Conical taper is the change in the diameter of a circular solid along its length. It can be expressed in linear units such as inches per foot or as an angle. When the decrease in diameter and the length are viewed as two sides of a right triangle, trigonometry can be used to convert the linear unit expression to an angle. A trigonometric calculator will do the conversion automatically. Trigonometric calculators are available online for free.
Convert the units of the conical taper so that all units are the same. If the taper unit is inches per foot, divide by 12 to make it inches per inch. Three inches per one foot would equal 0.25 inches per inch.
Visualize a cross section of the cone with the length being the height and the diameter being the base. The point of the cone is at the top of the triangle. The conical angle is the angle formed at the top of the triangle when a line is drawn straight down the center forming two right triangles.
Calculate the tangent of this angle by dividing half of the base distance of the original triangle by the height. For a conical taper of 0.25 inches per inch, divide 0.125 by 1. This equals 0.125 inches.
Use a trigonometric calculator or trigonometric tables to find the angle with the tangent you calculated. The angle with a tangent of 0.125 inches is 7.12 degrees. This is the conical taper expressed as an angle.
Some online trigonometric calculators allow you to input the length of the sides and will calculate the angle using only length data.