LogMAR Value Calculator

Calculate LogMAR Value

Enter the visual acuity score from either a Snellen or ETDRS chart to get the corresponding LogMAR value.

Understanding LogMAR Values

What is a LogMAR value?

A LogMAR value (Logarithm of the Minimum Angle of Resolution) is a numerical representation of visual acuity commonly used in ophthalmology and vision science. It provides a more linear and statistically manageable scale for measuring vision compared to traditional Snellen fractions (like 20/20 or 6/6). Better vision is represented by a lower LogMAR value, with 0.0 corresponding to “normal” vision (20/20 or 6/6), and higher positive values indicating poorer vision.

The LogMAR value scale is particularly useful in research and clinical settings because changes in LogMAR scores are more directly proportional to changes in the eye’s resolving power. Each 0.1 LogMAR unit change represents a consistent change in visual acuity across the scale, unlike the non-linear steps in Snellen notation. It is widely used with ETDRS (Early Treatment Diabetic Retinopathy Study) charts, which are designed with LogMAR principles in mind, having an equal number of letters per line and a consistent logarithmic progression in letter size between lines. Anyone undergoing a comprehensive eye examination, especially for clinical trials or monitoring eye conditions, might have their vision recorded as a LogMAR value.

A common misconception is that a negative LogMAR value is impossible or incorrect. However, negative LogMAR values simply indicate vision better than the standard 20/20 or 6/6 (e.g., 20/15 or 20/10).

LogMAR value Formula and Mathematical Explanation

The calculation of the LogMAR value depends on how visual acuity was measured:

1. From Snellen Fraction (e.g., 20/40)

The Snellen fraction represents Test Distance / Distance at which a normal eye can see the letter.
First, we calculate the Minimum Angle of Resolution (MAR):

MAR = 1 / Snellen Fraction = Denominator / Numerator

Then, the LogMAR value is the base-10 logarithm of the MAR:

LogMAR = log₁₀(MAR)

For example, for 20/40 vision: MAR = 40/20 = 2, LogMAR = log₁₀(2) ≈ 0.301

2. From ETDRS Chart (Letters Read)

ETDRS charts are designed so that each line represents a 0.1 LogMAR step, and each letter has a value of 0.02 LogMAR. If a patient reads a certain number of letters starting from a known line:

LogMAR value = LogMAR of Starting Line – (Number of Letters Read × 0.02)

For instance, if the starting line is 1.0 LogMAR (20/200) and the patient reads 35 letters: LogMAR = 1.0 – (35 × 0.02) = 1.0 – 0.7 = 0.3

Variables Table:

Variable	Meaning	Unit	Typical Range (for input)
Snellen Numerator	The testing distance (e.g., 20 feet or 6 meters)	Feet or Meters	20, 6
Snellen Denominator	The distance at which a person with normal vision can read the smallest line seen by the patient	Feet or Meters	5 – 800
MAR	Minimum Angle of Resolution (in minutes of arc)	minutes of arc	0.25 – 40
ETDRS Letters Read	Number of letters correctly identified on an ETDRS chart	Number	0 – 100
ETDRS Start Line LogMAR	The LogMAR value of the first (top) line presented or the reference line	Log unit	0.0 – 1.7 (typically 1.0 or 1.1)
LogMAR value	Logarithm of the MAR	Log unit	-0.3 to 2.0+

Practical Examples (Real-World Use Cases)

Let’s see how the LogMAR value is calculated in practice:

Example 1: Snellen Acuity of 20/50

• Numerator = 20, Denominator = 50
• MAR = 50 / 20 = 2.5
• LogMAR value = log₁₀(2.5) ≈ 0.398

This indicates vision that is worse than 20/40 (LogMAR ~0.3) but better than 20/60 (LogMAR ~0.477).

Example 2: ETDRS Score of 60 letters from 1.0 line

• Letters Read = 60, Starting Line LogMAR = 1.0
• LogMAR change = 60 × 0.02 = 1.2
• Final LogMAR value = 1.0 – 1.2 = -0.2

This LogMAR value of -0.2 corresponds to very good vision, better than 20/20 (which is 0.0 LogMAR). It’s roughly equivalent to 20/12.5.

For more details on converting Snellen, check our Snellen to LogMAR conversion guide.

How to Use This LogMAR value Calculator

1. Select Acuity Type: Choose whether you are inputting a “Snellen Fraction” or “ETDRS Letters”.
2. Enter Snellen Values: If Snellen, enter the numerator and denominator of the fraction (e.g., 20 and 40 for 20/40).
3. Enter ETDRS Values: If ETDRS, enter the number of letters read correctly and the LogMAR value of the starting line (often 1.0 or 1.1).
4. Calculate: Click “Calculate” or simply change input values to see the results update automatically.
5. View Results: The primary result is the calculated LogMAR value. Intermediate results like MAR (for Snellen) or the LogMAR change (for ETDRS) are also shown.
6. Interpret: A lower LogMAR value indicates better vision. 0.0 is 20/20, positive values are worse, negative values are better.
7. Reset: Click “Reset” to clear inputs and return to default values.
8. Copy: Click “Copy Results” to copy the main result and intermediate values to your clipboard.

Understanding the LogMAR value helps in precisely quantifying visual acuity and tracking changes over time, especially when managing eye conditions. Learn more about understanding visual acuity.

Key Factors That Affect LogMAR value Results

Several factors can influence the measured LogMAR value:

• Chart Type: Snellen and ETDRS charts, while both measuring acuity, have different designs that can yield slightly different results. ETDRS is generally considered more accurate and reliable for calculating the LogMAR value due to its standardized design. See our vision charts explained page.
• Testing Distance: The distance at which the test is performed (e.g., 20 feet or 6 meters) is crucial for Snellen fractions and must be accurately recorded.
• Lighting Conditions: The illumination of the chart and the room can affect how well a patient can see the letters. Standardized lighting is important.
• Patient Factors: Attention, fatigue, understanding of the test, and cooperation can influence performance and thus the measured LogMAR value.
• Optical Correction: Whether the patient is wearing their best possible glasses or contact lenses (best-corrected visual acuity – BCVA) or their habitual correction or no correction (uncorrected visual acuity – UCVA) will significantly change the LogMAR value.
• Scoring Method: With ETDRS, letter-by-letter scoring is standard (0.02 LogMAR per letter). Different scoring rules might be applied in other contexts. Our ETDRS testing guide provides more info.
• Presence of Eye Conditions: Diseases like cataracts, macular degeneration, or refractive errors directly impact the LogMAR value. Explore common eye conditions.

Frequently Asked Questions (FAQ) about LogMAR value

What is a good LogMAR value?

A LogMAR value of 0.0 is considered normal (equivalent to 20/20 or 6/6). Negative values (e.g., -0.1, -0.2) indicate better than normal vision, while positive values (e.g., 0.3, 1.0) indicate poorer vision.

Can LogMAR value be negative?

Yes, a negative LogMAR value is possible and indicates vision better than the 20/20 standard. For example, 20/10 vision corresponds to a LogMAR of -0.3.

How does LogMAR relate to Snellen 20/20?

A Snellen fraction of 20/20 means MAR = 20/20 = 1, and log10(1) = 0. So, 20/20 is equivalent to a LogMAR value of 0.0.

Why is LogMAR used instead of Snellen fractions?

The LogMAR value scale is preferred in research and many clinical settings because it is more linear and allows for more accurate statistical analysis of changes in vision. Each step on the LogMAR scale represents an equal proportional change in visual acuity.

What does a LogMAR value of 1.0 mean?

A LogMAR value of 1.0 means the Minimum Angle of Resolution (MAR) is 10 (since log10(10) = 1). This corresponds to Snellen 20/200 or 6/60, which is the threshold for legal blindness in many places when it is the best-corrected vision.

How many letters per line on an ETDRS chart?

Standard ETDRS charts have 5 letters per line, and each letter is worth 0.02 LogMAR units.

What if I can’t even read the top line of the chart?

If a patient cannot read the largest letters on the chart at the standard distance, vision might be recorded as Count Fingers (CF), Hand Motion (HM), Light Perception (LP), or No Light Perception (NLP). These have approximate, very high LogMAR value equivalents (e.g., CF ~1.6-2.0 LogMAR, HM ~2.3-2.7 LogMAR).

Is there a difference between LogMAR from Snellen and ETDRS?

While both aim to quantify vision, the LogMAR value derived from a properly administered ETDRS test is generally considered more precise than converting a Snellen fraction, due to the ETDRS chart’s design principles. For more on results, see interpreting eye exam results.