Taper Calculator

A taper represents a gradual, uniform change in the diameter of an object along its length. The calculations rely on basic trigonometry and dimensional ratios. The first core metric is Taper Per Inch (TPI), which measures the difference in diameter divided by the total length of the taper: TPI = (DiaL - DiaS) / Length, where DiaL is the large diameter, DiaS is the small diameter, and Length is the axial distance. The second core metric is the Taper Angle, which represents the angle of the slope relative to the centerline. This is derived using the inverse tangent function: TaperAngle = atan(TPI / 2).

Imagine you are turning a custom steel shaft on a lathe. You need to machine a section where the large diameter (DiaL) is 3.5 inches, the small diameter (DiaS) is 2.0 inches, and the total axial length of the tapered section is 6.0 inches. First, find the Taper Per Inch by subtracting the small diameter from the large diameter and dividing by the length: (3.5 - 2.0) / 6.0 = 1.5 / 6.0 = 0.25 inches per inch. Next, calculate the Taper Angle by taking the inverse tangent of half of the TPI: atan(0.25 / 2) = atan(0.125), which yields approximately 7.125 degrees. This gives you the exact compound rest or CNC slide angle needed for the cut.

Always measure your diameters at the exact points where the taper begins and ends, ignoring any rounded transition fillets or edge breaks. When setting a lathe compound rest using the calculated angle, double-check your setup with a dial indicator or a sine bar to account for any mechanical play or backlash in the machine tool. Finally, verify whether your project calls for Taper Per Inch (TPI) or Taper Per Foot (TPF)—multiplying your TPI result by 12 will easily convert your measurement to TPF if your blueprint uses foot-based standards.