In use, the preceding approach gives pretty good results but not without a residual element of trial and error. The biggest problem seems to be variability in the shape of the screw head. The method assumes that the measured diameter is that of a perfect 82 degree cone. But it rarely, if ever, is. The periphery of the screw head is almost always slightly flattened, removing the knife-edge that is needed for accurate measurement. A recess based on its diameter is too shallow, the screw head stands slightly proud of the surface and some additional deepening by eye-ball is required. So if all you can hope for is a first try that never goes too deep but is otherwise only approximate, surely there must be a simpler way.
Perfection, Imperfection and Correction