Pen Angle Thinning Calculator
Compute exact broad-nib stroke geometry for a nib of width w held at angle theta to the writing line: vertical stems take w*cos(theta), horizontal strokes w*sin(theta), and the thinning ratio is their quotient cot(theta).
Description
Compute exact broad-nib stroke geometry for a nib of width w held at angle theta to the writing line: vertical stems take w*cos(theta), horizontal strokes w*sin(theta), and the thinning ratio is their quotient cot(theta).
Pen Angle Thinning Calculator: Compute exact broad-nib stroke geometry for a nib of width w held at angle theta to the writing line: vertical stems take w*cos(theta), horizontal strokes w*sin(theta), and the thinning ratio is their quotient cot(theta).
When to use Pen Angle Thinning
Use this palaeographic utility to apply a stated dating, script, abbreviation, codicological, metrological, layout, or condition rule consistently while preparing manuscripts for scholarly review.
- Nib width (mm)
- Full width of the broad nib edge in mm.
- Pen angle (deg)
- Pen angle in degrees measured from the baseline (strictly between 0 and 90).
How Pen Angle Thinning works
Compute exact broad-nib stroke geometry for a nib of width w held at angle theta to the writing line: vertical stems take w*cos(theta), horizontal strokes w*sin(theta), and the thinning ratio is their quotient cot(theta). The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.1
- Stem width (mm)
- Width of a vertical stem: nib width times cos(angle).
- Horizontal width (mm)
- Width of a horizontal stroke: nib width times sin(angle).
- Thinning ratio
- Thinning ratio cot(angle) of stem over horizontal stroke.
Limitations and assumptions
- Script and manuscript evidence varies by language, region, institution, period, scribe, material, restoration, and cataloguing convention. A heuristic flag or score is not an authoritative date, hand attribution, reading, provenance, or conservation diagnosis.
- Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.
Alternative or Complementary approaches
Retain page images, scale, foliation, material, provenance, diplomatic transcription, uncertainty, and comparison exemplars; confirm conclusions with codicological context and specialist judgment.
References
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Palaeography — Wikipedia contributors
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