Drill Point Angle from Tip Length
The inverse of the drill-point-depth tile: the included point angle from the diameter and a measured or target point length (tip allowance), angle = 2 x atan( (diameter / 2) / point length ). A 0.5 in drill ground to a 0.15 in tip is a 118-degree point; a shorter tip is a blunter angle. The number you back out when you sharpen to a length or measure a tip on a comparator. Geometry only; the actual grind and web thinning govern.
Formula and source
included point angle = 2 x atan( (diameter / 2) / point length ); half (lip) angle = point angle / 2; the inverse of point length = (diameter / 2) / tan(point angle / 2).
Drill-point geometry; the 118 / 135-degree drill-point relation as in Machinery's Handbook (Industrial Press), by name; first-principles trigonometry, solved for the angle.
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