Free machining geometry tools

Angles, taper Z length, radii and hole patterns — with formulas you can check.

Choose the geometry you know

Start with the dimensions on your drawing. If you know the major and minor taper diameters and the angle to the spindle axis, use the taper Z calculator to find axial length. If the drawing gives the full included angle, select that convention so the calculator uses half of it in the formula.

Triangles and missing dimensions

Use the right triangle calculator when two sides are known, or the angle and missing side calculator when an angle and a side are known. Keep all lengths in one unit and check which side is adjacent or opposite to the chosen angle.

Circles, arcs and fillets

Use the radius, chord and arc calculator for circle geometry, or the fillet tangent calculator to connect straight features with a radius. These tools solve ideal geometry; drawing datums and tool compensation remain separate setup decisions.

Hole layouts

Find coordinates with the full bolt circle, partial bolt circle or linear hole pattern calculator. Review the origin and starting angle before transferring coordinates to a program.

Worked example and free access

Read how to calculate taper Z from X diameters for inch and metric examples. The current tools and formulas are free to use, without a subscription. Explore the complete machinist toolbox for cutting calculations and dimensional checks.