Pipe bending has benefited much from the trialanderror work of professional fabricators and artists that bend pipes for a living. Forming uniform bends in pipes keeps flows within them efficient, eases wire pulling through conduits, and eliminates fittings, simplifying projects. While bending tools ease simple 90degree and offset bends, calculating dimensions of compound bends may be a bit frustrating until the geometric basics of simple bends are better understood.
Simple Bend as Part of a Compound Bend

Define the simple bend problem. In this example, a 2 1/2inch diameter thinwalled 30inch steel pipe will be bent into a 90degree angle so that it has two equal length tangential legs. Industry practice recommends a minimum bend radius of five times pipe diameter. In this case, the smallest recommended bend radius will be 12 1/2inches.

Calculate the circumference of a full circle with a radius of 12 1/2 inches. Since circumference of a circle = 2 X pi X radius, 2 X 3.1416 X 12.5 = 78.54 inches. It is important to remember that as a pipe is bent, the inside radius of this circle will be 12 1/2inches – 2 1/2inches/2 = 11 1/4 inches and the outside radius = 12 1/2inches + 1 1/4inches = 13 3/4 inches, since the inside is compressed and the outside is extended.

Calculate the length of pipe out of the 30 inches that will be part of the circular bend. Here the full circumference is 78.54 inches, so a segment representing 90 degrees will be 90 degrees/360 degrees = 0.25 X 78.54 = 19.635 inches.

Calculate the length of the two equal sides extending from the bend. This calculation will be 30 inches total pipe length – 19.365 inches = 19.635/2 = 9.8175 inches.
Compound Bend

Define the compound pipe bending application. In this case, a 144 inchlong 3 inchdiameter truck exhaust pipe needs to bend 40 degrees up, then 100 degrees back down and finally 40 degrees to straight again toward the rear of the vehicle. The front remaining straight section of the pipe needs to be half the length of the rear section. With this information, you can calculate the compound bends and straight sections in the pipe.

Calculate the radius of the bends and the full circle circumference The minimum radius is 5 X 3 inchdiameter = 15 inches. 15 inches X 2 X pi = 15 X 2 X 3.1416 = 94.25 inches circumference.

Calculate the amount of pipe needed to form each bend arc. Each of the 40 degree bends will require a proportion of the circumference defined by 40 degrees/360 degrees/full circumference = 0.1111 X 94.25 inches = 10.47 inches. The 100 degree bend will require 100 degrees/360 degrees = 0.2777 X 94.25 inches = 26.18 inches.

Calculate the total length of pipe to form the three bends without any straight section between them. This comes to 10.47 + 26.18 + 10.47 inches for a total of 47.12 inches of pipe occupied in all the bends.

Calculate the remaining straight sections. Since the front straight section needs to be half the length of the rear section, 144 inches minus 47.12 inches for the bends = 96.88inches straight pipe remaining. Then L + 2L = 96.88 inches and L = 32.29 inches, and 2L = 64.58 inches.
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