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.
This Countersink Depth Calculator computes the axial plunge depth required to achieve a target countersink diameter in a workpiece — from three inputs: the included (full) angle of the countersink, the desired countersink diameter at the surface, and the through-hole diameter already drilled. It also resolves the chamfer face length, half angle, sharp apex reference depth, hole truncation percentage, and a full unit conversion to the opposing measurement system.
Countersink Depth Formula
The countersink is geometrically a truncated cone. The axial depth needed to reach a given surface diameter is found by applying right-triangle trigonometry to the half-angle of the cone and the radial distance from the through-hole edge to the countersink edge.
Depth = ( D_cs − D_h ) ÷ 2 ÷ tan( θ ÷ 2 )
The numerator (D_cs − D_h) / 2 is the radial difference — the horizontal distance the cone wall must travel from the edge of the through-hole to reach the target countersink diameter. Dividing by tan(θ/2) converts that radial distance into the equivalent axial depth using the half-angle of the cone.
Why the half-angle? The included angle θ is the full cone opening — measured across both sides of the axis. The trigonometry for depth uses a right triangle on one side of the axis only, so the included angle is halved before applying the tangent function.
Radial Difference = ( D_cs − D_h ) ÷ 2
The difference in radius between the countersink circle and the through-hole circle at the surface — the horizontal leg of the right triangle.
Side Edge = Radial Difference ÷ sin( θ ÷ 2 )
The actual slant length along the cone wall — the hypotenuse of the right triangle. This is the physical length of the chamfer face visible on a cross-section.
Face Angle = 90° − ( θ ÷ 2 )
The angle the chamfer face makes with the material surface (not with the axis). For an 82° countersink: face angle = 90° − 41° = 49°. Useful for checking chamfer angle with a protractor or gauge from the surface.
Truncation % = ( Apex-to-Hole Offset ÷ Sharp Apex Depth ) × 100
Expresses what percentage of the theoretical sharp-apex depth is removed by the through-hole. It is not a volume measure — it is the depth ratio between the through-hole cone intercept and the full theoretical sharp-apex depth. For the default 0.500 in / 0.250 in example: Truncation = 0.1438 ÷ 0.2876 × 100 = 50.0%, meaning the through-hole intercepts the cone exactly halfway down the theoretical sharp-apex depth.
How the Calculator Works
The calculator resolves every output from the three inputs in a fixed sequence. Each step feeds into the next.
Subtract the through-hole diameter from the countersink diameter. Divide by 2 to get the radial difference — the horizontal distance the cone wall spans from the bore edge to the countersink edge at the surface.
The included angle is divided by 2 before applying any trigonometric function. tan(θ/2) gives the ratio of the radial leg to the axial leg for the cone's right-triangle cross-section.
This is the primary calculation — the axial plunge depth the countersink tool must travel to reach the target diameter. The result is in the selected unit system (inches or millimetres).
Using the same right-triangle geometry, the calculator also resolves the slant length of the chamfer face (radial difference ÷ sin(θ/2)), the face angle from the material surface (90° − θ/2), the theoretical sharp-apex depth for both the full countersink and the through-hole, and the hole truncation percentage.
All primary dimensions are converted to the opposing unit system using the exact factor 1 inch = 25.4 mm. US Customary results appear in inches; converted values appear in millimetres — and vice versa for metric mode.
Worked Example
Using the calculator's default values — a common 82° unified countersink scenario — the following results are produced step by step.
Understanding the Results
The calculator returns one primary result and four supporting output cards. Each is explained below in the same order it appears in the calculator.
The axial plunge depth — how far the countersink tool must travel into the material from the surface to produce the specified countersink diameter. This is the value to set on a drill press depth stop, DRO Z-axis, or CNC Z-depth. It is measured from the material surface to the bottom of the countersink cone at the point where the cone wall intersects the through-hole edge.
( D_cs − D_h ) ÷ 2 ÷ tan( θ ÷ 2 )
This is the depth to the intersection of the cone wall with the through-hole — not to a hypothetical sharp apex. The through-hole is assumed to already be drilled; the countersink tool only needs to remove the material between the through-hole radius and the countersink radius.
These three values define the fundamental geometry of the cut — the size of the cone annulus being machined and the angle of the cone wall.
D_cs − D_h
( D_cs − D_h ) ÷ 2
θ ÷ 2
The radial difference is the horizontal leg of the right triangle used throughout the calculation. The half angle is the angle that same right triangle's hypotenuse makes with the axial direction — it is the angle the cone wall makes with the axis of the hole, not with the surface.
The chamfer face values describe the physical geometry of the machined cone wall — its actual slant length and the angle it presents to the material surface.
Radial Difference ÷ sin( θ ÷ 2 )
90° − ( θ ÷ 2 )
The side edge length is the hypotenuse of the same right triangle — the actual length of the chamfer surface measured along the cone wall. For a flat-head screw, this is the seating surface length. The face angle from surface tells you the angle between the chamfer face and the workpiece surface, which can be checked with a protractor or angle gauge from the flat surface rather than from the hole axis.
The sharp apex reference values describe what the cone geometry would look like if extended to a perfect point — and how much of that theoretical depth the through-hole removes.
( D_cs ÷ 2 ) ÷ tan( θ ÷ 2 )
( D_h ÷ 2 ) ÷ tan( θ ÷ 2 )
( Apex-to-Hole Offset ÷ Sharp Apex Depth ) × 100
The Sharp Apex Depth is a theoretical reference only — no real countersink tool comes to a true sharp point, and in practice the through-hole always removes that point. The Hole Truncation % expresses how far down the theoretical sharp-apex depth the through-hole intercepts the cone. In the default example (0.500 in CS / 0.250 in hole), the through-hole is exactly half the CS diameter, so it intercepts the cone exactly halfway down the theoretical apex depth — giving 50.0% truncation. This is a depth-ratio value, not a volume or material removal percentage.
Converts the calculated depth, countersink diameter, and through-hole diameter into the opposing unit system using the exact international conversion factor.
value (mm) = value (in) × 25.4
value (in) = value (mm) ÷ 25.4
The conversion uses the exact defined factor 1 inch = 25.4 mm (NIST SP 811). Useful when working from a metric drawing but machining on an inch-graduated machine, or vice versa.
Practical Machining Notes
The through-hole diameter must already be drilled before countersinking. The through-hole clears the material at the bore centre and defines the starting boundary of the countersink cut. Attempting to countersink into solid material will produce a depth result that does not account for the bore geometry.
82° is commonly associated with Unified flat-head screws in the US (per ASME B18.6.3 and related standards). 90° is often cited in metric and ISO contexts (per ISO 10642 and related standards). However, actual screw head angles vary by standard, manufacturer, and fastener series. Always confirm the included angle from the engineering drawing, screw specification, or tooling catalog — do not assume a standard angle without verifying your specific application.
The calculated depth is a mathematical result for a theoretically perfect cone, a perfectly centred through-hole, and a tool with no runout or tip wear. In practice, results are affected by tool tip condition, tool runout, chatter, workpiece material hardness, cutting speed, feed rate, coolant, and how the depth is measured. Apply appropriate process controls and verify with inspection before committing to final dimensions.
This calculator estimates countersink depth for setup, reference, and checking purposes. It does not verify compliance with engineering drawing tolerances, screw head seating requirements, coating thickness allowances, or any other specification on the drawing. Final part acceptance depends on the drawing requirements, applicable standards, and your organisation's inspection process.
⚠ Accuracy and Limitations
The Countersink Depth Calculator assumes a geometrically ideal straight conical countersink and a centred through-hole. The following factors are not accounted for:
- Straight cone assumption: The calculator assumes a perfectly straight conical surface at a constant included angle. It does not apply to parabolic, double-angle, or other non-straight countersink profiles.
- Centred through-hole: The through-hole is assumed to share the same axis as the countersink. Eccentricity between the bore and the countersink tool path is not modelled.
- Tool tip condition: Real countersink tools have a finite tip radius or flat rather than a perfect sharp point. This affects the practical bottom of the cut and can shift the effective depth by a small amount depending on tool geometry and tip wear.
- Tool runout: Radial runout of the countersink tool or spindle will produce a larger effective countersink diameter than the tool geometry alone, effectively requiring less axial depth to reach the target diameter.
- Burrs and material springback: Material raised at the countersink edge by the cutting action, and elastic springback after the tool lifts, are not modelled.
- Coating or plating thickness: If a surface coating, paint, or plating is applied after machining, the effective countersink depth at finished dimensions may differ from the as-machined depth.
- Tolerance stack-up: Drawing tolerances on the countersink diameter, through-hole diameter, and included angle all contribute to a range of acceptable depths. This calculator solves for a single nominal result — not a tolerance range.
- Non-standard screw head geometry: Screw head underside angles and seating contact geometry vary by manufacturer and standard. The depth from this calculator positions the cone surface at the specified diameter; whether a specific screw head seats flush at that depth depends on the screw geometry itself.
References
The trigonometric methods, variable definitions, and countersink angle conventions used in this calculator are consistent with the sources below. Verify which standard and edition applies to your drawing before machining.