CNC / machinist calculator
Countersink Depth Calculator
Cut a countersink to the right diameter the first time. Enter the finished top diameter you want and the countersink's included angle, and this calculator gives the Z stop-depth to plunge to. It covers the common 82, 90 and 100 degree angles for flat-head screws and any custom angle, so you can dial the depth on a mill or drill press instead of sneaking up on it.
How it works
A countersink is a cone, so the depth and the top diameter are linked by the cone's half angle. The radius at the surface equals the plunge depth times the tangent of half the included angle, which rearranges to a stop-depth equal to the top diameter divided by twice the tangent of half the included angle.
The included angle is set by the fastener: inch flat-head screws are usually eighty-two degrees, metric and many others are ninety degrees, and flush rivets are often one hundred degrees. A wider included angle produces the same top diameter at a shallower depth, because the cone opens out faster.
In practice you size the top diameter a little larger than the screw head so the head sits flush or just below the surface. Measure or look up the head diameter, add a small clearance, and use that as the top diameter here. The result is the depth from the part surface, assuming the countersink reaches full diameter before any pilot drill geometry interferes.
Worked example
A 90 degree countersink to a half-inch top diameter plunges 0.5 / (2 x tan 45) = 0.25000000000000006 in below the surface.
Frequently asked questions
How do I calculate countersink depth?
Divide the finished top diameter by twice the tangent of half the included angle. For a 90 degree countersink to a half-inch top diameter the depth is 0.5 divided by 2 times tan 45, which is 0.25 inch.
What countersink angle do I use for a flat-head screw?
Inch flat-head machine screws are typically 82 degrees included, while metric flat-head screws and many others are 90 degrees. Flush rivets are often 100 degrees. Match the countersink angle to the fastener head angle.
Why does a wider angle give a shallower countersink?
A wider included angle means the cone opens out faster, so it reaches a given top diameter with less plunge. That is why a 100 degree countersink is shallower than an 82 degree one for the same finished diameter.
What top diameter should I aim for?
Use the fastener head diameter plus a small clearance so the head finishes flush or slightly below the surface. Look up the head diameter for the screw and add a few thousandths, then enter that as the top diameter.
Does the pilot hole affect the depth?
The formula assumes the cone reaches full diameter on solid material. A large pilot hole removes the tip of the cone, so the actual plunge to a given top diameter is slightly less; check the result against the part if the pilot is close to the countersink size.
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Sources
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