ONLINE TURNING CALCULATOR / TAPER
Lathe taper calculator
Calculate diameter difference, taper ratio, and angles from the large-end diameter, small-end diameter, and axial taper length. Use the same unit for all three dimensions.
Formula and limits
Diameter difference ΔD = large diameter − small diameter; taper ratio = ΔD ÷ axial length; half angle = arctan(ΔD ÷ (2 × axial length)); included angle = 2 × half angle. For a 1:N ratio, N = axial length ÷ diameter difference.
The large diameter must exceed the small diameter and length must be positive. This assumes an ideal straight cone and excludes tool-nose radius, setup error, measurement uncertainty, and machine coordinate conventions. It is a geometry reference, not a toolpath or machine-ready value. Verify against the part drawing, tolerances, and machine procedures.