Description
Return 2 × distance × tan(angle/2) as capHeight and divide by capHeightFraction for emHeight.
Apparent size depends on both physical dimensions and viewing distance. Pixel dimensions additionally require a scale to physical size; a geometric visual angle by itself is not a reading-performance or accessibility assessment.
Return 2 × distance × tan(angle/2) as capHeight and divide by capHeightFraction for emHeight.
When to use this tool
Use Poster Safe View Distance Letter Height Term when you need to relate supplied viewing geometry to a design dimension.
How to use the tool and how it works
- Enter viewDistance, angularHeightRadians, capHeightFraction. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read capHeight, emHeight. Use the output convention below.
Require nonnegative viewDistance, angularHeightRadians in [0, π), and capHeightFraction in (0, 1]. Return 2 × distance × tan(angle/2) as capHeight and divide by capHeightFraction for emHeight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| viewDistance | View Distance | Required. Finite number; minimum 0. |
| angularHeightRadians | Full angular cap height in radians, not a half angle. | Required. Finite number; minimum 0. |
| capHeightFraction | Cap-height/em-height ratio in (0, 1]. | Required. Finite number; maximum 1; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| capHeight | Cap Height | Required. Finite number. |
| emHeight | Modeled em height in the viewing-distance length unit. | Required. Finite number. |
{
"input": {
"viewDistance": 10,
"angularHeightRadians": 0.02,
"capHeightFraction": 0.7
},
"output": {
"capHeight": 0.20000666693334415,
"emHeight": 0.28572380990477736
}
}Limitations and assumptions
- Angle is the full apparent letter-height angle in radians and lengths retain the distance unit; no legibility threshold, eyesight, contrast, viewing conditions, or safety standard is selected.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a final-size visual proof under representative viewing conditions. Legibility evaluation may also require font metrics, contrast, content, and accessibility testing.
References
Similar or alternative tools
- Type Cap Height Xheight Ratio
Return xHeight/capHeight and scale both design-unit heights by fontPixels/unitsPerEm.
- Type Capheight Lineheight Share
Return cap/line share, ascender+descender occupiedHeight, and lineHeight minus that total.