Triangle Calculator

Why Machinists Need Triangle Math

Triangle calculations show up constantly in the machine shop — setting angles on a sine bar, calculating bolt hole positions, figuring taper dimensions, programming chamfers, and solving for unknown dimensions on blueprints. SOH-CAH-TOA isn't just a school memory trick; it's how you figure out the gage block stack for a 7° 14' angle or the Z-depth for a chamfer mill at 45°.

• Right triangle shortcuts: Most shop problems are right triangles. If you know any two values (one side + one angle, or two sides), you can solve for everything else. This calculator handles that automatically.
• Oblique triangles: When there's no 90° angle, the Law of Sines and Law of Cosines take over. Common when working from prints with angular dimensions that don't reference a right angle.
• The 3-4-5 rule: A triangle with sides in a 3:4:5 ratio is always a right triangle. Machinists use this to square up fixtures and vises — measure 3" on one jaw, 4" on the other, and the diagonal should be exactly 5".

Common Shop Applications

• Sine bar setups: Stack height = sine of the angle × distance between rolls. This calculator solves the triangle that makes sine bars work.
• Taper calculations: Every taper is two right triangles back to back. The half angle, length, and diameter difference form the triangle you need to solve.
• Coordinate hole locations: When a print gives an angle and a radius to a hole, you need sine and cosine to get the X/Y coordinates for the CNC program.
• Chamfer depths: A 45° chamfer at 0.030" width means 0.030" depth. But a 30° chamfer at 0.030" width? You need the triangle to find the depth.
• Blueprint interpretation: When a print dimensions an angle and one side of a feature, you're solving a triangle to get the missing dimensions for programming or setup.

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