Checked against primary sources 2026-09-04

Conduit Bending Math: Offset Multipliers, Shrink and Take-Up

Every bend on a hand bender comes down to three numbers: a multiplier that turns a rise into a distance between marks, a shrink figure that moves the first mark, and the take up cast into the tool. Get those three straight and the layouts stop being memorized recipes.

Open the simulator: drag the rise, turn the dial, read the marks

The offset is one right triangle

An offset lifts a run over something and puts it back on the same line. Two bends of the same angle in opposite directions, and the piece of pipe between them is the only thing that changes length.

Draw it and you have a right triangle. The rise is the short side, the run under it is the base, and the length of pipe between the two bends is the hypotenuse. The multiplier is the number that turns the rise into that hypotenuse, which is the distance between your two marks.

So the whole method is one line of arithmetic. Distance between marks equals the rise times the multiplier for the angle you picked. A 6 inch rise at 30 degrees puts the marks 12 inches apart, because the multiplier at 30 degrees is 2.0.

The five multipliers, and the cosecant behind them

The five angles a hand bender is marked for are 10, 22-1/2, 30, 45 and 60 degrees, and the multipliers printed in the bender guides are 6.0, 2.6, 2.0, 1.4 and 1.2 in that order. The same numbers are cast into the bender beside each angle mark.

They are not arbitrary. In that triangle the sine of the bend angle is the rise divided by the hypotenuse, so the hypotenuse is the rise divided by the sine. One divided by the sine is the cosecant, and each printed multiplier is that cosecant rounded to a number you can work with on a tape.

Check it at three angles. The sine of 30 degrees is exactly 0.5, so the cosecant is exactly 2.0 and the guides print 2.0. At 45 degrees the cosecant is about 1.414 and the guides print 1.4. At 10 degrees the cosecant is about 5.76 and the guides print 6.0, so the printed constants sit near the cosecant rather than on it, because you are marking a pipe with a tape measure and not a micrometer.

This is why 30 degrees is the angle most people reach for. The multiplier is a whole number, so the mental arithmetic is doubling, and doubling is hard to get wrong on a ladder.

Shrink, and why the far end moves

Sending the pipe up and over uses more pipe than going straight, so the far end of the stick comes back toward you. That loss is shrink, and it is the part most people leave out of the layout.

The bender guides give it per inch of rise: 1/16 inch at 10 degrees, 3/16 at 22-1/2, 1/4 at 30, 3/8 at 45 and 1/2 at 60. Multiply by the rise and you have the total. A 6 inch offset at 30 degrees loses 1-1/2 inches.

The geometry behind those figures is the cosecant less the cotangent. The pipe between the bends is the rise times the cosecant, while the horizontal ground it covers is the rise times the cotangent, and the difference is what the run gives up. The figures on the guide are the working numbers to lay out with.

Using it is simple. Measure to where the far end has to land, then move your first mark out by the shrink, and the pipe ends up where you wanted it. Skip it and the run comes up short by exactly the amount the guide printed.

Take up belongs to the bender, not to the code

A 90 is not a corner. The shoe of the bender uses a length of pipe to make the curve, and that length is take up. The mark for a stub therefore goes take up short of the finished height, and then the arrow on the bender lines up with the mark.

Take up is a property of the tool. Klein prints 5 inches for the 1/2 inch EMT bender, 6 inches for the 3/4 inch and 8 inches for the 1 inch, published as the stub-up height on the product page for each head.

A bender with a different figure stamped on it is telling you the truth about itself, so read the tool before you trust a number off a page. Nothing in the code sets take up, because it is a fact about the shoe rather than a rule about the installation.

A worked one: a 12 inch stub on 1/2 inch EMT. Twelve less five is seven, so the mark goes 7 inches from the end of the pipe, the arrow goes on the mark, and you pull to 90.

Gain, in plain words

Measure a 90 to the outside corner and you count more pipe than the bend actually uses, because the pipe turns on a radius rather than at a point. The difference is gain.

Geometrically it is two minus half of pi, times the bend radius, which works out at about 0.43 of the radius. That is a relation you can check rather than a figure off a chart, and the bender guides do not print a gain number at all.

For most work you never touch it, because the take up stamped on the bender already carries the gain for that shoe. Subtract take up, bend at the mark, and gain has been handled for you.

The three bend saddle

A three bend saddle carries a run over a single round obstruction, a pipe crossing your route. It is one center bend of 45 degrees with a 22-1/2 degree bend on each side of it, which is the rule that the center bend is twice each side bend.

The layout works out from the middle. Find the center of the obstruction, add 3/16 inch of shrink for every inch of obstruction, and mark that as the center. The two side marks then sit 2-1/2 inches out from the center mark for every inch of obstruction.

A 3 inch pipe in the way, then: the side marks land 7-1/2 inches each side of the center, and the run shrinks 9/16 of an inch. The published zip guide gives the same relation at both ends of its range, 2-1/2 inches and 3/16 of shrink for a 1 inch obstruction, and 15 inches and 1-1/8 inches for a 6 inch one.

The four bend saddle

A four bend saddle is two offsets back to back. Up and over on the first pair, along the top, then down and back on the second pair.

That means there is nothing new to learn. It uses the offset multiplier twice and the offset shrink twice, at whatever angle you picked for the two pairs.

Reach for it when the obstruction is wide, because a three bend saddle is built around a single crossing point and a wide one leaves the pipe resting on the obstruction. The four bend version gives you a flat length on top that you set to the width.

Back to back 90s

A pair of back to back 90s makes a U, and the measurement that matters is between the backs of the two bends, which is where the pipe sits against the wall or the strut.

The first bend is an ordinary stub. Mark at the finished height less the take up, arrow on the mark, pull to 90.

The second mark then goes the back to back distance further along the pipe, measured from the first mark, and that bend is set with the star rather than the arrow, because the star is what lines the shoe up with the back of a finished bend.

What the code says about bends

Two rules in 358.24 cover field bends in EMT, and both of them show up on the paper.

358.24(A) says a bend has to be made so the tubing is not damaged and its internal diameter is not effectively reduced, and it sends the radius of a field bend, measured to the centerline, to Chapter 9 Table 2 for one shot and full shoe benders. The shoe of a hand bender is built to that radius, so the tool settles it. The table belongs to NFPA and is not printed here, so look the row up in your own book.

358.24(B) holds the total degrees of bend in a tubing run to 360 degrees between pull points. That is four 90s. It is also six 60 degree bends, which is only three offsets, so a route with a lot of dodging eats the allowance faster than people expect. A pull point is what buys you more, which makes a box in the middle of a long run a decision rather than an accident.

One numbering note worth carrying into the exam room. The degrees in one run rule sat at 358.26 in older editions and a lot of study material still cites it that way. In the 2026 text there is no 358.26 at all, because the rule is part of 358.24. Cite the subdivision, not the memory.

Questions people ask

What is the multiplier for a 30 degree offset?

It is 2.0, so the two marks sit twice the rise apart. A 6 inch offset puts 12 inches between them. That number is the cosecant of 30 degrees, which is exactly 2 because the sine of 30 degrees is exactly one half.

How do you figure shrink on an offset?

Multiply the rise by the shrink figure for the angle. The guides give 1/16 inch per inch at 10 degrees, 3/16 at 22-1/2, 1/4 at 30, 3/8 at 45 and 1/2 at 60. A 6 inch offset at 30 degrees therefore loses 1-1/2 inches, and you move your first mark out by that much so the far end still lands where you measured.

What is take up on a 1/2 inch bender?

Klein publishes 5 inches for the 1/2 inch EMT bender, which is the stub-up height on the product page for that head. It is 6 inches for the 3/4 inch bender and 8 inches for the 1 inch. Subtract take up from the finished stub height, mark there, and put the arrow on the mark.

How many degrees of bend are allowed between pull points?

For EMT, 358.24(B) holds a tubing run to 360 degrees of bend between pull points. Four 90s reach it. So do six 60 degree bends, which is only three offsets, so the allowance goes faster on a route with a lot of dodging.

Why is the offset multiplier the cosecant of the angle?

Because the offset is a right triangle. The sine of the bend angle is the rise over the length of pipe between the bends, so that length is the rise divided by the sine. One over the sine is the cosecant, and the guide prints that cosecant rounded off: 1.4 for the 1.414 at 45 degrees, and 6.0 for the 5.76 at 10.

How do you lay out a three bend saddle?

Measure to the center of the obstruction, add 3/16 inch of shrink for every inch of obstruction, and mark that as the center. The center bend is 45 degrees and each side bend is 22-1/2, so the center is twice the sides. The side marks sit 2-1/2 inches from the center for every inch of obstruction.

When do you use a four bend saddle instead of a three bend?

When the obstruction is wide. A three bend saddle is built around one crossing point, so a wide obstruction ends up carrying the pipe. A four bend saddle is two offsets, giving a flat length on top you can set to the width, and it uses the offset multiplier and the offset shrink twice.

What sets the radius of a field bend?

358.24(A) says the bend has to be made so the tubing is not damaged and its inside diameter is not effectively reduced, and it sends the radius to Chapter 9 Table 2 for one shot and full shoe benders. A hand bender shoe is built to that radius, so the tool does that part. Read the row in your own book, because the table is not printed here.

What this page cites

• NEC 358.24 Bends in electrical metallic tubing, in two subdivisions. Read in the 2026 edition and paraphrased here.
• NEC 358.24(A) How the bend is made: no damage to the tubing, no effective reduction of the internal diameter, and the radius of a field bend to the centerline not less than Chapter 9 Table 2 shows for one shot and full shoe benders.
• NEC 358.24(B) The total degrees of bend in a tubing run, not more than 360 degrees between pull points. There is no 358.26 in the 2026 text, so this is the subdivision to cite.
• NEC Chapter 9, Table 2 Radius of conduit and tubing bends. Named here and not printed. Read the row for your trade size in your own code book.
• Klein Tools, Conduit Bender and Angle Setter guide The zip guide rows for offsets and for saddles, and the bender take up table. source
• Klein Tools product pages, catalog 51606, 51604 and 51605 Take up published as the stub-up height for each head: 5 inches on the 1/2 inch EMT bender, 6 inches on the 3/4 inch, 8 inches on the 1 inch. source
• Greenlee hand bender instruction manual The five multipliers and the five shrink figures as one set, and the rule that the center bend of a three bend saddle is twice each side bend. source