Countersink / Internal Taper Over Ball
Use a precision ball to turn an awkward diameter measurement into an easy height or depth measurement. The ball must contact the conical surface—not the sharp edge of the opening or the bottom of the hole.
What is being measured? The ball touches both sides of the cone at a mathematically fixed location. Once the ball diameter and included angle are known, its top position tells us where the cone lies relative to the reference face.
Calculated Countersink
Two-Ball Internal Taper
Measure two different precision balls in the same internal taper, one at a time, from the same reference face. The difference in where the balls sit reveals the taper angle—no known angle is required.
Why two balls? A larger ball sits farther out of the same cone than a smaller ball. That change in axial position depends only on the ball-size difference and cone angle. Using the same reference face cancels the unknown cone depth.
Measured Taper
How the ball geometry works
Known-angle method: in an axial cross-section, the ball is a circle tangent to the two straight sides of the cone. The perpendicular distance from the ball center to either cone side is exactly the ball radius. That tangent relationship determines the ball-center position from the theoretical cone apex.
Two-ball method: each ball sits at a different axial position in the same cone. Subtracting the two readings removes the unknown location of the cone relative to the reference face, leaving enough information to solve the half-angle.
Important limitation: these equations assume ideal cone-to-ball tangency. Do not use the result if a ball bottoms out, bridges the opening, contacts a chamfer/radius instead of the true cone, or if the reference face/readings are not repeatable. For inspection decisions, use calibrated balls and appropriate measurement uncertainty.
About external tapers: an external “over balls/rollers” measurement requires a defined axial locating method or fixture; the measurement is not unique from ball diameter and cone angle alone. This tool intentionally covers the unambiguous internal-taper methods rather than pretending those setups are interchangeable.