/− letters like 20/40-2), decimal acuity and ETDRS letters; quantify CF, HM, LP and NLP; and measure the change between two acuities in lines and letters.

LogMAR = log10(Snellen denominator ÷ numerator), so 20/20 (6/6) is 0.00, 20/40 (6/12) is 0.30 and 20/200 (6/60) is 1.00.

Visual Acuity Input

Input Format

LogMAR (e.g. 0.00, 0.30, 1.00) Snellen feet (e.g. 20/40, 20/200, or 40) Snellen meters (e.g. 6/12, 3/60, 1/60, or 60) Decimal Acuity (e.g. 1.0, 0.5, 0.05) ETDRS Letter Score (e.g. 85, 70, 35)

Value or Fraction

Snellen also accepts letter scores (20/40-2, 6/9+1). Any format accepts CF, HM, LP or NLP.

Notice: Output values represent mathematical notation equivalences and estimated scoring formulas. They do not constitute an eye examination, diagnosis, or assessment of visual disability.

Equivalent Notations

Enter an acuity value or fraction and click Calculate to view equivalents.

Standard Milestone Equivalents

Values reflect standard geometric logMAR progression chart lines (-0.30 to 1.30) and low-vision reference distances.

LogMAR	Snellen 20/x	Snellen 6/x	Decimal	Est. ETDRS	Milestone Description
-0.30	20/10	6/3	2.00	100	Standard chart progression line
-0.20	20/12.5	6/3.8	1.60	95	Standard chart progression line
-0.10	20/16	6/4.8	1.25	90	Standard chart progression line
0.00	20/20	6/6	1.00	85	Standard reference normal (MAR = 1′)
0.10	20/25	6/7.5	0.80	80	Standard chart progression line
0.20	20/32	6/9.5	0.63	75	Standard chart progression line
0.30	20/40	6/12	0.50	70	Common driving-standard reference line in many US states
0.40	20/50	6/15	0.40	65	Standard chart progression line
0.50	20/63	6/19	0.32	60	Standard chart progression line
0.54	20/70	6/21	0.29	58	Common US low-vision reference value
0.60	20/80	6/24	0.25	55	Standard chart progression line
0.70	20/100	6/30	0.20	50	Standard chart progression line
0.80	20/125	6/38	0.16	45	Standard chart progression line
0.90	20/160	6/48	0.13	40	Standard chart progression line
1.00	20/200	6/60	0.10	35	Common 20/200 reference line; legal definitions require a full jurisdiction-specific assessment
1.30	20/400	3/60	0.05	20	Reduced distance Snellen equivalent
1.78	20/1200	1/60	0.017	0	Low-vision test distance milestone

Off-Chart Vision: CF, HM, LP, NLP in LogMAR

Used to include very low vision in statistics. Values are not on an interval scale; report the convention and the test distance.

Code	Meaning	LogMAR	Decimal	Other protocols	Basis
CF	Counting fingers	1.9	0.013	1.8–2.0	Measured (Schulze-Bonsel et al. 2006, FrACT)
HM	Hand motion	2.3	0.005	2.3	Measured (Schulze-Bonsel et al. 2006, FrACT)
LP	Light perception	2.7	0.002	2.6	Imputed convention (Bach)
NLP	No light perception	3.0	0.001	2.9	Imputed convention (Bach)

Sources: Schulze-Bonsel K, et al. IOVS 2006;47:1236–40; Bach M, Visual acuity cheat sheet.

Compare Two Acuities

Uses the input format selected above. Lower logMAR is better vision.

Before (baseline)

After (follow-up)

Enter both values to see the change in logMAR, lines and letters.

Factual Unit Relationships & Method Limitations

Mathematical Definitions: Minimum Angle of Resolution (MAR) = 1 / Decimal Acuity = Snellen Denominator / Snellen Numerator. LogMAR = log₁₀(MAR) = -log₁₀(Decimal).
ETDRS Letter Score Formula: Calculated as 85 - (50 × LogMAR). 20/20 corresponds to 85 letters; each 0.1 logMAR change represents 5 optotypes (0.02 logMAR per letter). Clamped between 0 and 100 letters.
Partial lines: Each letter is 0.02 logMAR on 5-letter-per-line charts, so 20/40-2 = 0.30 + 0.04 = 0.34 and 20/40+1 = 0.28. A change of 0.1 logMAR is one line or 5 letters.
Reduced Test Distances: Snellen fractions with reduced numerators (e.g. 3/60, 1/60) are evaluated via MAR = Denominator / Numerator (MAR = 20 for 3/60, LogMAR = 1.30; MAR = 60 for 1/60, LogMAR = 1.78).
Chart Protocol Disagreements: Published clinical trials (AOS, DRCR Retina Network) confirm that direct mathematical translation between Snellen and ETDRS charts exhibits systematic divergence due to differing termination rules, optotype legibility, and geometric scaling.

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Quick answer

LogMAR = log10(Snellen denominator ÷ numerator), so 20/20 (6/6) is 0.00, 20/40 (6/12) is 0.30 and 20/200 (6/60) is 1.00. Each 0.1 logMAR is one chart line of 5 letters, so one letter = 0.02 logMAR and 20/40-2 is 0.30 + 0.04 = 0.34. The ETDRS letter score is about 85 − 50 × logMAR.

Examples

Snellen (ft)	Snellen (m)	Decimal	LogMAR	ETDRS letters
20/20	6/6	1.00	0.00	85
20/40	6/12	0.50	0.30	70
20/70	6/21	0.29	0.54	58
20/100	6/30	0.20	0.70	50
20/200	6/60	0.10	1.00	35
20/400	3/60	0.05	1.30	20

Enter any notation, including 20/40-2 or CF, to see every equivalent and the nearest chart line.

Summary

Calculates notation equivalents between LogMAR (log10 of the Minimum Angle of Resolution), Snellen fractions (including reduced distances such as 3/60 and partial-line scores such as 20/40-2), decimal acuity, and estimated ETDRS letter scores (85 − 50 × LogMAR). Off-chart vision (counting fingers, hand motion, light perception) uses published research conventions. Mathematical equivalence does not replace standard clinical testing or account for chart protocol differences.

How it works

Select the input notation format (LogMAR, Snellen feet, Snellen meters, Decimal, or ETDRS letter score).
Enter your measurement. Snellen accepts full fractions (20/40, 3/60), denominator shorthand (40), and letters missed or extra on the next line (20/40-2, 6/9+1). You can also type CF, HM, LP or NLP in any format.
Each letter counts 0.02 logMAR: 20/40-2 = 0.30 + 2 × 0.02 = 0.34; 20/40+1 = 0.30 − 0.02 = 0.28.
View converted notations, exact values, nearest standard chart lines, and the estimated ETDRS score (85 − 50 × LogMAR).
Use "Compare two acuities" to express a change as logMAR, chart lines (0.1 each) and ETDRS letters (0.02 each).

Use cases

Convert study LogMAR values into standard Snellen equivalents for presentation.
Turn clinic notes such as 20/40-2 or 6/9+1 into logMAR for statistics.
Assign logMAR values to counting fingers and hand motion for research data.
Report a treatment effect as lines or letters gained or lost.
Evaluate low-vision reduced-distance notations (such as 3/60 or 1/60) in standard LogMAR.
Translate clinical chart entries between metric (6/x) and imperial (20/x) test distances.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu