Calculate countersink depth, surface diameter, or flat-head screw size from hole size, cut depth, and included angle for metric or imperial screws.
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Countersink Depth Formula
- h = countersink depth measured from the surface to the bottom of the cone
- D = surface countersink diameter (the wide opening at the top)
- d = existing hole or pilot diameter (use 0 for a full cone into solid stock)
- A = included angle of the countersink tool, in degrees
Rearranged forms used by the other modes:
For flat-head screws, D is the screw head diameter and d is the clearance hole, so the depth becomes:
The formula assumes a sharp, symmetrical conical tool and a flat workpiece surface. Real cutters have a small flat or radius at the tip, so measured depth on a finished part will be a few thousandths shallower than the theoretical value.
Common Angles and Screw Head Sizes
Match the included angle in the calculator to the screw or fastener standard you are using.
| Angle | Typical use |
|---|---|
| 60° | Lathe centers, deburring |
| 82° | Imperial flat-head machine and wood screws |
| 90° | Metric flat-head screws, general chamfering |
| 100° | Aerospace flat-head screws (NAS, MS) |
| 120° | Sheet metal rivets, thin-stock countersinks |
| Screw | Head Ø | Normal clearance | Depth at standard angle |
|---|---|---|---|
| #6 (82°) | 0.279 in | 0.150 in | 0.075 in |
| #8 (82°) | 0.332 in | 0.177 in | 0.089 in |
| #10 (82°) | 0.385 in | 0.201 in | 0.105 in |
| M3 (90°) | 6.0 mm | 3.4 mm | 1.3 mm |
| M5 (90°) | 10.0 mm | 5.5 mm | 2.3 mm |
| M6 (90°) | 12.0 mm | 6.6 mm | 2.7 mm |
Worked Example and Notes
Example. You need an 82° countersink for a #8 flat-head screw with a normal clearance hole of 0.177 in. Head diameter is 0.332 in.
h = (0.332 − 0.177) / [2 × tan(41°)] = 0.155 / 1.7391 ≈ 0.089 in.
That depth puts the head flush with the surface. Add a few thousandths if you want the head slightly below the surface for filling or finishing.
Should the head sit flush, proud, or sub-flush? Flush is the default for cabinetry and machinery. Sub-flush by 0.005 to 0.015 in is common when the surface will be filled, painted, or sanded. Proud heads are a sign the countersink is too shallow.
What if the hole is not drilled yet? Enter 0 for the existing hole diameter to get the depth of a full cone. Subtract that from the screw-head depth to see how much of the cut is in solid material.
Why does my measured depth differ slightly? Most countersink cutters have a small chamfered or radiused tip rather than a true sharp point. Expect a difference of 0.002 to 0.010 in between the calculated theoretical depth and a depth gauge reading on the finished hole.
