# Measuring Countersink Angle Using Gage Balls

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Figure 1: Example of a Countersink Specification. (Source)

This post will cover how to measure a countersink angle using gage balls. Figure 1 shows how a countersink is normally specified on an engineering drawing. I frequently use countersinks in my wood and metal working hobbies. In addition, using gage balls to measure the countersink angle provides a good example of how to apply basic geometry concepts to a practical problem.  I use this example in my role as a volunteer adult math tutor at our local library.

Two gage balls of different diameters are used to measure the countersink angle (θ). Figure 2 shows the key variables involved: the diameter of ball 1 (B1), the diameter of ball 2 (B2), and the height difference when placed into the countersink (M). Figure 2 also presents the formula for the countersink angle θ.  The derivation requires only to apply the definition of the sine of a right triangle.

Figure 2: Illustration Defining the Variables Used in This Derivation.

Figure 3 shows a scale drawing of a countersink angle measurement example.

Figure 3: Countersink Angle Determination Example.

Figure 4 shows how I performed the calculations in Mathcad.

Figure 4: Example Calculations.

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### 2 Responses to Measuring Countersink Angle Using Gage Balls

1. Max says:

Thank you for this article. You should make a youtube video of this. I hate eyeballing for such simple things and need to re-drill another hole, specially for metal parts.

• mathscinotes says:

You are correct – I should do I Youtube video. I just downloaded a video editor and I am going to do video versions of some of these posts.

Thanks for prodding me!

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