Countersink depth and diameter calculator

What it computes

A drawing usually calls out a countersink by its diameter at the surface and its included angle, for example ⌵ Ø10.4 × 90° on a Ø5.5 hole. A machinist setting a stop, or an inspector checking the feature without a gauge, often needs the depth instead. A CAM program that drives a pointed tool needs the depth of the tool's tip. The calculator gives all three from the callout, and works backwards from a depth when that is what is known.

Formulas

The countersink is a cone. Half its included angle, θ/2, sets how fast its diameter grows with depth, so one right triangle gives every figure:

• Depth from the surface to the hole: h = (D − d) / (2 tan(θ/2)).
• Surface diameter from a depth: D = d + 2h tan(θ/2).
• Depth of the cone's theoretical point below the surface: D / (2 tan(θ/2)).
• At 90°, tan 45° = 1, so h = (D − d) / 2 and the point depth is D / 2.

D is the countersink diameter at the surface, d the hole diameter and θ the included angle: the full angle of the cone, not the half angle. At 90° every figure is exact decimal arithmetic. At other common angles, such as 82° and 100°, the tangent is irrational, so the figures are shown rounded to the decimals you choose, with the full value marked ≈.

Which angle

The angle comes from the callout, and the callout normally follows the fastener. Metric countersunk screws have a 90° head, while unified inch flat-head screws use 82°. 100° heads are common in aerospace fastening. A 60° cone is the usual center hole for turning between centers. Using a 90° countersink for an 82° head seats the screw on the hole's edge, not its head face, so check the angle before you check the depth.

Worked example

Limitations

• Sharp edges assumed. A chamfered or broken hole edge, or a rounded tool tip, changes where the cone meets the hole.
• No screw-head data. The head's diameter, its angle and how far below flush it should sit come from the screw standard and the drawing.
• No tolerance. The depth comes from nominal values; the tolerances on the diameter and angle give a range of depths.
• The countersink diameter must be larger than the hole's, and the angle must lie between 0° and 180°.

When to involve a qualified engineer

Ask the drawing's owner when a callout gives a depth and a diameter that disagree at its angle, when the angle does not match the fastener, or when a flush or recessed head matters to the function. Ask, too, before you countersink thin material. Once the cone reaches the far side, the head is no longer supported.