Countersink Depth Calculator | Diameter & Angle

What Is a Countersink Depth Calculator?

A countersink depth calculator works out how deep to drill a cone-shaped recess so that a flat-head screw sits flush with a surface. It takes two inputs, the diameter of the countersink and the angle of the drill bit, and returns the depth. Countersinking cuts a funnel-shaped dip that matches the tapered underside of a flat-head screw, so the screw head does not stick up above the surface or sink too far below it.

How Countersink Depth Is Calculated

A countersink is shaped like a cone with its point pushed into the material. The diameter is the width of the opening at the surface. The angle is the full angle at the top of that cone, measured between the two sloped sides. Common bit angles are 82°, 90°, and 100°.

Because the recess is a cone, its depth follows from right-triangle trigonometry. Cut the cone in half down the middle and each half is a right triangle: the radius (half the diameter) is one side, the depth is another side, and half the countersink angle sits between the depth side and the sloped side of the cone.

$\text{Depth} = \frac{\text{Diameter} / 2}{\tan(\text{Angle} / 2)}$

A wider diameter needs a deeper cone to reach the same opening width. A wider angle makes the cone flatter, so the depth becomes shallower for the same diameter.

Worked example

For a 10 mm diameter countersink cut with a 90° bit:

• Radius = 10 ÷ 2 = 5 mm
• Half angle = 90 ÷ 2 = 45°
• tan(45°) = 1
• Depth = 5 ÷ 1 = 5.00 mm

The same 10 mm diameter gives a different depth at other common angles:

• 82°: about 5.75 mm
• 90°: 5.00 mm
• 100°: about 4.20 mm

A wider angle always produces a shallower countersink for the same diameter.

How to Use This Calculator

1. Measure the diameter of the screw head with calipers or a ruler, then add about 0.5 mm for clearance. Enter that number as the countersink diameter.
2. Check the angle stamped on the countersink bit. If it is not marked, measure the screw head's angle with a protractor, or assume 82° for wood screws and 90° for machine screws.
3. Enter the diameter and angle. The result is the depth from the surface down to the point of the cone.
4. Use that number to set a depth stop, wrap tape around the bit at that mark, or set a drill press stop.

The diameter must be greater than zero, and the angle must be between 1° and 179°. A 180° angle would be a flat surface with no cone at all.

Common Countersink Angles

The bit angle needs to match the screw head's angle. A mismatched angle leaves a gap around the head, and the screw will not sit flush even when the depth is exactly right.

Countersinking vs. Counterboring

Countersinking cuts a cone for a tapered, flat screw head. Counterboring cuts a flat-bottomed cylinder for a screw with a straight-sided head, such as a socket head cap screw. The formula above applies only to countersinking. Counterbore depth is set instead by the height of the screw head plus a small clearance, not by this trigonometric relationship.

Practical Notes

Real drilling rarely matches the geometry exactly. A few things shift the actual result:

• Material springback. Softwood compresses slightly under the screw head and can spring back afterward, leaving the screw a little proud. Adding roughly 0.3–0.5 mm to the calculated depth compensates for this in wood.
• Bit wear. A dull bit cuts a slightly wider or rougher cone than a sharp one.
• Coated or layered materials. Painted or plated metal parts need extra depth so the screw still sits flush once the coating is added.
• Extreme angles. Below about 30°, the depth grows very large for the same diameter; a 10 mm countersink at 20° needs nearly 28.4 mm of depth. Above about 140°, the cone becomes so shallow it barely recesses the screw head at all.

Because of this, machinists and woodworkers usually test the depth setting on a scrap piece before drilling the final part.

Frequently Asked Questions

What is a countersink?

A countersink is a cone-shaped recess cut into a surface so a flat-head screw sits flush with, or below, that surface. Without it, the flat underside of the screw head rests on top of the material instead of sitting into it.

What is the countersink depth formula?

Depth equals half the diameter divided by the tangent of half the angle: depth = (diameter ÷ 2) ÷ tan(angle ÷ 2). Diameter and angle should use the units the calculator expects, millimeters and degrees.

What angle should I use?

Match the bit angle to the screw head's angle; they need to be the same for the screw to sit flush. 82° is standard for wood screws, 90° is common for machine screws and metric fasteners, and 100° appears in some aerospace applications.

What countersink diameter should I use for a given screw?

Measure the screw head's diameter and add about 0.5–1 mm of clearance. A countersink that is too tight makes the screw head bind before it seats; one that is too loose leaves a visible gap around the screw.

Does this calculator work with inches?

The calculator's inputs are in millimeters, but the underlying formula works with any consistent unit. Either convert inches to millimeters first (multiply by 25.4), calculate, and convert the answer back, or apply the same formula directly using inches for the diameter, which then returns the depth in inches. For example, a 0.375 in diameter countersink at 82° gives a depth of about 0.216 in.

Why does my screw still sit proud even though the depth matches the calculation?

The most common cause is an angle mismatch between the bit and the screw head. Other causes include material springback in softwood and normal variation in screw head dimensions between manufacturers. Test the setting on scrap material and adjust the depth slightly if the screw still sits proud.