The two numbers behind every offset

Every apprentice learns the table: thirty degrees, multiply by two. Forty-five, multiply by one point four. It works, right up until you need an angle the table does not have, or you are second-guessing whether the number you remembered was the multiplier or the shrink.

Both numbers come out of a single right triangle, and once you have seen it you stop needing the table at all.

The triangle

An offset takes the pipe off its line, across, and back parallel. Between the two bends the conduit runs on a diagonal. The depth of the offset is the side opposite your bend angle, and the diagonal is the hypotenuse.

So the length of pipe between your two marks — the travel — is the depth divided by the sine of the angle. That is the multiplier. It is not a magic constant; it is one over the sine.

• 10° — 1 ÷ sin 10° = 5.76, rounded to 6
• 22.5° — 2.61, rounded to 2.6
• 30° — exactly 2.00
• 45° — 1.41, rounded to 1.4
• 60° — 1.15, rounded to 1.2

Why it mattersThirty degrees is the one everybody uses because it is the only one that is exactly a whole number. That is the entire reason, and it is a good one.

Shrink is the other side of the same triangle

While the pipe travels that diagonal, it only advances along the run by the adjacent side. The pipe is using more length than it is gaining in distance, so the far end comes back toward you. That is shrink, and it is why an offset bent to the right depth can still land the box an inch short.

Travel minus run advanced works out to the depth times the tangent of half the angle. Per inch of offset depth:

Every chart constant sits below the formula, and the obvious conclusion is that the charts are lazy. That conclusion is wrong, and it is worth understanding why, because acting on it puts your work long.

Why the chart beats the formula

The triangle assumes the pipe turns at a point. Your bender turns it through an arc — a 1/2″ EMT shoe has a centerline radius of about four inches — and a rounded corner is a shorter path than a sharp one. The bend gives some length back, so the real shrink is always less than the formula says.

Run the real geometry on a 6″ offset in 1/2″ EMT and the gap is not academic:

From 22.5° up, the chart is the better number — not because it is more precise, but because it was built around real benders. Trusting the formula instead runs you about a third of an inch long at 45° and most of an inch at 60°, and it gets worse on bigger pipe.

At 10° the formula is nearly exact and the chart is the one that is off, by about an eighth of an inch on that same 6″ offset. Shallow bends barely curve, so there is almost no radius to give anything back.

Why it mattersSo the honest rule is the opposite of clever: use the chart for the angles it covers. Reach for tan(angle ÷ 2) when you are off-chart, knowing it is an upper bound — you will finish slightly long, which you can cut, rather than short, which you cannot.

Doing it without the chart

Pick the angle for the room you have. Shallow angles eat length and need a long clean run; steep ones fit tight spaces and shrink hard.

• Measure the depth you need to clear.
• Travel = depth ÷ sin(angle). That is the distance between your two marks.
• Shrink: take it off the chart if the angle is on it. Add it to the distance from the end of the pipe to your FIRST mark, so the far end still lands where you measured.
• Bend the first mark to angle. Then roll the pipe 180° in the bender so the second bend opposes the first — that is what brings it back parallel — and bend the second mark to the same angle.

The part that goes wrong most often is not the math. It is the second bend landing out of plane with the first, which turns a flat offset into a corkscrew no multiplier will fix. Sight down the pipe before you pull the second one.

What the bender itself tells you

Take-up — how far back from your mark the bend has to start for a 90° stub — is not universal. It depends on the bender and the conduit size, and most benders carry it cast into the head or on a label. A 1/2″ EMT bender and a 3/4″ bender do not share a number. Across the major makes, standard-radius EMT benders do tend to agree at a given size, but short-radius and rigid shoes do not, so the tool in your hand is the authority rather than a figure someone quoted you.

So read the shoe rather than a number somebody told you. The offset math above is geometry and travels with you; take-up is a property of the tool in your hand.

And the limit nobody checks until the pull

Bending math will happily let you build a run you cannot pull wire through. The NEC caps how much total bend is allowed between pull points — the equivalent of four quarter bends, 360 degrees — and sets a minimum bend radius. For EMT those live in Article 358, with the radius values in Chapter 9, Table 2. The cap counts every bend in the run — offsets, kicks and saddles, not just the 90s.

Section numbers move between editions and jurisdictions adopt them at different times, so check the edition your authority having jurisdiction has actually adopted. The rule of thumb that survives every edition: count your bends as you go, not when the pull sticks.

The short version

• Multiplier is 1 ÷ sin(angle). Thirty degrees gives exactly 2.
• Shrink from the chart, not the formula — the formula assumes a sharp corner your bender does not make.
• Take-up belongs to the bender, not to the trade. Read the tool.
• Total bend between pull points is capped. Count as you go.

Bending is the half of this job where the math is honest and the pipe tells you immediately whether you got it right. Worth knowing why the numbers are what they are.

This guide is general information to help you check your work. It is not legal advice or an official inspection, and it does not replace the requirements that apply to you, the manufacturer’s instructions, or a determination by an inspector or the authority having jurisdiction. Requirements vary by location and change over time; check the current rules where you work.