How this calculator works
The diameter difference is twice the radial change. Dividing radial change by axial length gives the tangent of the half angle. The 1 in N ratio uses diameter change rather than radius change. Cylinders are excluded because their taper ratio would be infinite.
Formula
T = (D-d)/L; half angle = atan[(D-d)/(2L)]; included angle = 2 x half angle; N = L/(D-d).
Worked example
A 20 mm to 10 mm taper over 100 mm has T = 0.1, a 1 in 10 taper, half angle 2.862405 degrees and included angle 5.72481 degrees.
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Frequently asked questions
Is taper per length based on radius?
This page uses diameter change per axial length. The radial slope is half that value.
Which angle sets a lathe compound slide?
The half angle to the spindle axis is the geometric setting, subject to the machine scale convention.
Can the minor diameter be zero?
Yes. That describes a cone ending in an ideal point.