Visual acuity can be expressed in several different notations. In most US clinical settings, the familiar Snellen fraction (20/20, 20/40) is used. In research, clinical trials, and increasingly in academic ophthalmology centers, LogMAR (logarithm of the minimum angle of resolution) is the preferred system. As an ophthalmic assistant, you will encounter both and need to understand what each number means.
This guide explains the mathematical basis of each system, provides a complete conversion table for the values you will encounter clinically, and clarifies when each notation system is appropriate. Understanding both systems also deepens your comprehension of how optotypes and chart design actually work.
The Snellen Fraction System
The Snellen system, introduced in 1862, expresses acuity as a ratio between the test distance and the distance at which a normal observer could read the same optotype. The fraction 20/X means: the patient reads at 20 feet what a person with normal acuity reads at X feet.
Snellen Fraction Structure
Numerator
The testing distance in feet (US) or meters (metric). Usually 20 feet or 6 meters. Always fixed during a standard exam.
Denominator
The distance at which a person with normal acuity could read the same letter. This value changes based on which line the patient reads correctly.
Key insight: The denominator equals (test distance) / (decimal acuity). Larger denominator = worse vision.
The Snellen system has known limitations: the number of letters per line is not standardized across the chart, and the spacing between lines is not mathematically uniform. This means that improving from 20/200 to 20/100 represents a different relative change than improving from 20/40 to 20/20, even though both appear to be one "step" of improvement to the casual observer.
The LogMAR System
LogMAR stands for the logarithm of the Minimum Angle of Resolution. The minimum angle of resolution (MAR) is the smallest angle subtended by a detail that a person can discriminate. For a person with 20/20 vision, the MAR is 1 minute of arc. The LogMAR value is simply the base-10 logarithm of that angle.
The Conversion Formula
LogMAR = log₁₀(denominator / numerator)
Example 1: 20/20 → log₁₀(20/20) = log₁₀(1) = 0.0
Example 2: 20/40 → log₁₀(40/20) = log₁₀(2) = 0.3
Example 3: 20/200 → log₁₀(200/20) = log₁₀(10) = 1.0
Example 4: 20/10 → log₁₀(10/20) = log₁₀(0.5) = -0.3
0.0
LogMAR for 20/20
Normal vision baseline
Positive
LogMAR > 0.0
Worse than normal vision
Negative
LogMAR < 0.0
Better than normal vision
Complete Conversion Reference Table
The table below shows the most clinically common acuity values in all three notation systems: US Snellen (feet), metric Snellen (meters), and LogMAR. Memorize the key values — 20/20 = 0.0, 20/200 = 1.0, 20/400 = 1.3 — and use the formula for less common values.
| US Snellen (feet) | Metric Snellen (m) | Decimal VA | LogMAR | Clinical Context |
|---|---|---|---|---|
| 20/10 | 6/3 | 2.0 | -0.3 | Better than normal (uncommon) |
| 20/15 | 6/4.5 | 1.33 | -0.12 | Slightly better than normal |
| 20/20 | 6/6 | 1.0 | 0.0 | Normal acuity reference |
| 20/25 | 6/7.5 | 0.8 | 0.1 | Near-normal |
| 20/30 | 6/9 | 0.67 | 0.18 | Mildly reduced |
| 20/40 | 6/12 | 0.5 | 0.3 | DMV driving threshold (most states) |
| 20/50 | 6/15 | 0.4 | 0.4 | Moderate reduction |
| 20/80 | 6/24 | 0.25 | 0.6 | Significant impairment |
| 20/100 | 6/30 | 0.2 | 0.7 | Moderate-severe impairment |
| 20/200 | 6/60 | 0.1 | 1.0 | Legal blindness threshold (US) |
| 20/400 | 6/120 | 0.05 | 1.3 | Severe low vision |
Practice COA Questions
Opterio includes VA notation questions within the COA Assessments domain. Build confidence on this topic and all others before exam day.
The ETDRS Chart and LogMAR Scoring
The ETDRS (Early Treatment Diabetic Retinopathy Study) chart was developed in the 1980s specifically to enable precise, reproducible LogMAR scoring. Unlike the standard Snellen chart, the ETDRS chart has exactly 5 letters per line, and the lines are spaced in equal 0.1 LogMAR increments. This design allows scoring at the letter level: each letter read correctly contributes 0.02 LogMAR units to the score.
ETDRS charts are tested at 4 meters (not 20 feet), which reduces the need for patients to squint and provides a more controlled testing environment. They are considered the gold standard for visual acuity measurement in clinical research, pharmaceutical trials involving vision endpoints, and low vision rehabilitation assessments.
ETDRS vs. Standard Snellen: Key Differences
Standard Snellen Chart
- Variable letters per line (typically 1 at top to 8 at bottom)
- Unequal spacing between lines
- 20-foot testing distance
- Cannot score individual letter performance
- Faster to administer clinically
ETDRS Chart
- 5 letters per line (standardized)
- Equal 0.1 LogMAR spacing between lines
- 4-meter testing distance
- Letter-by-letter scoring possible (0.02 LogMAR/letter)
- Gold standard for research and clinical trials
When Each System Is Used
Snellen Fraction (20/X)
- • Routine clinical practice in US ophthalmology offices
- • Patient communication and insurance documentation
- • DMV standards and driving eligibility assessment
- • Legal blindness determination
- • COA, COT, and COMT exam scenarios
LogMAR
- • Clinical research and pharmaceutical trials
- • Low vision rehabilitation assessment
- • Monitoring small changes in acuity over time
- • Statistical analysis requiring interval-scale data
- • Academic ophthalmology centers and teaching hospitals
Exam Study Tip
For the COA exam, focus primarily on Snellen notation. Know the formula LogMAR = log₁₀(denominator/numerator) and the key equivalents: 20/20 = 0.0, 20/40 = 0.3, 20/200 = 1.0. You are unlikely to be asked to perform the full logarithmic calculation, but understanding the relationship between the two systems shows conceptual mastery.