Countersink Depth Calculator uses Depth=((CS dia-hole dia)/2)/tan(angle/2) to find axial plunge depth from included angle, countersink diameter, and through-hole diameter in inches or mm, exact setup.
Getting countersink depth wrong is one of those mistakes that only shows up after the screw is already flush — or worse, sitting proud of the surface because the cone wasn’t cut deep enough. The depth isn’t something you eyeball. It’s a direct function of the tool’s included angle and the diameter difference between the countersink and the through-hole beneath it, and the math behind it is exact.
This calculator handles that geometry for you. Enter the included angle of your countersink bit, the target countersink diameter at the surface, and the diameter of the through-hole below it. The result is the precise axial depth you need to plunge to achieve that surface diameter — along with the chamfer face length, sharp apex reference, and unit conversions you might need on the shop floor.
How the Depth Is Calculated
A countersink is a truncated cone. The tool cuts a conical recess, and you stop at the point where the wide end of that cone — measured at the surface — matches your target diameter. The through-hole beneath it creates the truncation.
The formula at the core of this calculator is:
Depth = (D_cs − D_hole) / 2 ÷ tan(included angle / 2)
Where D_cs is your countersink diameter, D_hole is your through-hole diameter, and the included angle is the full tip angle of the cutting tool — not the half angle. Dividing that angle by two gives you the half-angle at the cone wall, and the tangent of that half-angle converts the radial distance into axial depth.
The radial difference — that is, (D_cs − D_hole) / 2 — is the horizontal distance from the edge of the through-hole to the outer rim of the countersink. Depth is just that radial distance projected along the cone’s slope. Steeper angles (larger included angle) mean shallower depth for the same diameter; sharper angles mean you have to plunge deeper to open the cone wide enough at the surface.
The chamfer face length — what the calculator labels as the slant side of the cut — comes from the same radial difference divided by the sine of the half-angle, giving you the actual edge length of the chamfer wall rather than its vertical projection. This matters when checking whether a countersunk fastener head will seat fully on the bevel.
The sharp apex reference is a separate calculation: it tells you how deep the cone would go if the through-hole weren’t there and the tool cut all the way to a point. That number, compared against the actual depth to the hole floor, gives you the hole truncation percentage — a useful sanity check that confirms your hole and countersink diameters are proportionally reasonable for the fastener you’re using.
Worked Example — 82° Bit, #10 Screw Setup
Drilling for a #10 flat-head screw. The screw head’s maximum diameter is 0.373 in, so the countersink target is set slightly larger at 0.390 in to ensure full seating. The through-hole for a #10 clearance is 0.200 in. Standard 82° countersink bit.
- Included angle: 82°
- Countersink diameter: 0.390 in
- Through-hole diameter: 0.200 in
Half angle = 41°. Radial difference = (0.390 − 0.200) / 2 = 0.095 in. Depth = 0.095 ÷ tan(41°) = 0.095 ÷ 0.8693 ≈ 0.1093 in.
The chamfer face length works out to about 0.145 in, and the hole truncation sits around 51% — meaning roughly half the theoretical sharp cone is consumed by the through-hole, which is completely normal for a properly proportioned clearance hole. The alternate units card immediately shows the metric equivalent: approximately 2.78 mm depth, which is handy when the CNC operator is running metric offsets.
That 0.109 in depth gets programmed as a Z-axis plunge on the drill cycle. No measuring the cone with calipers mid-cut, no guessing from a depth stop.
The Sharp Apex Number Is a Reference, Not a Target
The “Sharp Apex Reference” output trips up new users more than anything else in this calculator. It is not a recommended depth. It’s the theoretical depth at which a perfectly sharp-tipped bit would reach a point — a dimension that physically cannot exist on any real countersink because all tools have a finite tip and all setups have a through-hole beneath them.
Its value is diagnostic. If your hole truncation percentage is very low — say, under 20% — your through-hole is small relative to the countersink, and the fastener head may not have enough bearing surface. If it’s over 75–80%, the through-hole is consuming most of the cone and your countersink may not have much material left to seat against.
Flat-head screws in wood applications typically land in the 40–60% truncation range. Aerospace countersinks in thin sheet metal often run higher. The percentage alone doesn’t tell you whether the setup is right — but it gives you a fast cross-check against the fastener’s own specification.
Frequently Asked Questions
Why does the calculator reject a countersink diameter equal to the through-hole diameter?
If the two diameters are identical, the radial difference is zero — which means the required depth is also zero. There’s no cone to cut; the “countersink” would just be the hole itself. The tool flags this as invalid input because the geometric result is meaningless for any real machining operation. The countersink diameter must be strictly greater than the through-hole diameter.
My countersink bit is marked 90° but the results look different from what I expected. What’s happening?
Make sure you’re entering the included angle — the full tip angle of the tool, measured from one side of the cone to the other. Some tooling catalogs list the half-angle instead (the angle measured from the centerline to the wall). A bit marked as “45° per side” is a 90° included angle tool. Entering 45 instead of 90 will produce a much deeper calculated depth than you actually need.
When I switch between US and metric, the input values change automatically. Why?
The calculator resets to sensible defaults when you switch unit systems — 82° / 0.500 in / 0.250 in for US Customary, and 90° / 12 mm / 6 mm for metric. This prevents nonsensical results from carrying over inch values into millimeter fields (a 0.500 mm countersink diameter is not a useful default). If you have specific values to enter after switching, simply overwrite the defaults.
Does the included angle affect the chamfer face angle shown in the output?
Directly. The face angle from surface — what the calculator shows as the angle the chamfer wall makes with the material’s flat surface — is simply 90° minus the half-angle. An 82° included tool has a 41° half-angle, so the chamfer face sits at 49° from the surface. A 60° tool produces a 60° face angle. This distinction matters when checking whether a flat-head screw’s underside geometry matches the recess it’s seating in — a mismatched angle leads to edge loading rather than full conical contact.
Can I use this for spotface or chamfer operations that don’t have a through-hole?
Not directly. The calculator requires a through-hole diameter greater than zero because the formula is built on the truncated cone geometry — the difference between the countersink opening and the hole below it. A chamfer on a solid surface (no through-hole) is a different geometry where depth relates only to the outer diameter and the half-angle, with no lower boundary. Entering a very small through-hole diameter as a workaround will produce results, but they won’t be meaningful for a solid-surface chamfer.