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

  1. Palaeography — Wikipedia contributors

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