Leather sewing points on curves

A clean rounded corner needs evenly spaced holes all the way around the curve. Pick your pricking iron pitch and how many holes you want on the curve, and you get the radius to draw. Or lock a different value and play with the other two.

Values

The locked value is never changed by the calculation. Edit either of the other two and the third one follows.

Hole spacing [[ t.badge_computed ]]

[[ unit === 'mm' ? 'mm' : 'in' ]]

[[ pitchHint ]]

[[ fmt(t.field_effective, { value: len(result.L) }) ]]

Holes on the curve [[ t.badge_not_whole ]] [[ t.badge_computed ]]

[[ fmt(t.field_exact_holes, { exact: exactHoles }) ]]

Stitch line radius [[ t.badge_computed ]]

[[ unit === 'mm' ? 'mm' : 'in' ]]

[[ fmt(t.min_radius, { r: len(shown.L / Math.SQRT2) }) ]]

[[ fmt(t.field_effective, { value: len(result.R) }) ]]

[[ t.error_title ]]

[[ errorText ]]

[[ t.out_holes ]]

[[ result.n ]]

[[ fmt(t.out_exact_holes, { exact: exactHoles }) ]]

[[ t.out_radius ]]

[[ len(result.R) ]]

[[ t.out_pitch ]]

[[ len(result.L) ]]

[[ fmt(t.snap_title, { exact: exactHoles }) ]]

[[ snapText ]]

[[ t.chart_title ]]

[[ t.legend_curve ]]
[[ t.legend_tangent ]]
[[ t.legend_straight ]]

[[ c.v === 'n' ? t.label_holes : c.v ]] [[ unit === 'mm' ? 'mm' : 'in' ]] ([[ exactHoles ]])

[[ t.chart_note ]]

[[ t.table_toggle ]]

[[ t.table_help ]]

[[ t.table_holes ]]	[[ fmt(t.table_radius, { L: len(shown.L) }) ]]	[[ fmt(t.table_pitch, { R: len(shown.R) }) ]]
	[[ len(row.R) ]]	[[ len(row.L) ]]

How it works

Hand stitching leather starts with the holes: a pricking iron (or stitching chisel) punches a row of evenly spaced slits, then the thread goes through. On straight runs you just walk the iron along. On a curve every hole has to land on the arc, at the same spacing, or the stitch line looks stepped.

The calculator works on a 90° corner. The two holes where the curve meets the straight runs belong to both; between them sit the n holes on the curve. So the arc is split into n + 1 equal chords, each as long as the pitch L and each spanning 90° / (n + 1). Chord geometry gives L = 2 · R · sin(angle / 2), and from there the three formulas:

R = L / (2 · sin(45° / (n + 1)))

L = 2 · R · sin(45° / (n + 1))

n = 45° / arcsin(L / 2R) − 1

The first one is the same as R = ½ · L · csc(π / (4 (n + 1))), written in degrees. The number of holes has to be whole: when it is the computed value it gets rounded to the nearest integer, and the value you typed is adjusted to match (the page tells you by how much).

Why lock a value

Usually the pitch is set by the iron you own, so it is locked: you change the number of holes and read the radius to draw. If you already have a corner punch or a template, lock the radius and see how many holes fit with your pitch. You can always change the locked value yourself; the calculation just won't touch it.

Tips

With 0 holes on the curve the stitch cuts the corner with a single straight stitch at 45°. That's the tightest radius a given pitch can turn.
The radius here is the stitch line's. The edge of the piece has a larger radius: stitch radius plus the stitch line's distance from the edge (often 3 mm). That's the size of corner punch you need.
If the radius you need doesn't work with your iron's pitch, punch the curve with a single-prong iron at the spacing the calculator gives you with the radius locked.
Scribe the arc with dividers first, punch the tangent point on both sides, then split the arc between them.