Visual acuity (VA) is one of the most important measures of our visual performance. Further aspects like visual field, contrast sensitivity, color vision, motion perception etc. are not covered here.
There exist (too) many measures to quantify visual acuity. Luckily, they can all be converted into each other. Which is best? Most people prefer the one they were brought up with… See next section and the historical review by Colenbrander (2008).
Definitions and conversion
All acuity measures relate to the visual angle of the smallest perceived (or discriminable) structure. Whichever way we define “smallest perceived structure”, let’s call it “MAR” for “minimum angle of resolution”, and let its dimension be minutes of arc. Then:
What
Decimal acuity
Snellen Ratio (ft)
Snellen Ratio (m)
LogMAR
Lines
Letters, Letter score
Shorthand
VAdec
VASnellen
VASnellen
VALogMAR
don’t use (see below)
Formula
1 / MAR
20 / (20 · MAR)
6 / (6 · MAR)
log10(MAR)
“normal”
1.0
20/20
6/6
0.0
“low”
0.1
20/200
6/60
1.0
Conversion
10^(-VALogMAR)
VASnellen ≡ VAdec
VASnellen ≡ VAdec
–log10(VAdec)
1 line = 0.1 LogMAR
1 letter = 0.02 LogMAR
The “20” resp. “6” in the Snellen columns correspond to a testing distance of 20 ft resp. 6 m. For the “opposite direction” of LogMAR versus the other acuity measures: think of LogMAR in terms of “visual loss”.
So which one is best?
Snellen ratio and decimal acuity are identical after you simply calculate the fraction.
Decimal acuity and Snellen ratio are not useful for calculations, for instance you must never calculate the mean!
LogMAR “runs the wrong way round”, unless you think of it as measuring “visual loss”.
LogMAR is approximately normally distributed. That means you can calculate means, SDs, t-tests, whatever, to your heart’s desire.
As the first analysis step, convert everything to LogMAR. After analysis, one can convert back to Snellen or Decimal to reach the pertinent audience. I suggest to plot LogMAR on an inverted axis, so “good” acuity is up and/or right.
Lines? →This is not an ISO Standard term. Acuity charts are typically arranged in lines, with equal optotype grade along a line. Following ISO the lines should have equidistant progressive acuity grades with 0.1 LogMAR increments. Then 1 Line is equivalent to 0.1 LogMAR.
“Letters”? →This is not an ISO Standard term. It is used as equivalent to a step of 0.02 LogMAR. “Letters” is often used in the same sense as “Letter Score”. I understand the attraction of “Letters”: You can say “vision improved by 15 letters”, sounds mor intuitive than “vision improved by –(minus!)0.15 LogMAR”. It is just so obnoxious that LogMAR “runs the wrong way round”.
“Letter Score”? →This refers to the count of letters read (see previous item). Its absolute value is not well defined, as it depends on the distance. I avoid Letters or Letter Scores, they are needless additions since everything can be expressed in LogMAR. You can still count letters on the last line read, should you wish for a (slightly) higher resolution, on whichever chart you use (with a sensible progression and 5 optotypes per line), and calculate “0.02 LogMAR” per letter. [There also exists a slightly different Letter Score, where errors before the threshold line also omitted from counting.] To convert from Letter Score to LogMAR with a standard ETDRS chart (Ferris et al. 1982) at a distance of 4 m this formula applies: LogMAR = 1.1 – 0.02 · (number of letters correctly identified).
“ETDRS”? →ETDRS is not a VA unit; ETDRS charts use LogMAR.
Averaging acuities
For studies, visual acuity data frequently needs to be quantitatively processed, e.g. averaged. For instance if you measure everything twice (my recommentation), and/or for treatment group comparisons. As Holladay (1997) clearly explains, there are wrong ways to go about this. So how to average?
LogMAR values can be averaged in the normal arithmetic way [e.g. (val1+val2)/2] because LogMAR is an (approximate) interval scale
Decimal acuity MUST NOT be averaged arithmetically (its “scale of measurement” is only ordinal). You could calculate the geometric mean, but best: Convert to LogMAR, then average. If desired you can then convert back to decimal notation.
Snellen Fraction: convert to LogMAR, then average. If desired you can then convert back to Snellen Fraction.
Low vision categories (CF, HM, …)
For very low vision, categories are used routinely, namely counting fingers (CF), hand motion/movement (HM), light perception (LP) and no light perception (NLP). Based on finger size, Holladay (2004) suggested that CF is equivalent to ≈2.3 LogMAR at 1 foot (my conversion); he considers HM as having 10× worse Snellen acuity, resulting in ≈3.3 LogMAR for HM at 1 foot. [Fun fact (2024): “hand movement” is 5× more often used than “hand motion”.]
CF: counting fingers, HM: hand movement, LP: light perception, NLP: no LP. ¹WHO definitions of distance vision impairment. ²Based on data from Schulze-Bonsels et al. (2006) and Lange et al. (2009). ³Imputations / suggestions. I agree with Holladay (2004) “[these] are not actually visual acuity measurements, but simply the detection of a stimulus … should be excluded.” Numbers here can be useful though, e.g. to quantitatively document intervention success. Note: these values are not on an interval scale. ⁴The “simple” Letter Score, where errors before the last line are not considered. ⁵Values in parentheses represent plausible extensions of ISO 8596. ⁶Beck al. 2003, page 197, Table 1; see References
CF & HM equivalents: Bach M, Schulze-Bonsel K, Feltgen N, Burau H, Hansen LL (2007) Author Response: Numerical Imputation for Low Vision States. Invest Ophthalmol Vis Sci. eLetter, Aug 2007 [PDF]
Beck RW, Moke PS, Turpin AH, et al (2003) A computerized method of visual acuity testing: adaptation of the early treatment of diabetic retinopathy study testing protocol. Am J Ophthalmol 135:194–205
Colenbrander A (2008) The Historical Evolution of Visual Acuity Measurement. Visual Impairment Research 10:57–66
Holladay JT (1997) Proper Method for Calculating Average Visual Acuity. J Refract Surg 13(4):388–391
CF depending on distance (not based on acuity data): Karanjia (2016)
Normal acuity in age range 20–65 is ≈–0.2 LogMAE = 1.6 decimal: Frisén L, Frisén M (1981) How good is normal visual acuity? Albrecht von Graefes Arch Klin Ophthalmol 215:149–157
My (co-authored) papers on behavioural acuity
Bach M (2024) Freiburg Vision Test (FrACT): Optimal number of trials? Graefes Arch [PDF]
Bailey I, Bach M, Ferris R, Johnson C, Bittner A, Colenbrander A, Keeffe J (2020) Visual acuity. In: Ayton L et al. for the HOVER International Taskforce (2020) Harmonization of Outcomes and Vision Endpoints in Vision Restoration Trials: Recommendations from the International HOVER Taskforce. Transl Vis Sci Technol 9:25–25 [PDF]
Bach M (2016) Dichoptisches Training bei Amblyopie. Der Ophthalmologe 113(4):304–308
Bach M, Reuter M, Lagrèze WA (2016) Vergleich zweier Visustests in der Einschulungsuntersuchung – E-Haken-Einblickgerät versus Freiburger Visustest. Der Ophthalmologe 113:684–689
Bach M, Schäfer K (2016) Visual acuity testing: feedback affects neither outcome nor reproducibility, but leaves participants happier. PLOS ONE 11(1):e0147803
Heinrich SP, Krüger K, Bach M (2010) The effect of optotype presentation duration on acuity estimates revisited. Graefe’s Arch Clin Exp Ophthalmol 248:389–394
Bach M, Kommerell G (1998) Sehschärfebestimmung nach Europäischer Norm – wissenschaftliche Grundlagen und Möglichkeiten der automatischen Messung. Klin Mbl Augenheilk 212:190–195 (→HTML)
Bach M (1997) Anti-aliasing and dithering in the “Freiburg Visual Acuity Test’. Spatial Vision 11:85–89
Bach M (1996) The “Freiburg Visual Acuity Test” – Automatic measurement of visual acuity. Optometry and Vision Science 73:49–53
My (co-authored) papers on objective acuity assessment
Heinrich SP, Strübin I, Bach M (2021) VEP-based acuity estimation: unaffected by translucency of contralateral occlusion. Doc Ophthalmol 143:249–257
Heinrich SP, Marhöfer D, Bach M (2010) “Cognitive” visual acuity estimation based on the event-related potential P300 component. Clin Neurophysiol 121:1464–1472
Bach M, Maurer JP, Wolf ME (2008) Visual evoked potential-based acuity assessment in normal vision, artificially degraded vision, and in patients. Br J Ophthalmol 92:396–403