EMT Electrical Conduit Pipe Bending - the Math Formulas and Multipliers Behind a Conduit Bending Guide

Very few beginning electricians are taught anything beyond common electrical conduit pipe bending instructions, and can have enormous difficulty when trying to bend larger conduit (greater than 1") as a result. Even more experienced journey level electricians seldom have any idea of the wide range of possibilities available to them when needed. Learning how to bend conduit to very nearly any angle desired is not difficult, however.

The math and formulas behind a simple conduit bending guide is actually quite simple and easily learned. The only tools necessary for more complex bends is a cheap scientific type hand calculator and an angle finder and any electrician bending large conduit should already have the angle finder.

The math of bending conduit consists of two main categories; that math that is built into a common hand bender and the geometry of a triangle. Each will be discussed separately. In addition, making concentric bends requires use of math that is not discussed in this article.

Much of the math used by the electrician in bending conduit is built into the hand benders used and is unchangeable. Only a few numbers and math operations need to be memorized to make offsets, saddles and 90 degree bends - by far the most common bends made and what is normally taught to beginning electricians. Even the multiplier and deduct figures are usually stamped onto the bender.

It is not the purpose of this article, however, to delve into the mechanics of common usage of a hand bender. If that is what is needed, instructions are given at the links in the preceeding paragraph or in the title page link given in the final paragraph in this article.

Most conduit bending outside of a 90º bend can be calculated using the geometry of a common triangle. In the drawing above, the heavy black line represents an offset bent into a conduit, while the green color is an imaginary trangle that it is bent around. Note that a 3 point saddle could be drawn by placing one more triangle back to back to the one drawn, while a 4 point saddle would also have a second triangle with some space between the two trangles. Understand that conduit is not a one dimensional line, but rather a three dimensional object with curved, not sharp, corners. These considerations will affect the measurements used, but only to very minor amounts; in everyday usage they can be ignored.

In the drawing the sides of the triangle are labeled a,b and c; these are the lengths of the sides. Angle "d" is also indicated; this is the angle the conduit is bent at. One of the remaining angles is always 90º while the other always depends on the first, being 90 minus angle d.

The math formulas we will be using are sine, cosine and tangent operations and are listed below, with algebraic equivalents in each case. Each set of formulas are thus the same formula, simply expressed differently.

1. Sine Calculations

Sine(d) = a/c [That is, the sine of angle d = side a divided by side c]

a = sine(d) * c [Side a = sine(d) times side c.]

c = a/sine(d) [Side c = a divided by sine(d)

2. Cosine Calculations

Cos(d) = b/c

b = cos(d) * c

c = b/cos(d)

3. Tangent calculations

Tan(d) = a/b

a = tan(d) * b

b = a/tan(d)

As each calculator may have a different order of key presses to obtain results, you will have to read and understand the instructions for your particular calculator to use the trigonometric functions in it. In particular, the method of finding the inverse functions will be needed; these functions convert a sine, cosine or tangent figure into the degrees of bend. Make sure that your calculator is set to read in degrees; they will often give angles in radians, which is useless for the electrician.

• Assume that we need a 2" offset in 3 1/2" conduit. Normally, this would be impossible even using a 10º bend as two bends cannot be made that close (12") together in that large a conduit. Using the Sine formulas let's try a 2º bend. We know side a to be 2" and the calculator shows that the sine(2º) = .0349. 2 / .0349 = 57". That's a little far apart for our bends, so lets try again using a 5º bend. The sine(5º) = .087, and 2 / .087 = 22.98 or about 23". That's a more reasonable length for an offset in 3 1/2" pipe, so it can be used where a 10º offset cannot.
• As an exercise, consider an offset of 12" using 22º bends. Again, c = a / sine(22º). Note that this can also be written as c = a * (1 / sine(22º). The sine(22º) = .3846, and 1 / .3846 = 2.6, which is the familiar multiplier for a 22º offset. This kind of math is where those multipliers come from!
• Assume we need a 4" offset, and that it must take place in exactly 15". What is the angle to be used? We know that a = 4 and b = 15. We also know that tan(d) = 4 / 15, or .2666. The calculator tells us that the inverse tangent of .2666 = 15º.
• Assume we need a 4" 3 point saddle, and that we will use 45º as the center bend with 22.5º angle bends on each end. What is the conduit shrinkage (the center of the bend will be closer to the end of the conduit than measured - by how much)? We know that a = 4" and angle d = 22.5º. What are b and c? Side c = 4 / sine(22.4º), or 10.45". Side b = 4 / tan(22.5º) or 9.65". The difference between b and c is our shrinkage; the center of our 3 point saddle will move just under 1". Most electricians forget about or ignore this shrinkage on 3 point saddles and the center of their bend is therefore not centered over the obstruction they are crossing.

Usage of these formulas will enable the electrician to bend very nearly any angle he or she wants to. As an electrician myself, I have often found myself attempting to bend large conduit into odd angles and dimensions to match building or appearance demands; to do so with 3 or 4" conduit by trial and error gets very expensive very quickly. Memorizing these simple formulas can make the bending of large conduit much easier. My own memory aid is that:

Sine(d) = opposite / hypotenuse

Cosine(d) = adjacent / hypotenuse

Tangent(d) = opposite / adjacent

where the hypotenuse is the longest side, opposite is the side opposite the angle and adjacent is the side touching the angle but is not the hypotenuse. Or simply tape the formulas to the back of your calculator; believe it or not I grew up before there were calculators and had to memorize.

A final note - this article is but one of several written by an electrician, for electricians.  A comprehensive guide to bending conduit has been written that gives a brief description of each page, along with a link to individual pages as well as a handful of other links to pages electricians might find useful.  Feel free to check out this title page for anything else that looks interesting.  If you don't find what you are looking for, leave a comment and it will be considered for future pages; the whole series is, and will continue to be, a work in progress.