How to use this calculator
- Enter the included angle. Enter the countersink included angle — 82°, 90°, 100° or 120° to match the fastener.
- Enter the top diameter. Enter the desired top (rim) diameter at the surface.
- Enter the existing hole. Enter the pilot / through-hole diameter, or 0 when cutting into solid.
- Read the results. Read the countersink depth below the surface and the chamfer width along the cone face.
How it works
A conical countersink of included angle A grows in diameter as it goes
deeper. Starting from an existing hole of diameter D_hole at the surface,
it reaches the desired top (rim) diameter D_top at an axial depth of:
z = (D_top − D_hole) / (2·tan(A/2))
The cone diameter at any depth is D = D_hole + 2·z·tan(A/2). Cutting into
solid stock with no pilot hole simply sets D_hole = 0.
The chamfer width is the contact length along the slanted cone face,
w = (D_top − D_hole) / (2·sin(A/2)) — larger than the straight-down depth
because it follows the slope. This depth z is measured from the surface (or
from the pilot-hole rim); the machine Z-depth from the tool tip differs by the
countersink tool’s own geometry, so set Z off the rim diameter you measure.
Worked example
Verified against the live calculator
A 90° countersink widening a 5 mm pilot hole to a 10 mm rim reaches
z = (10 − 5) / (2 × tan 45°) = 5 / 2 = 2.5 mm below the surface, with a
chamfer width w = 5 / (2 × sin 45°) ≈ 3.54 mm along the cone face.
Cutting that same 10 mm rim into solid stock (no pilot hole) is deeper:
z = 10 / 2 = 5.0 mm. The calculator returns these on load.
Frequently asked questions
How do I calculate countersink depth?
Countersink depth is the axial distance below the surface where the cone reaches the desired rim diameter: z = (D_top − D_hole) / (2·tan(A/2)), where A is the included angle, D_top the top (rim) diameter and D_hole the existing hole. For a 90° countersink widening a 5 mm hole to a 10 mm rim, z = 5 / (2 × tan 45°) = 2.5 mm.
What is the countersink depth for cutting into solid?
When there is no pilot hole, set D_hole = 0 and the depth is z = D_top / (2·tan(A/2)). A 90° countersink cutting a 10 mm rim into solid material reaches z = 10 / (2 × 1) = 5.0 mm deep — the cone half-diameter equals the depth at 90°.
Is this the depth from the surface or from the tool tip?
This z is measured from the surface (or from the pilot-hole rim) down to where the cone hits the top diameter. The machine Z-depth from the tool tip differs by the countersink tool’s own geometry — its tip flat, point, or any pilot. Set your Z off the rim diameter you can measure, not off the tip.
Which included angle should I use?
Match the fastener. 82° is the standard for UNC/inch flat-head screws, 90° for metric/ISO flat heads, and 100° or 120° appear on aerospace and some deburring/chamfer work. A smaller included angle is a steeper, deeper cone for the same rim diameter.
What is the chamfer width on the cone face?
The chamfer width is the contact length measured along the slanted cone face, not straight down: w = (D_top − D_hole) / (2·sin(A/2)). It is always larger than the axial depth z (they are equal only as the angle approaches a flat 180°). For the default 90° case widening 5 mm to 10 mm, w ≈ 3.54 mm.
Does this work in metric and imperial?
Yes — enter the diameters in mm or inches and the depth and chamfer width are shown in the same unit; the included angle is in degrees either way. Toggle SI/Imperial in the header.
Method & assumptions
- The countersink is a true cone of the stated included angle, centred on the existing hole, and the surface is flat and perpendicular to the hole axis.
- Depth z is from the surface (or pilot-hole rim) to where the cone reaches the top diameter. The machine Z-depth from the tool tip differs by the tool’s own geometry (tip flat, point, or pilot) — measure off the rim diameter, not the tip.
- The top diameter must be at least the existing hole diameter; a countersink can only widen a hole, never shrink it.