A countersink lets a flat-head screw sit flush by cutting a cone that matches the underside of the head. This calculator works out how deep to plunge that cone so the resulting top diameter equals the screw head diameter, using the countersink angle and the pilot hole you are starting from.
How it works
A countersink of included angle A is a cone. The vertical depth needed to open the cone to a given diameter is that diameter divided by twice the tangent of half the angle. Because the tool starts from an existing pilot hole rather than a point, you subtract the pilot diameter first:
depth = (head diameter − pilot diameter) / (2 × tan(angle / 2))
full cone = head diameter / (2 × tan(angle / 2))
The full-cone figure is the depth measured from a sharp point, useful when a combined drill-and-countersink leaves no separate pilot. The plunge depth is what you set on a drill-press stop or program as a Z move.
Example and notes
A number 10 flat-head screw with a 0.385 inch head, an 82 degree countersink, and a 0.196 inch pilot hole needs about 0.109 inch of plunge depth. Keep the units consistent — if you enter millimetres for the diameters, the depth comes out in millimetres. Cut slightly deeper rather than shallower so the head finishes flush or just below the surface, and always confirm on a scrap piece before running the real part.