Countersink Depth Calculator
Enter the countersink surface diameter and included angle to get the exact plunge depth for your bit. Switch to Diameter mode to reverse-solve: enter a target depth and get the surface diameter. Works for both sharp-point and flat-end (truncated) countersink tools, in millimetres or inches.
What is a countersink and why does depth matter?
A countersink is a conical recess cut into the surface of a material so that a flat-head (countersunk) screw, bolt or rivet can sit flush with or below the surface. The geometry is simple: a cone-shaped bit removes material in a V-shape whose diameter grows as the bit plunges deeper. Getting the depth right is critical - too shallow and the screw head protrudes; too deep and the joint loses clamping strength and the fastener can wobble in the recess. In woodworking a slightly proud or slightly recessed head is often acceptable, but in metalworking, aerospace, and precision assembly work a tolerance of a few hundredths of a millimetre matters.
The countersink depth formula
The depth-from-diameter formula derives directly from right-triangle trigonometry. If the included angle of the bit is A and the surface diameter of the countersink (the opening at the workpiece surface) is D, then the depth is: depth = (D / 2) x cot(A / 2). The factor cot(A / 2) is constant for a given angle, so you can precompute it: for an 82-degree bit it is approximately 0.4503; for a 90-degree bit it is exactly 0.5. For a truncated (flat-end) bit with tip diameter T and tip clearance a the formula becomes: depth = ((D - T) / 2) x cot(A / 2) + a. To reverse-solve for the surface diameter from a known depth D = 2 x depth x tan(A / 2). This calculator handles all four variants automatically.
Standard countersink angles and their applications
The included angle stamped on a countersink bit determines which fastener standard it matches. 82 degrees is the ANSI/inch standard, used for flat-head machine screws and wood screws in the United States. 90 degrees is the ISO/metric standard, covering the vast majority of metric flat-head cap screws (DIN 7991, ISO 10642). 100 degrees appears in aerospace and aviation riveting (AS standards). 118 degrees matches the standard twist-drill point angle, so a standard drill bit can be used to spot-drill or lightly chamfer a hole. 120 degrees is a wide-angle countersink used for deburring and chamfering where flush seating is not the goal. 60 degrees is a deep narrow cone used for spot-drilling centre marks or where significant material clearance is needed under the head. Always confirm the angle stamped on your bit before machining.
Sharp-point vs truncated countersink bits
Standard countersink bits taper to a perfect point (sharp-point). The formula depth = (D / 2) x cot(A / 2) applies directly. Combination countersink-and-drill bits (also called countersink-and-pilot or truncated bits) have a small drill at the tip that bores the pilot hole while the outer cone cuts the seat. For these tools the tip has a non-zero diameter T and an additional axial clearance a must be added. The effective depth is computed on the annular ring ((D - T) / 2) and then the clearance is added. Failing to account for this offset would cause you to plunge the bit too shallow, leaving the screw head proud. Enter the tip diameter and clearance in the calculator when using truncated or combination bits.
Standard screw countersink dimensions
| Size | Standard angle | Surface diam (approx) | Depth (approx) |
|---|---|---|---|
| #4 (imperial) | 82 deg | 0.225 in | 0.101 in |
| #6 (imperial) | 82 deg | 0.279 in | 0.125 in |
| #8 (imperial) | 82 deg | 0.322 in | 0.145 in |
| #10 (imperial) | 82 deg | 0.373 in | 0.168 in |
| #12 (imperial) | 82 deg | 0.420 in | 0.189 in |
| 1/4 in (imperial) | 82 deg | 0.477 in | 0.214 in |
| 5/16 in (imperial) | 82 deg | 0.567 in | 0.255 in |
| 3/8 in (imperial) | 82 deg | 0.682 in | 0.307 in |
| M3 (metric) | 90 deg | 6.94 mm | 3.47 mm |
| M4 (metric) | 90 deg | 9.18 mm | 4.59 mm |
| M5 (metric) | 90 deg | 11.47 mm | 5.74 mm |
| M6 (metric) | 90 deg | 13.71 mm | 6.86 mm |
| M8 (metric) | 90 deg | 18.25 mm | 9.13 mm |
| M10 (metric) | 90 deg | 22.73 mm | 11.37 mm |
| M12 (metric) | 90 deg | 27.21 mm | 13.61 mm |
Inch sizes use 82 deg (ANSI); metric sizes use 90 deg (ISO). Surface diameter is the countersink opening at the workpiece. Depths are for sharp-point bits.
Frequently asked questions
What angle do I use for standard inch flat-head screws?
82 degrees. ANSI B18.3 specifies 82 degrees as the included head angle for inch-series flat-head machine screws and socket-head cap screws. Most countersink bits sold in the United States as general-purpose or flat-head bits are ground to 82 degrees. If you are using metric screws, switch to 90 degrees.
What angle do I use for metric flat-head screws?
90 degrees. ISO 10642 and DIN 7991 specify 90 degrees for metric flat-head socket screws. Most metric hardware sold globally (M2 through M20) follows this standard. At 90 degrees the depth equals exactly half the surface diameter, which makes mental arithmetic easy: a 10 mm surface opening requires a 5 mm plunge depth.
How do I find the countersink diameter I need for a specific screw?
Look up the head diameter in the screw manufacturer data sheet (often listed as dk or DK in ISO/DIN tables), then add a small clearance - typically 0.1-0.3 mm for metal, up to 0.5 mm for wood. Use that value as the surface diameter in this calculator. The reference table on this page lists common ISO and ANSI screw sizes with their recommended countersink diameters.
What is the depth-to-diameter ratio and why is it useful?
At a given angle, depth is always a fixed fraction of the surface diameter. That fraction - cot(angle/2) / 2 - is the depth-to-diameter ratio. For 90 degrees it is 0.5; for 82 degrees it is approximately 0.4503. Once you know the ratio for your bit, you can multiply any surface diameter by it without re-entering anything in the calculator. This is especially handy in production settings where you are cutting many holes of different diameters with the same bit.
What happens if I drill the countersink too deep?
The screw head will sit below the surface (a recessed or plug-covered finish, which is sometimes intentional in woodworking). More importantly, the bearing area under the head shrinks as the head drops into a deeper cone, reducing clamping force. In structural metal joints this can allow the fastener to loosen under vibration. In thin sheet metal, cutting the countersink too deep can break through to the back face of the part. Aim for flush seating or a controlled recess that keeps the full underside of the head in contact with the material.
Can I use this calculator for rivets?
Yes - most countersunk (flush) rivets follow 100-degree or 120-degree standards, depending on the aerospace specification. Select the appropriate angle, enter the rivet head diameter as the surface diameter, and read off the required depth. For 100-degree aerospace rivets (AN426 / MS20426 series) you would select 100 degrees; for MS20827 or some structural rivets, check the drawing for the specified angle.
How do I reverse-solve for the diameter when I know the depth?
Switch the "Solve for" dropdown to "Surface diameter". Enter your target depth and the included angle. The calculator applies D = 2 x depth x tan(angle / 2) and returns the surface diameter needed to achieve that depth. This is useful when you are programming a CNC machine and the depth is constrained by material thickness, and you need to know whether the resulting surface opening will still accept the screw head.