Calculate countersink diameter, depth, screw diameter, or included angle from any 3 values in inch, cm, or mm units for holes and screws.
Countersink Diameter Formula
The main relationship used for a straight countersink is:
CD = d + 2*h*tan(theta/2)
- CD = countersink top diameter
- d = hole diameter or screw diameter at the bottom of the countersink
- h = countersink depth
- theta = included countersink angle, in degrees
The calculator can solve for any one missing value when you enter the other three values.
h = (CD - d)/(2*tan(theta/2))
- Use this form to find countersink depth when you know the top diameter, hole diameter, and included angle.
d = CD - 2*h*tan(theta/2)
- Use this form to find the hole or screw diameter when you know the countersink diameter, depth, and angle.
theta = 2*atan((CD - d)/(2*h))
- Use this form to find the included countersink angle. The calculator reports the angle in degrees.
Length inputs can be entered in inches, centimeters, or millimeters. The calculation converts lengths internally to inches, applies the formula, then converts the result back to the selected output unit.
Common Countersink Angles
Use the included angle that matches the screw head or the cutting tool. The included angle is the full cone angle, not the half-angle used inside the tangent function.
| Included angle | Common use | Half-angle used in formula |
|---|---|---|
| 82° | Common inch flat-head machine screws | 41° |
| 90° | Common metric flat-head screws and general countersinking | 45° |
| 100° | Some aerospace and thin-material fasteners | 50° |
Length Unit Conversions
| Unit | In inches | Typical entry use |
|---|---|---|
| 1 in | 1 in | Inch drawings and screw sizes |
| 1 cm | 0.3937007874 in | Metric measurements in centimeters |
| 1 mm | 0.03937007874 in | Metric drawings and machining dimensions |
Example Calculations
Example 1: Find countersink top diameter
You have a 0.250 in hole, a countersink depth of 0.080 in, and an 82° included angle.
CD = 0.250 + 2*0.080*tan(82/2)
CD = 0.250 + 0.160*tan(41)
CD = 0.3891 in
Example 2: Find countersink depth
You have a 6 mm hole, a 10 mm countersink top diameter, and a 90° included angle.
h = (10 - 6)/(2*tan(90/2))
h = 4/(2*tan(45))
h = 2 mm
FAQ
What is the difference between countersink diameter and hole diameter?
The hole diameter is the smaller diameter where the screw body or pilot hole passes through the material. The countersink diameter is the larger top diameter at the surface. For a valid countersink depth, the countersink diameter must be greater than the hole diameter.
Should I enter the full countersink angle or the half-angle?
Enter the full included angle. For example, enter 82 for an 82° countersink and 90 for a 90° countersink. The formula automatically uses half of that angle inside the tangent function.
Why does a 90° countersink make the math simpler?
For a 90° included angle, the half-angle is 45°, and tan(45°) equals 1. That makes the formula reduce to CD = d + 2h. If the countersink is 2 mm deep, the top diameter is 4 mm larger than the hole diameter.
