How this instrument works
A countersink is a cone-shaped recess cut into a material so a flat, tapered screw head can sit flush with — or slightly below — the surrounding surface instead of sticking proud. Cutting it to the right depth matters: too shallow and the screw head stands above the surface; too deep and the screw head sinks below it, leaving a visible gap around the fastener or weakening the material right where the screw needs to bite.
The depth depends on two things: the screw head's diameter and the countersink cutter's included angle — the full cone angle stamped on the cutter itself, commonly 82° for US flat-head machine screws or 90° for many metric and general-purpose cutters. Because the cutter cuts a cone, half of that included angle is the angle from the cone's centerline out to its sloped wall, and basic right-triangle trigonometry — depth equals half the head diameter times the tangent of half the included angle — gives the exact depth needed for the head's full diameter to sit flush at the surface.
This is a real, standardized figure rather than a rule of thumb: ASME B18.6.3 fixes 82° as the included angle for US flat countersunk-head machine screws, and Machinery's Handbook publishes matching countersink-depth tables that machinists and cabinet-hardware installers check work against. Getting the angle right matters as much as getting the depth right — a countersink cut with the wrong included angle leaves the screw head sitting on a narrow ring of contact at the rim rather than seated flush against the full cone, even if the depth number happens to be correct.
- Enter the fastener's head size into Screw head diameter (in) — the widest point of the screw's flat, tapered head.
- Enter the cutter's cone angle into Included angle (deg) — 82° is standard for US flat-head machine screws, 90° is common for metric and general-purpose cutters.
- Read Countersink depth for how far to sink the cutter, measured straight down from the surface, so the head finishes flush.
- Confirm your countersink cutter's stamped angle before cutting — mixing an 82° screw head with a 90° cutter (or the reverse) will not seat flush even at the correct depth.
Worked example — a 0.5-inch head at 82°
Enter 0.5 into Screw head diameter (in) and leave Included angle (deg) at its default of 82°, the ASME B18.6.3 standard angle for US flat-head machine screws. Countersink depth reads 0.21732 in.
By hand: half the head diameter is 0.25 in, half the included angle is 41°, and tan(41°) ≈ 0.8693, so 0.25 × 0.8693 ≈ 0.2173 in — matching the depth this same standard's own reference tables publish for a countersink sized to a 0.5-inch flat head.
Questions
Why does the formula use half the head diameter and half the angle?
Because the countersink cuts a symmetric cone, and the depth calculation reduces to a single right triangle: the radius of the head (half the diameter) as one leg, the depth as the other leg, and half the cutter's included angle as the angle between the depth leg and the sloped cone wall. Using the full diameter or full angle instead would double-count the cone's symmetry and give a depth roughly twice too deep.
What included angle should I use — 82° or 90°?
82° is the ASME B18.6.3 standard for US flat countersunk-head machine screws, while 90° is common on many metric flat-head screws and general-purpose countersink bits sold for woodworking and cabinet hardware. Check the angle stamped on your specific screw's head profile or your cutter's packaging rather than assuming — mixing angles leaves the screw seated only at the rim, not flush across the full cone.
What happens if I cut the countersink too shallow?
The screw head will stand proud of the surrounding surface instead of sitting flush, because the cone hasn't been cut deep enough to swallow the full head diameter. This is usually the safer mistake to make, since a shallow countersink can be deepened with another light pass, while cutting too deep removes material that can't be put back.
What happens if I cut the countersink too deep?
The screw head sinks below the surrounding surface, leaving a visible recessed gap around the fastener and, in thin material, risking a cutter that breaks through to the back side. Because material removed can't be replaced, most machinists sneak up on the target depth in light passes and test-fit the actual screw rather than cutting the full calculated depth in one pass.
Does this depth account for the screw's total length under the head?
No — this figure is only the depth of the countersunk cone itself, measured from the surface to where the cone's diameter matches the screw head's full diameter. It says nothing about how deep the screw's threaded shank needs to go beyond that point, which depends on the screw's total length and the thickness of material being fastened.
Is a 90° included angle just an easier number to cut, or does it change the depth a lot?
It changes the depth meaningfully for the same head size — a 0.5-inch head countersunk at 82° needs about 0.2173 in of depth, while the identical head at 90° needs exactly 0.25 in, since tan(45°)=1 by the elementary 45-45-90 right-triangle identity. That's roughly a 15 percent difference in depth for the same screw, which is large enough to matter in thin stock.