# Visual Acuity Converter

> Converts a visual acuity written as a Snellen fraction in feet or metres, a decimal or a logMAR value into all four notations plus the minimum angle of resolution, the nearest ETDRS/logMAR chart line and the WHO ICD-11 distance-vision-impairment category.

- Calculator id: `snellen-vision-conversion` · Category: Medical & Clinical (`medical`) · Tool name: `convert_visual_acuity`
- Canonical page: https://tttkmbb.com/medical/snellen-vision-conversion · This document: https://tttkmbb.com/medical/snellen-vision-conversion.md · JSON definition: https://tttkmbb.com/medical/snellen-vision-conversion.json

## Purpose

Converts a visual acuity written as a Snellen fraction in feet or metres, a decimal or a logMAR value into all four notations plus the minimum angle of resolution, the nearest ETDRS/logMAR chart line and the WHO ICD-11 distance-vision-impairment category.

**Use when:** You need to translate an acuity between US Snellen (20/40), metric Snellen (6/12), decimal (0.5) and logMAR (0.3) notation, or to place it against the WHO impairment thresholds or the US legal-blindness acuity criterion.

**Do not use when:** The acuity is recorded as counting fingers, hand motion or light perception (no numeric conversion), or the problem is visual-field loss; results are informational and not medical advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `acuity` | string |  | required | Acuity in any common notation: Snellen feet "20/40", Snellen metres "6/12", decimal "0.5" or "logMAR 0.3". A plain number is read as decimal acuity unless format says otherwise (a negative number is read as logMAR). |
| `format` | enum: auto \| snellen_ft \| snellen_m \| decimal \| logmar |  | optional, default "auto" | How to read acuity; auto recognises fractions, the word logMAR and plain decimals. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `snellen_feet` | string |  | 20/x notation. |
| `snellen_metres` | string |  | 6/x notation. |
| `decimal_acuity` | number |  | numerator / denominator (1.0 = 20/20 = 6/6). |
| `logmar` | number |  | log10 of the minimum angle of resolution: 0 = 20/20, higher is worse, each 0.1 is one ETDRS line. |
| `mar_arcmin` | number | arcmin | 1 / decimal acuity (1 arcmin at 20/20). |
| `category` | string |  | Distance vision impairment category (mild: worse than 6/12 to 6/18; moderate: worse than 6/18 to 6/60; severe: worse than 6/60 to 3/60; blindness: worse than 3/60), applied to this acuity. |
| `us_legal_blindness` | string |  | Whether the acuity meets the US statutory criterion (20/200 or worse in the better eye with best correction; the alternative visual-field criterion is not assessed). |
| `nearest_standard_line` | string |  | Nearest ETDRS/logMAR chart line (0.1 logMAR steps from 20/10 to 20/800) with its Snellen equivalents. |
| `input_interpreted_as` | string |  | How the acuity text was interpreted. |

## Formula

`decimal = numerator / denominator (Snellen) or 10^(−logMAR); logMAR = log10(1 / decimal) = log10(denominator / numerator); mar_arcmin = 1 / decimal; snellen_feet = 20 / (20 / decimal); snellen_metres = 6 / (6 / decimal); nearest line = logMAR rounded to the nearest 0.1`

The notations are exact transforms of one another (20/40 = 6/12 = 0.5 = logMAR 0.30); denominators are rounded to whole numbers above 20 and to one decimal below. ICD-11 categories are defined on presenting acuity in the better eye, and the US definition of legal blindness also accepts a visual field of 20° or less. Results are informational only and not a substitute for clinical judgement or medical advice.

## Data Sources

- WHO – Blindness and vision impairment fact sheet (ICD-11 distance vision impairment categories) — https://www.who.int/news-room/fact-sheets/detail/blindness-and-visual-impairment (standard, retrieved 2026-09-24)
- Wikipedia – Visual acuity (Snellen, decimal and logMAR notation, US legal blindness) — https://en.wikipedia.org/wiki/Visual_acuity (reference, retrieved 2026-09-24)
- Wikipedia – LogMAR chart (ETDRS lines and Snellen equivalents) — https://en.wikipedia.org/wiki/LogMAR_chart (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/snellen-vision-conversion?acuity=…`
- `POST https://tttkmbb.com/api/v1/calculate/snellen-vision-conversion` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/snellen-vision-conversion · OpenAPI operationId `convert_visual_acuity` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "snellen-vision-conversion", "inputs": {…}}`

## Example

- 20/40: inputs `{"acuity":"20/40"}` → `{"snellen_feet":"20/40","snellen_metres":"6/12","decimal_acuity":0.5,"logmar":0.3,"mar_arcmin":2,"nearest_standard_line":"20/40 (6/12), logMAR 0.3"}`
- 6/6: inputs `{"acuity":"6/6","format":"auto"}` → `{"snellen_feet":"20/20","snellen_metres":"6/6","decimal_acuity":1,"logmar":0,"mar_arcmin":1,"category":"Normal vision (6/6 = 20/20 or better)"}`

```
GET https://tttkmbb.com/api/v1/calculate/snellen-vision-conversion?acuity=20%2F40
```

## Limitations

The acuity is recorded as counting fingers, hand motion or light perception (no numeric conversion), or the problem is visual-field loss; results are informational and not medical advice. The notations are exact transforms of one another (20/40 = 6/12 = 0.5 = logMAR 0.30); denominators are rounded to whole numbers above 20 and to one decimal below. ICD-11 categories are defined on presenting acuity in the better eye, and the US definition of legal blindness also accepts a visual field of 20° or less. Results are informational only and not a substitute for clinical judgement or medical advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How do I read logMAR values?**

0.0 is 20/20, each +0.1 is one line worse (0.3 = 20/40, 1.0 = 20/200) and negative values are better than 20/20 (−0.1 = 20/16). It is the scale used in research and ETDRS charts.

**Why does 20/30 convert to 6/9 rather than the 6/9.5 on my chart?**

The conversion is exact (20/30 = 0.667 = 6/9); ETDRS charts step in 0.1 logMAR, so their 6/9.5 line is 20/32 (logMAR 0.2), which nearest_standard_line reports.

**What is legal blindness?**

In the US, best-corrected acuity of 20/200 or worse in the better eye, or a visual field of 20° or less; other countries use different thresholds (the UK certifies severe sight impairment around 3/60).

## Related

- [Angle Converter](https://tttkmbb.com/conversion/angle.md) — Convert the minimum angle of resolution between arcminutes and degrees.
- [Glasgow Coma Scale Calculator](https://tttkmbb.com/medical/glasgow-coma-scale.md) — Another bedside neurological assessment converted to a standard scale.