What it is
The ligne (often written L) is the button-trade unit for diameter. 1 ligne = 1/40 inch = 0.635 mm. It is not the old Paris typographic line, not Chinese market cun, and not Japanese wasai sun.
How to use
Divide the millimeter diameter by 0.635 to get ligne. Equivalently multiply by 40/25.4 (1 inch = 25.4 mm = 40 ligne). 15.24 mm = 24 ligne. The converter above uses this factor.
ligne = mm × 1.57480315
Example: 1 mm = 1.57480315 ligne
Common uses
Shirt buttons about 16-18 ligne (about 10-11.5 mm); suit front buttons often 24-28 ligne; coats 32-36 ligne. A 3/4-inch button on a pattern is 30 ligne. For buying buttons, buttonholes, and imported notions.
Conversion tips
40 ligne = 1 inch. 16L ~ 10 mm, 18L ~ 11.4 mm, 24L ~ 15.2 mm, 30L = 19.05 mm. Do not mix ligne with denier in the same column.