Taper is a gradual decrease in height or width. It is usually expressed in inches over 1 foot. An engineer might demand a taper of 2.5 inches per foot, meaning a drop of 2.5 inches for every foot of length, or she might use degrees. For example, she might specify a 12-degree slope. Because both systems are in wide use, it might be necessary to convert from one to the other. The process requires basic math skills.
Convert to a Ratio
Convert the taper into a ratio. For example, a taper might be described as 2 inches for every foot, but you need to use equivalent units: 2 inches for every 12 inches. If the taper includes a fraction, such as 2 3/4 inches per foot, convert the fraction to a decimal value. For example, 2 3/4 is 2.75, so the ratio becomes 2.75 to 12.
Divide by the Second Number
Divide the first number in the ratio by the second number. The result is the tangent of the taper expressed in degrees. For example, the ratio 2.75 to 12 becomes 0.22917, or 2.75 / 12 = 0.22917.
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Determine the Arctangent
Determine the arctangent of the result from Step 2. This is shown on scientific calculators as "tan-1." The result is the angle of the taper expressed in degrees. For example, the arctangent of 0.22917 is 12.91, so a taper of 2.5 inches in 1 foot is equivalent to 12.91 degrees.
TL;DR (Too Long; Didn't Read)
The tangent of an angle is the ratio of the opposite side of the triangle over the adjacent side. This is the same ratio as a taper.
If your calculator does not have the arctangent function, use an online angle calculator.