Recognizing and honouring Louise L Sloan (1898 – 1982), pioneer of visual acuity assessment.

# Visual Acuity “Cheat Sheet” for high and low vision

### by Michael Bach

Snellen ratio, decimal acuity, LogMAR, Letters, Counting Fingers, Hand Movement, Light Perception…

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:

WhatDecimal
acuity
Snellen
Ratio (ft)
Snellen
Ratio (m)
LogMARLinesLetters,
Letter score
(see below)
Formula1 / MAR20 / (20 · MAR)6 / (6 · MAR)log10(MAR)
“normal”1.020/206/60.0
“low”0.120/2006/601.0
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”.
• “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 all 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. 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× used more often than “hand motion”.

With the help of the FrACT Vision test, which can present very large optotypes, we were able to measure reproducible values for CF and HM (Schulze-Bonsel et al. 2006, Bach et al. 2007, Lange et al. 2009). The values for light perception (LP) and no light perception (NLP) are imputations (Bach et al. 2007, footnote³ below).

Measure Finger counting
(at 30 cm ≅ 1 ft)
Hand
movement
Light
perception
No light
perception
ShorthandCFHMLPNLP
Suggested value1.9 LogMAR2.3 LogMAR(2.7 LogMAR)(3.0 LogMAR)
Conversion / equivalence table (decimal⇄Snellen⇄LogMAR…)
LogMARLetter score⁴
@4 m
-0.30702.020/106/3.0
-0.20651.620/12.56/3.8
-0.10601.2620/166/4.8
0.00551.020/206/6.0
0.10500.820/256/7,5
0.20450.6320/306/9,5
0.30400.520/406/12
0.40350.420/506/15mild impairm.¹
0.50300.3220/606/19moderate
impairment¹
0.60250.2520/806/24
0.70200.220/1006/30
0.80150.1620/1256/38
0.90100.1320/1606/48
1.0050.1020/2006/60
1.10“off chart”
@ 4 m distance
0.0817/2506/75severe
impairment¹
1.200.06320/3006/95
1.300.05020/4006/120
1.400.040(20/500)(6/150)↓ blindness¹
1.500.032(20/600)(6/190)
1.600.025(20/800)(6/240)
1.70“off chart”
@ 1 m distance
0.020(20/1000)(6/300)
1.800.016
Values in parentheses above
represent plausible extensions
but are not defined in ISO 8956
CF²
1.900.013CF²
2.000.010CF²
2.100.0079
2.200.0063HM²
2.300.0050HM²
2.400.0040HM²
2.500.0032
2.600.0025
2.700.0020LP³
2.800.0016
2.900.0013
3.000.0010NLP³

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 largely with Halladay (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. ⁴Letter scores are in grey because they are superflous (IMHO, rationale above).

References
• CF & HM equivalents: Schulze-Bonsel K, Feltgen N, Burau H, Hansen LL, Bach M (2006) Visual acuities “Hand Motion” and “Counting Fingers” can be quantified using the Freiburg Visual Acuity Test. Invest Ophthalmol Vis Sci 47:1236–1240   [PDF]
• 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]
• 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 & HM equivalents: Lange C, Feltgen N, Junker B, Schulze-Bonsel K, Bach M (2009) Resolving the clinical acuity categories “hand motion” and “counting fingers” using the Freiburg Visual Acuity Test (FrACT). Graefe’s Arch Clin Exp Ophthalmol 247:137–142 read→here, [PDF]
• CF depending on distance (but 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
Papers on behavioural acuity where I participated
1. Farassat N, Jehle V, Heinrich SP, Lagrèze WA, Bach M (2024) The Freiburg Acuity Test in preschool children: Testability, test–retest variability, and comparison with LEA symbols. Translational Vision Science & Technology 13:14]
2. 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]
3. Freundlieb P, Kramer F, Herbik A, Bach M, Hoffmann MB (2020) Scotopic and photopic conventional visual acuity and hyperacuity. Graefes Archives 258(1):129–135   [→read]
4. Wesemann W, Schiefer U, Heinrich SP, Jägle H, Bach M (2020) Neue DIN- und ISO-Normen zur Sehschärfebestimmung. Der Ophthalmologe 117(1):19–26
5. Rohrschneider K, Spittler AR, Bach M (2019) Vergleich der Sehschärfenbestimmung mit Landolt-Ringen versus Zahlen. Der Ophthalmologe 116(11):1058–1063
6. Reiniger J, Lobecke A, Sabesan R, Bach M, Verbakel F, Brabander J, Holz F, Berendschot TTJM, Harmening W (2019) Visual hyperacuity and acuity in the presence of ocular aberrations. JOV 1;19(5):11
7. Bach M (2016) Dichoptisches Training bei Amblyopie. Der Ophthalmologe 113(4):304–308
8. Bach M, Reuter M, Lagrèze WA (2016) Vergleich zweier Visustests in der Einschulungsuntersuchung – E-Haken-Einblickgerät versus Freiburger Visustest. Der Ophthalmologe 113:684–689
9. Bach M, Schäfer K (2016) Visual acuity testing: feedback affects neither outcome nor reproducibility, but leaves participants happier. PLOS ONE 11(1):e0147803
10. Bartholomew AJ, Lad EM, Cao D, Bach M, Cirulli ET (2016) Individual differences in scotopic visual acuity and contrast sensitivity: genetic and non-genetic influences. PLOS ONE 11(2):e0148192
11. Tebartz van Elst L, Bach M, Blessing J, Riedel A, Bubl E (2015) Normal visual acuity and electrophysiological contrast gain in adults with high functioning autism spectrum disorder. Front Hum Neurosci 9:460
12. König S, Tonagel F, Schiefer U, Bach M, Heinrich SP (2014) Assessing visual acuity across five disease types: ETDRS charts are faster with clinical outcome comparable to Landolt Cs. Graefe’s Arch Clin Exp Ophthalmol 252:1093–1099
13. Heinrich SP, Bach M (2013) Resolution Acuity versus Recognition Acuity with Landolt-style Optotypes. Graef Arch Clin Exp 251:2235–2241
14. Dehnert A, Bach M, Heinrich SP (2011) Subjective visual acuity with simulated defocus. Ophthalmic Physiol Optics 31:625–631
15. Heinrich SP, Krüger K, Bach M (2011) The dynamics of practice effects in an optotype acuity task. Graefe’s Arch Clin Exp Ophthalmol 249:1319–1326
16. Tavassoli T, Latham K, Bach M, Dakin SC, Baron-Cohen S (2011) Psychophysical Measures of Visual Acuity in Autism Spectrum Conditions. Vision Res 51:1778–1780
17. 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
18. Wesemann W, Schiefer U, Bach M (2010) Neue DIN-Normen zur Sehschärfebestimmung. Der Ophthalmologe 107:821–826 [→Visustafeln zum Ausdrucken ]
19. Bach M, Dakin SC (2009) Regarding “Eagle-Eyed Visual Acuity: An Experimental Investigation of Enhanced Perception in Autism” Biol Psychiat 66:e19–e20
20. Lange C, Feltgen N, Junker B, Schulze-Bonsel K, Bach M (2009) Resolving the clinical acuity categories “hand motion” and “counting fingers” using the Freiburg Visual Acuity Test (FrACT). Graefe’s Arch Clin Exp Ophthalmol 247:137–142 [→PDF]
21. Bach M (2007) The Freiburg Visual Acuity Test – Variability unchanged by post-hoc re-analysis. Graefe’s Arch Clin Exp Ophthalmol 245:965–971
22. Schulze-Bonsel K, Feltgen N, Burau H, Hansen L, Bach M (2006) Visual acuities “hand motion” and “counting fingers” can be quantified with the Freiburg visual acuity test. Invest Ophth Vis Sci 47: 1236–1240
23. Jägle H, de Luca E, Serey L, Bach M, Sharpe LT (2006) Visual acuity and X-linked color blindness. Graefe’s Arch Clin Exp Ophthalmol 244:447–453
24. Bach M, Kommerell G (1998) Sehschärfebestimmung nach Europäischer Norm – wissenschaftliche Grundlagen und Möglichkeiten der automatischen Messung. Klin Mbl Augenheilk 212:190–195 (→HTML)
25. Bach M (1997) Anti-aliasing and dithering in the “Freiburg Visual Acuity Test’. Spatial Vision 11:85–89
26. Bach M (1996) The “Freiburg Visual Acuity Test” – Automatic measurement of visual acuity. Optometry and Vision Science 73:49–53
My papers on objective acuity assessment
1. Heinrich SP, Strübin I, Bach M (2021) VEP-based acuity estimation: unaffected by translucency of contralateral occlusion. Doc Ophthalmol 143:249–257
2. Hamilton R, Bach M, Heinrich SP, Hoffmann MB, Odom JV, McCulloch DL, Thompson DA (2021) VEP estimation of visual acuity: a systematic review. Doc Ophthalmol 142:17–24 [→PDF]
3. Hamilton R, Bach M, Heinrich SP, Hoffmann MB, Odom JV, McCulloch DL, Thompson DA (2021) ISCEV extended protocol for estimating visual acuity using VEP spatial frequency thresholds. Doc Ophthalmol 142:25–74 [→PDF]
4. Bach M, Farmer JD (2020) Evaluation of the “Freiburg Acuity VEP” on commercial equipment. Doc Ophthalmol 140:139–145   [→PDF]
5. Bach M, Heinrich SP (2019) Acuity VEP: Improved with machine learning. Doc Ophthalmol 139(2):113–122. read→here
6. Hoffmann MB, Brands J, Behrens-Baumann W, Bach M (2017) VEP-based acuity assessment in low vision. Doc Ophthalmol 135(3):209–218 read→here
7. Heinrich SP, Bock CM, Bach M (2016) Imitating the effect of amblyopia on VEP-based acuity estimates. Doc Ophthalmol 133:183–187
8. Heinrich SP, Lüth I, Bach M (2015) Event-related potentials allow for optotype-based objective acuity estimation. IOVS 56:2184–2191
9. Marhöfer DJ, Bach M, Heinrich SP (2015) Objective acuity assessment with self-face P300 responses. Doc Ophthalmol 131(2):137–148
10. Wenner Y, Heinrich SP, Beisse C, Fuchs A, Bach M (2014) Visual evoked potential-based acuity assessment: overestimation in amblyopia. Doc Ophthalmol 128:191–200
11. Heinrich SP, Marhöfer D, Bach M (2010) “Cognitive” visual acuity estimation based on the event-related potential P300 component. Clin Neurophysiol 121:1464–1472
12. 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

Thanks to Herbert Jägle for corrections.