Countersink Depth Calculator

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Depth

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Table of Contents

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What is Countersink Depth?

A countersink is a conical recess at the mouth of a hole, commonly made so a flat-head screw can sit flush with the surrounding surface. This calculator finds the height of an ideal cone from its largest diameter and included angle. It is useful for checking drawing geometry, comparing tool angles, and making a quick setup estimate. The answer is given in centimetres after the entered diameter is converted from centimetres, inches, metres, or feet.

The calculated value runs all the way from the large circular face to an imaginary sharp apex. A real countersink normally ends at an existing pilot hole, so its actual cutting depth is shallower. Tool tip shape, runout, material, tolerances, and the measured diameter also matter in finished work.

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How to Use This Calculator

  1. Enter the largest diameter of the countersink and select the diameter unit.
  2. Enter the full included angle of the cone. The current form accepts degrees; typical fastener and aerospace drawings may use angles such as 82°, 90°, or 100°, so copy the drawing rather than assuming one.
  3. Select Calculate. The diameter is converted to centimetres, the angle is halved, and the calculator applies right-triangle trigonometry.
  4. Read the ideal full-cone depth in centimetres. If the countersink opens into a pilot hole, calculate the practical depth separately from the difference between the two diameters.

Use positive measurements and an angle between 0° and 180°. An angle close to either limit produces an impractical cone and can make the tangent calculation unstable.

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Formula Used

Ideal full-cone depth: h = D ÷ [2 × tan(A ÷ 2)]

For a countersink that ends at a pilot hole of diameter d, the axial depth between the two circular edges is hcut = (D − d) ÷ [2 × tan(A ÷ 2)]. The page calculates the first expression because it asks only for D and A.

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Variables Explained

Symbol or entryMeaningHow to use it
DMajor countersink diameterEnter the widest finished diameter, not the pilot-hole diameter. The page converts the selected unit to centimetres.
AIncluded angleEnter the full angle from one conical side to the other, in degrees.
hIdeal full-cone depthDistance from the major-diameter plane to the imaginary cone apex, reported in centimetres.
dPilot-hole diameterUsed only in the practical-depth formula above; it is not an input on this page.
tanTangent functionThe formula uses half of the included angle because a centreline section splits the cone into two right triangles.
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Worked Example

Suppose the largest diameter is 10 mm and the included angle is 90°. Enter 1 cm, because 10 mm equals 1 cm, and enter 90 for the angle. Half the angle is 45°, and tan(45°) = 1. Therefore h = 1 ÷ (2 × 1) = 0.50 cm, or 5.0 mm. That is the result displayed for the ideal cone.

If the same countersink meets a 4 mm pilot hole, the material-cutting depth is based on the diameter difference: (10 − 4) ÷ [2 × tan(45°)] = 3 mm. The two answers describe different reference points, which is why a shop-floor depth can be smaller than this page’s result.

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Why Use This Calculator?

Treat the answer as nominal geometry. A deeper value means the imaginary apex lies farther below the major-diameter plane. At a fixed diameter, a smaller included angle makes a longer, deeper cone; a larger angle makes a shallower cone. If you double the diameter without changing the angle, the ideal depth also doubles.

For inspection or machining, compare like references. A drawing may control major diameter, included angle, actual axial depth, or the position of a screw head. Burrs and edge breaks can alter where a gauge contacts. Preserve more digits during planning than the tolerance requires, then round the final working value to a precision supported by the drawing and measuring equipment.

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Common Mistakes

    • Entering the half-angle instead of the full included angle. A 90° countersink requires 90, because the formula performs the division by two.
    • Reading the full-cone result as the depth from the surface to an existing pilot hole. Use both diameters for that depth.
    • Mixing millimetres with the centimetre output. The page does not currently offer millimetres, so convert before entering or after reading.
    • Assuming every flat-head screw uses the same angle. Match the fastener specification and drawing.
    • Using a nominal tool diameter as though it were the measured finished diameter. Feed depth, runout, wear, and material can change the cut.
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Frequently Asked Questions

Is countersink angle the full angle or the angle from the centreline?

Use the full included angle shown between the two sides of the conical section. The equation halves it internally. Entering 45° for a 90° countersink would produce the geometry of a much narrower cone.

Why is the result shown in centimetres?

The current calculator converts every diameter selection to centimetres before calculating and labels the result in centimetres. Multiply centimetres by 10 for millimetres or divide by 2.54 for inches.

Can this calculate how far to feed a countersink tool?

It gives ideal geometry, but feed depth also depends on the starting hole, tool point and chosen reference. For a straight pilot hole, the diameter-difference formula gives a better nominal axial depth. Confirm the setup with the drawing and a suitable gauge.

Why does a 90-degree countersink have a depth equal to half its diameter?

Half of 90° is 45°, whose tangent is 1. The denominator becomes 2, so the full-cone depth is D ÷ 2. That relationship applies to the imaginary sharp cone, before subtracting a pilot-hole radius.

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Sources & References

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