Holemaking and tapping
Countersink calculator
Countersink depth from diameter, or diameter from depth, for 82°, 90°, 100° and 120°.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Countersink depth
in
h = C / (2 x tan(A/2)) = 0.5 / (2 x tan(82°/2)) = 0.2876 in
0.2876 in (7.30 mm). Depth from the face to the point of a sharp countersink.
Source: Machinery's Handbook (trigonometry; countersunk head screw dimensions); head angles per ASME B18.6.3, ASME B18.3 and ISO 10642
| Included angle | tan(A/2) | Depth factor, 1 / (2 x tan(A/2)) | Diameter factor, 2 x tan(A/2) | Depth for a 0.500 in diameter (in) |
|---|---|---|---|---|
| 82° | 0.8693 | 0.5752 | 1.7386 | 0.2876 |
| 90° | 1.0000 | 0.5000 | 2.0000 | 0.2500 |
| 100° | 1.1918 | 0.4195 | 2.3835 | 0.2098 |
| 120° | 1.7321 | 0.2887 | 3.4641 | 0.1443 |
Depth = (C - d) x depth factor. Diameter = d + depth x diameter factor. Factors are unitless.
How it works
h = (C - d) / (2 x tan(A/2))
| Symbol | Meaning | Unit |
|---|---|---|
| h | Depth from the face to where the cone meets the hole (to the point when d = 0) | in or mm |
| C | Countersink diameter at the face | in or mm |
| d | Pilot hole diameter; 0 with no hole | in or mm |
| A | Included angle of the countersink | degrees |
Turned around for the diameter: C = d + 2 x h x tan(A/2). The formula treats the countersink as a sharp cone. Most tools have a small flat or a pilot at the tip, so touch off on the cone or measure the diameter rather than trusting a depth taken from the tip.
Worked example: depth from diameter
An 82° countersink to a 0.500 in diameter, first with no hole, then over a 0.257 in pilot hole.
- Half the angle: 82° / 2 = 41°. tan(41°) = 0.8693, so 2 x tan(41°) = 1.7386.
- No hole: 0.500 / 1.7386 = 0.2876 in to the point.
- With the hole: 0.500 - 0.257 = 0.243 in, and 0.243 / 1.7386 = 0.1398 in from the face to the hole edge.
Result: 0.2876 in (7.30 mm) to the point; 0.1398 in (3.55 mm) of cone over the hole.
Worked example: diameter from depth
A 90° countersink cut 0.100 in deep over a 0.250 in hole.
- Half the angle: 45°. tan(45°) = 1.0000.
- C = 0.250 + 2 x 0.100 x 1.0000 = 0.450 in.
Result: 0.450 in (11.43 mm) countersink diameter.
Shop notes
- Angles in use: 82° for inch flat head screws (ASME B18.6.3, ASME B18.3), 90° for metric countersunk head screws (ISO 10642 and others), 100° for aircraft flush rivets and screws. Match the fastener drawing.
- Countersinks chatter. Slow the spindle and feed steadily; on a light drill press or benchtop mill, a stiff setup and a sharp tool matter more than the speed setting.
- On a rigid CNC machine, program the tip depth from the no-hole result and adjust after measuring the first part.
- Measure the diameter, not the depth: a gauge pin, a countersink gauge, or the screw itself tells you more than the quill scale.
FAQ
What angle countersink do flat head screws need?
Inch flat head screws use 82°: machine screws per ASME B18.6.3 and socket flat head cap screws per ASME B18.3. Metric countersunk head screws, such as ISO 10642 socket heads, use 90°.
How deep do you countersink for a 0.500 in diameter at 82°?
To the point of a sharp countersink, 0.2876 in: 0.500 / (2 x tan(41°)). Over a 0.257 in hole, the cone runs 0.1398 in deep from the face to the hole edge.
How do you find the countersink diameter from the depth?
C = d + 2 x h x tan(A/2). A 90° countersink cut 0.100 in deep over a 0.250 in hole gives a 0.450 in diameter.
What countersink diameter fits a flat head screw?
Take the head diameter from ASME B18.6.3 (or ASME B18.3 for socket flat heads) and size the countersink so the head sits flush or a little below. Check it with the screw.
Last updated