Countersink Diameter from a Plunge Depth
The inverse of the countersink tile: the finished (major) diameter a set plunge depth opens, D_cs = 2 Z tan(angle/2) + d_hole, so a machinist reading a dial or a Z stop can check the diameter. A 0.1438 in plunge with an 82 deg tool and a 0.250 in pilot hole opens a 0.500 in countersink; a shallower (larger) angle opens wider for the same depth. 82 deg (inch) and 90 deg (metric) are NOT interchangeable. A setup aid; the tool geometry and the fastener callout govern.
Formula and source
D_cs = 2 x Z x tan(angle/2) + d_hole; cone_dia = 2 x Z x tan(angle/2); the inverse of Z = (D_cs - d_hole) / (2 x tan(angle/2)).
Countersink diameter-to-depth relation (Machinery's Handbook countersinking; 82 deg inch and 90 deg metric flat-head standards), first-principles trigonometry, by name, solved for the diameter; the tool geometry and the fastener callout govern.
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