Countersink Diameter from a Plunge Depth
The finished (major) diameter a set plunge depth opens.
Example
You enter
- Plunge depth from the tool zero Z (in) 0.1438
- Included angle (deg) 82
- Diameter at the Z zero (in): the hole edge the cone first touches, or a flat-tip tool; 0 if a pointed tool is zeroed at the surface 0.25
You get
- Finished countersink diameter D_cs 0.5 in
- Cone diameter from the plunge alone 0.25 in
Checked against published worked examples from: GoEngineer (K. Petersen).
Details, formula, and sources
ScopeD_cs = 2 Z tan(angle/2) + d, with Z from the tool zero and d the diameter there (the hole edge the cone first touches, a flat tip, or 0 for a pointed tool zeroed at the surface). A 0.1438 in plunge past the edge of a 0.250 in hole with an 82 deg tool opens a 0.500 in countersink; zeroed at the surface the same plunge opens only 0.250 in; 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 or tableD_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)).
Source and editionCountersink 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.
Free accessThe countersink depth-to-diameter relation is first-principles cone trigonometry; the depth, angle, and pilot hole come from the setup and the tool.
What governsEstimate. AHJ and licensed professional govern.
API field namesplunge_depth_in, included_angle_deg, pilot_hole_dia_in, countersink_dia_in, cone_dia_in
- Depth to diameter the finished diameter is read back from the plunge depth the machine is set toMachinery's Handbook
- Angle standard 82 deg inch flat-head and 90 deg metric are not interchangeableflat-head fastener standards
- Angle drives depth a shallower included angle opens a wider diameter for the same depthcone geometry