About

Countersink depth errors produce either protruding screw heads or weakened material around the bore. Both outcomes compromise structural integrity and surface finish. This calculator derives the required countersink depth d from the geometric relationship between the pilot hole diameter D_hole, the screw head diameter D_head, and the included countersink angle θ. It applies standard trigonometric decomposition of the conical frustum formed during the countersinking operation. Results assume a sharp-edged, ideal conical cutter with no deburring allowance.

The tool covers standard included angles of 60°, 82°, 90°, 100°, and 120° per ISO 7721 and ANSI B18.6.7M. For flush-mount results, add 0.1 - 0.2 mm to the computed depth to account for tool wear and material spring-back. Aluminum alloys require less overcut than stainless steels. Note: the formula assumes a symmetrically aligned pilot hole. Misalignment shifts the effective contact diameter and invalidates the depth calculation.

Formulas

The countersink forms a conical frustum. Given the included angle θ, the depth d is the vertical distance from the workpiece surface to the apex intersection of the cone walls.

d = D_head − D_hole2 × tan(θ2)

Where d = countersink depth (mm), D_head = outer countersink diameter or screw head diameter (mm), D_hole = pilot or through-hole diameter (mm), θ = included countersink angle (°).

The volume of material removed is the conical frustum volume:

V = π ⋅ d3 ⋅ (R² + R ⋅ r + r²)

Where R = D_head ÷ 2 (outer radius), r = D_hole ÷ 2 (inner radius). The angle conversion from degrees to radians uses θ_rad = θ × π ÷ 180.

Reference Data

Standard	Fastener Type	Nominal Size	Head ∅ mm	Hole ∅ mm	Angle °	Depth mm
ISO 10642	Hex Socket CSK	M3	6.72	3.4	90	1.66
ISO 10642	Hex Socket CSK	M4	8.96	4.5	90	2.23
ISO 10642	Hex Socket CSK	M5	11.20	5.5	90	2.85
ISO 10642	Hex Socket CSK	M6	13.44	6.6	90	3.42
ISO 10642	Hex Socket CSK	M8	17.92	9.0	90	4.46
ISO 10642	Hex Socket CSK	M10	22.40	11.0	90	5.70
ISO 10642	Hex Socket CSK	M12	26.88	13.5	90	6.69
DIN 7991	Hex Socket CSK	M5	10.00	5.5	90	2.25
DIN 7991	Hex Socket CSK	M6	12.00	6.6	90	2.70
DIN 7991	Hex Socket CSK	M8	16.00	9.0	90	3.50
DIN 965	Phillips CSK	M3	6.00	3.4	90	1.30
DIN 965	Phillips CSK	M4	8.00	4.5	90	1.75
DIN 965	Phillips CSK	M5	10.00	5.5	90	2.25
DIN 965	Phillips CSK	M6	12.00	6.6	90	2.70
ANSI B18.6.7M	Flat Head (82°)	#6	8.33	3.50	82	2.95
ANSI B18.6.7M	Flat Head (82°)	#8	10.31	4.16	82	3.76
ANSI B18.6.7M	Flat Head (82°)	#10	12.29	4.83	82	4.56
ANSI B18.6.7M	Flat Head (82°)	1/4"	14.27	6.35	82	4.84
ISO 2009	Slotted CSK	M4	8.40	4.5	90	1.95
ISO 2009	Slotted CSK	M6	12.60	6.6	90	3.00
ISO 2009	Slotted CSK	M8	16.80	9.0	90	3.90
DIN 7991	Hex Socket CSK	M10	20.00	11.0	90	4.50
DIN 7991	Hex Socket CSK	M12	24.00	13.5	90	5.25
ISO 10642	Hex Socket CSK	M16	29.00	17.5	90	5.75
ISO 10642	Hex Socket CSK	M20	36.00	22.0	90	7.00

Frequently Asked Questions

A smaller included angle means the cone walls are steeper. The tangent of half the angle decreases as the angle decreases, which increases the quotient in the depth formula. For the same diameter difference, an 82° countersink yields approximately 11% more depth than a 90° countersink. This is why ANSI-standard flat head screws (82°) require deeper recesses than their ISO metric (90°) equivalents for comparable head sizes.

Add 0.1-0.2 mm beyond the calculated depth for most metals. This compensates for elastic spring-back of the material and minor tool wear. In soft materials like aluminum or plastics, 0.05 mm is often sufficient. In stainless steel or titanium, use 0.2-0.3 mm. Over-countersinking beyond 0.3 mm wastes material and reduces clamping force on the screw head.

No. The formula assumes a sharp-edged pilot hole with no prior chamfer. If the pilot hole already has a chamfer or deburring cut, subtract that chamfer depth from the calculated countersink depth to avoid over-cutting. A typical deburr adds 0.1-0.15 mm of effective countersink.

The geometry is universal. However, wood screws often have a 90° included angle head and the pilot hole in wood is smaller relative to the shank than in metal. Enter the actual head diameter and the pilot hole you drilled. Be aware that wood compresses under the head, so the effective depth may be 0.3-0.5 mm less than calculated.

The included angle is the full apex angle of the cone measured from one side of the taper to the other. The half-angle is exactly half that value. A 90° included angle has a 45° half-angle. Countersink tools are specified by included angle. The depth formula divides the included angle by 2 internally because it uses the tangent of the half-angle to compute the cone's axial depth from its radial extent.

The removed volume is useful for estimating material waste in batch production, calculating cutter wear rates, and determining chip evacuation requirements. In CNC programming, it helps estimate cycle time since the volume directly correlates with the material removal rate. For a single hole it is negligible, but across thousands of holes in a production run, the aggregate volume informs coolant flow and chip management.