Formulas and Multipliers For Bending Conduit or Electrical Pipe
Helpful Formulas for Bending Electrical Conduit
Very few beginning electricians are taught anything beyond the most basic instructions for bending electrical conduit pipe (EMT, electrical metallic tubing). As a result, they can have enormous difficulty when trying to bend larger conduit (greater than 1”). Even more experienced journeylevel electricians seldom have any idea of the wide range of possibilities available. Nevertheless, learning how to bend conduit to very nearly any angle you want is not difficult.
The math and formulas that make up a simple conduitbending guide are actually quite simple and easily learned. The only tools you need for more complex bends are an angle finder and a cheap scientifictype hand calculator.
Any electrician bending large conduit should already have an angle finder as without a hand bender to tell the angle being bent an angle finder is necessary. If you don't, there are some examples at the end of this article. And now that we have smartphones, the calculator isn't just cheap; it's free. Recommended for Android phones is the RealCalc scientific calculator app, available from the Google Play store at no charge. Simply search the store for RealCalc and download it.
Math Used for Bending Conduit
The math of conduitbending that we will discuss here comes from two sources. Some of the math is already built into a common hand bender device, and the rest of it involves the geometry of a triangle.
Note that making concentric bends requires using some additional math not discussed in this article.
Math From Hand Benders
Deducts, bend radiuses, and multipliers
Lots of math is built into the hand bender device. Only a few numbers and math operations need to be memorized to make offsets, saddles and 90 degree bends. Even the “multiplier” and “deduct” figures are usually stamped onto the bender device.
For more information on using a hand bender, see my comprehensive guide to bending conduit.
Radius and Deduct Figures for Conduit
Size of Conduit
 Radius of Bend
 Deduct for 90 degrees


1/2"
 4"
 5"

3/4"
 4 1/2"
 6"

1"
 5 3/4"
 8"

Multipliers for Conduit Offsets
Degree of Bend
 Multiplier


10 degrees
 6.0

22 degrees
 2.6

30 degrees
 2.0

45 degrees
 1.4

60 degrees
 1.2

Math From Triangles
The geometry of a triangle provides formulas useful for many conduit bends
Most conduit bends, in addition to a simple 90degree bend, can be understood and calculated using the geometry of a right triangle.
Using a Triangle to Understand an Offset
The pipe above is bent into an offset. In the diagram below, the heavy black line represents the bent piece of conduit; the green triangle shows some useful lengths and angles.
The angle "d" is the angle at which the conduit is bent. One of the remaining angles of the triangle is always 90 degrees, while the third angle always depends on the first, being 90 degrees minus angle d. The sides of the triangle are labeled A, B and C; these letters represent the length of each side. From the angle, using formulas below, you can get the relationships between these lengths.
In real life, of course, conduit is not a onedimensional line, but rather a threedimensional object with curved, not sharp, corners. But these considerations only affect the measurements you use in a very minor way; in everyday work you can ignore them.
Using Triangles to Understand Saddles
Saddles are used to route conduit around an obstruction. Look at the photos below to see how you would use the triangle concept for a threepoint saddle (by placing a second triangle backtoback with the first one) and a fourpoint saddle (by placing a second triangle divided from the first one by a length of straight conduit).
Math Formulas From Triangles
The math formulas we will be using are sine, cosine, and tangent. These are just the relationships between the sides of a right triangle; they depend on the angle (“d”) of the triangle. The formulas are listed below, with algebraic equivalents in each case. Each set of formulas—sine, cosine, and tangent—are just the same formula expressed three different ways.
Calculations Using the Sine
Sine(d) = A/C
That is, the sine of angle d is the length of side A divided by the length of side C.
A = sine(d) * C
The length of side A is sine (d) times the length of side C.
C = A/sine(d)
The length of side C is the length of side A divided by sine (d).
Calculations Using the Cosine
Cos(d) = B/C
The cosine of angle (d) is the length of side B divided by the length of side C.
B = cos(d) * C
The length of side B is the cosine of angle (d) multiplied by the length of side C.
C = B/cos(d)
The length of side C is the length of side B divided by the cosine of angle (d).
Calculations Using the Tangent
Tan(d) = A/B
The tangent of angle (d) is side A divided by the length of side B.
A = tan(d) * B
The length of side A is the tangent of angle (d) times the length of side B.
B = A/tan(d)
The length of side B is the length of side A divided by the tangent of angle (d).
Your calculator will give you the sine, cosine, and tangent of any angle. Because different calculators want you to press the keys in different sequences to get your results, you will have to read and understand the instructions for your particular calculator to use the trigonometric functions in it. In particular, you will have to know how to get inverse functions on your calculator; these functions convert a sine, cosine or tangent figure into an angle, into the degrees of bend you need.
And make sure that your calculator is set to describe angles in degrees, not in radians; radians are useless for the electrician.
Examples
Examples Using Math to Bend Conduit
 Assume that we need a 2" offset in 3 1/2" conduit. Normally, this would be impossible using a 10º bend, as two bends cannot be made that close together (12”) in that large a size of conduit. Using the sine formulas above, let's try a 2º bend. We know side A is 2". The calculator shows that the sine of a 2degree angle is .0349. Two inches divided by .0349 = 57". That's a little far apart for our bends, so let's try again using a 5º bend. The sine of 5 degrees is .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 two 22º bends. Again, C = A / sine(22º). Note that this can also be written as C = A * (1 / sine(22º)). The sine of 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. At the same time we can find the multiplier of a 15º bend by dividing one by the sine of 15º; the answer comes back that the multiplier for 15º is 3.86.
 Assume we need a 4" 3point saddle, and that we will use 45º as the center bend with 22.5º angle bends on each end. What is the conduit shrinkage—that is, the amount by which the center of the bend will be closer to the end of the conduit than the measured length of pipe? 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 threepoint saddle will move just under 1". Most electricians forget about or ignore this shrinkage on threepoint saddles and as a result the center of their bend is not centered over the obstruction they are crossing.
Bend Any Angle You Want
Using 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 the demands of a building or get the appearance people want. Bending 3" or 4" conduit into odd angles 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 this:
Sine(d) = opposite / hypotenuse
Cosine(d) = adjacent / hypotenuse
Tangent(d) = opposite / adjacent
where the “hypotenuse” is the longest side, the “opposite” is the side opposite the angle, and the “adjacent” is the side that touches the angle but is not the hypotenuse.
“SOHCAHTOA” is the acronym you may hear for this memory aid.
Or simply tape the formulas to the back of your calculator; believe it or not I grew up before there were calculators and I had to memorize.
A final note: this article is but one of several written by an electrician, for electricians. If you don't find what you are looking for among my other articles, leave a comment and I’ll consider addressing your question in future articles; the whole series is a work in progress.
Electricians and Trigonometry
Have you ever used trigonometry functions to bend pipe?
Angle Finders On Amazon
Two examples of angle finders from Amazon are shown below. One is considerably cheaper, but the other more accurate and easier to use. Either will work, just make sure that any one you choose has a magnet on at least one side to hold it to the pipe.
© 2010 Dan Harmon
Comments
Holy moly  you are an artist with this hub! Great incontent links, very relevant to the review, and as a former electrician, good information to boot!
I didn't even realize that trig would be pertinent to bending conduit! I'll use this new knowledge when teaching my reluctant math students.
Thank you so very much for sharing your knowledge. It's much appreciated.
thanks for sharing knowledge and teaching others
One of the hardest things to teach to "newbies" can be conduit bending if they do not understand math sometimes.
I always start with the basic bends first. After they master these, I will then show them more bending techniques and formulas.
One I use all the time is the "rolling offset."
hey what's the take up for rigid conduit 3/4, 1'' 1 1/2, 2'' and 3'' asap need info fast rigid pipe not imc
going to school for conduit bending with union and learning about shrink and gain. I just passed ac theory and im having trouble with switching decimals and fractions. They keep saying it so close with my answers. but i know i wouldn't use them in the feild. I only bent conduit by eye and a tape measure.Could you give me some advice.
deduct 6 inches for a 90. If your using a hand, dunno why you would cuz it will look like crap, but it will be stamped on the side.
I have tried using these calculations to recreate the results I had at work today. I needed a 5 to 5 1/2" offset in a 3 inch conduit. I tried 22 degrees as close together as possible, it was over 9 inches. I previously tried your multiplier of 6, and was unsuccessful, today I tried 5.75 with a spacing of 28.75. I resulted with a 6.5" offset. Please verify if my calculations are off or if I am missing something, I never took trig but my calculator did and I can recreate your results on paper with it but the multipliers don't seem to be working..
Sorry I left out a few words, may be confusing so..
After I bent the first at 22, I then tried 10 degrees but it seems the multiplier (6) is too big. I then tried 5.75 spaced 28.75 apart and came out with a 6.5" offset
So...
Sine(10)=.174
6.5/.174= 37
I didn't space my bends at 37 like i said they were 28.75. My boss said there was no formula but I know there is.. Maybe greenlee has multipliers that are used for certain benders.
I guess my almost perfect pipe will be getting outfitted with a nice new coupling lol :) at least it wasn't too small..
Thanks a lot for the speedy response and lengthy information!
I use the bender standing upright it has the stand and the little plate thing it slides along as its being bent. We have a little roofers' angle finder at our shop that I use for finding angles.
I'm guessing I over bent the pipe when I was actually trying to compensate for the "spring effect" when being released.
I think these benders should be made with more precision, like I said the thing that holds the pipe to the shoe and the shoe has too much play and ends up bending the pipe where u had not anticipated. I am going to keep trying to use these formulas and keep my calculator in my truck. We just got this bender about 6 months ago and I'm always the one running to the shop to bend pipe, If I can get it down to the science that I know it is, I would b happy :)
I'm still having a little trouble understanding the calculations probably because when in high school I finished all my math early and opted against trig so I could talk to all the honeys in business math, now look where I'm at!! Hahahahah
Very intense information. Will take days to understand and experience I'm sure. But thanks all the same
for a memory aid: Chief Sohcahtoa... S= O/H C=A/H T=O/A
probably works for me since I'm Cherokee ;)
your multiplier of 6 is wrong if you are using a 30 degree angle your mutiplier is 2. 22 degree is around 2.4
i believe what jerome meant by "take up" is the amount that you loose in your entire length of pipe when bending a 90. (not to be confused the shrinkage you get with offsets) it's useful to know if you want to cut and thread your pipe before bending it.
@wilderness, the angle is 22.5 is because it is 1/4th of a 90. Making concentric bends easier. I also wanted to add, as a general rule, I find that,if you need to make an uncommonon degree offset (such as 17°), your multiplier is how many times the degrees goes into 60. So, 60\17 = 3.5. I applied this to bending rigid ocal, and it got me pretty darn close. Within an 1/8th.
I want to be an electrician. From my understanding I'm going to learn about electrician tools, wiring, how to wire up motors, PLC n controls, power distribution, electric codes, blueprints schematics, electronic component circuits, a little construction, and how to bend conduit. Is there anything else I should learn and which is the toughest thing to learn. I've heard ppl say that AC theory n conduit bending are a bitch.
I been doing electrical work for about 35 years. Started out wiring house's, then on to schools, hospitals, grocery stores and now work as a lineman at a utility company in substations. I really enjoy the information you have shared here and find it not only usefull, but necessary to do a professional job. When working with large rigid conduit a wrong bend is not a easy fix, and also expensive.
Shrinkage per inch of rise :
22 degrees  3/16"
30 degrees  1/4"
45 degrees  3/8"
3 point saddle :
Mark center line "A" after adding shrinkage first bend
Then mark line "B" after adding 2.5" per inch of rise from center line.
Then mark line "C" using same measurement as line "B" above but mark on opposite side of center Line "A".
Tnen bend conduit in order A, B, C.
Multipliers :
10 degrees  6.0
22 degrees  2.6
30 degrees  2.0
45 degrees  1.4
60 degrees  1.2
What is the shrink per inch of rise for 10 and 60 degree bends ?
When bending a 3 bend saddle , my mark A is 30 inches and im crossing a 3 inch object then what are my measurements for mark B and C
How do I find the multiplier of a degree
How do I find shrink
shrink = hypotenuse(offset bend marks)  cos of angle X hypotenuse
Mack,
What you're referring to is called a parallel offset. You'd make a mark on your first pipe of where the off set starts. The mark on your second pipe will be moved based on the distance between your pipes and the diameter of your second pipe. The formula is (distance between pipe + diameter of pipe) x tan(half the offset angle). For example, if you had from left to right, 1/2" pipe and a 3/4" pipe, the offset on your 1/2" starting at 24" and you were bending 30 degree bends for a 6" offset, and you wanted 1" between your pipes, you'd make the following marks, measuring from bottom up. 1/2" pipe Mark 1 at 24", Mark 2 at 36" (offset height, which is 6" x offset multiplier, which is the cosecant of bending angle, which is csc(30), which is 2, therefor 12" between marks) Now, for the 3/4" pipe, we take the O.D of the pipe, which we'll say is an inch and an eighth, and we add it to the distance we want between pipes, which is 1". This gives us 2.125". Now we multiply this 2.125" by the tangent of half the offset angle, which happens to be 30 degrees, so half will be 15 degrees. So, we have 2.125" x tan(15), or 2.125" x .268, which gives us .5695. To covert this to inches, we multiply by 16, which gives us 9.122, so we now know .5695 is real close to 9/16". Finally, we subtract this 9/16" from 24" to yield 23 and 7/16". This is our first mark for the 3/4" pipe. Our second mark will be 12" away at 35 and 7/16". This is a lot easier to understand if you draw your pipes first so you can visualize how your marks will be moving on each subsequent pipe. The joys of being able to draw on the unfinished drywall.
Hey Dan,
I'm curious as to why you would add 1.25" to determine the minimum radius of a 2" conduit (as used in ugly's multishot:90 degree bending example
Thanks for the explanation, that makes sense. And, yes it's an example in ugly's from the 2011 edition pg. 160 (they also reference the wrong page which brings you to hand signals, ha,ha). I'm glad I found your blog!!
Interesting & extremely valuable info here !! I often use the trig functions to design pipe work & am pretty lost otherwise .
In contrast, a few months ago my partner 'cautioned' me that he definitely wasn't going to have anything to to with the cable tray offset we were about to build if I was going to use any "math" along the way. Well then, sez I,... If you want to design the thing & tell me what to do ... have at it. Seems like you have a different/ better way to proceed than me. I'm ready to learn something new. A long pause followed. And it got a little longer...
He finally decided to weather the awful process of my 'math' usage, and sunnuva'gun if he didn't ask me later if I would go over some of the fine points with him , etc.
Of course it was all about the basic trig which many learned to be afraid of way back when in some classroom or other.  Joslin ( Detroit )
How can i know the different take off of degree of pipe using tangent
Thank you! I have been taught this in class and doubted I would ever have to approach conduit bending with trigonometry but after having some difficulty bending large conduit today here I am!
Wow this is great! My husband is an electrician and he has tried to show me how he calculates all of this but it has just been beyond me. Your easy to follow explanations, pictures and images really helped it make sense. Thank you :o)
This is a very detailed and superb write up! I always wondered how some of those pipes were bent in such a precise way. It was a formula this entire time. You learn something new everyday! Thank you
By the time you re done reading this, you WILL be a better Electrician. GREAT WRITE UP!!!
Excellent / even us amateurs can gain some knowledge from it.
Point me to how we deturmine the deduct for a bend. I figured a 5 1/8" to drop with 22° bends 2 1/8"... if that is right, didn't write it down when doing it... but I'm not sure what to add to account for the loss in the bend. (3/4 conduit). Well, it's my first non90 bend, and I'll be "winging it" in a second here. I'd eye off the 90 right, but I need a banger at starting height.
I enjoyed your article, particularly the comments. I am a EC in Cook and DuPage Counties in Illinois. All wiring must be in metallic raceways, so bending conduit is one of the first things every apprentice learns. My undergraduate degree is in applied mathematics and I often make the mistake of assuming that my new hires are equally versed in trigonometry. I found your explanations of the calculations easy to follow and I have sent links to your articles to all of my employees. I am certain they will find them helpful.
Amazing. Thank you! Brought back memories from trig. There is a use for it!!!
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