Conduit bending multipliers
The offset multiplier is how many times the rise you space your marks: rise × multiplier is the distance between the two bends. It depends only on the angle. Pick an angle above for the exact figure, or read the table below for the five common angles beside the rounded rules the trade carries — the shop rule, the same words every calculator on the site uses.
On the bender
A multiplier on its own does not bend anything — it is the one number in the middle of a procedure. This is where it goes.
- Measure the rise. Centre of the pipe where it runs now to centre of where it has to end up. Centre to centre, not edge to edge — measuring the gap you can see is how a rise ends up a pipe diameter short.
- Pick the angle. 30° for most offsets, 45° when the rise is deep and the run is short, 22.5° or 10° when there is room and you want an easy pull. The angle is a choice; the multiplier follows from it.
- Multiply. Rise × multiplier is the distance between your two marks. Read the exact figure off the calculator above, or use the shop rule if the rise is small enough that they land on the same sixteenth.
- Add the shrink to the length. The shrink ratio × rise is the length the offset eats out of the finished run. It goes on the overall measurement — the cut length, or the distance to the far box — not on mark 1, which sits on straight pipe and never moves.
- Mark twice, bend twice. Mark 1, then mark 2 further along by the distance you just worked out. Arrow on mark 1 and pull the angle; roll the pipe over, arrow on mark 2, pull the same angle back the other way.
- Check the angle you actually got. Lay a level or an angle finder on the jog. A shoe that reads 30° and a pipe that sprang back to 28° is a different multiplier, and that is a figure worth writing on your own bender — how to measure it.
The reference table
Exact multiplier and shrink ratio (multiply it by the rise, in inches or millimetres) on the left, the shop rule of thumb on the right. The exact values come straight from the trigonometry, so they are correct to as many places as you care to read. The shop-shrink column is the exact figure rounded up to the next sixteenth, not down: a shrink figure that is always low lands the run short, which is the one failure worth avoiding. Rounded up it errs long, and pipe you can trim. The shop multipliers are not one rounding rule — they are the numbers the trade says out loud. ×2.6, ×1.4 and ×1.15 are a shade light, so they lay the jog out short; ×6 at 10° and ×3.9 at 15° are a shade heavy, so they lay it out long. The drift table below is how much, and which way.
| Ángulo | Multiplier | Shop rule | Shrink × rise | Shop shrink (in per in) |
|---|---|---|---|---|
| 10° | 5.759 | 6 | 0.087 | 1/8 |
| 15° | 3.864 | 3.9 | 0.132 | 3/16 |
| 22.5° | 2.613 | 2.6 | 0.199 | 1/4 |
| 30° | 2.000 | 2 | 0.268 | 5/16 |
| 45° | 1.414 | 1.4 | 0.414 | 7/16 |
| 60° | 1.155 | 1.15 | 0.577 | 5/8 |
Worked examples
5" (127 mm) at 22.5° — the shop rule is fine
You need a 5" (127 mm) offset at 22.5°. The exact multiplier is 2.613, so the marks go 5 × 2.613 = 13.06 → 13 1/16" (332 mm) apart. The shop rule of 2.6 would give 13" (330 mm) — a sixteenth short, which nobody would notice here. On a 20" (508 mm) offset the same rounding is 1/4" (6.4 mm), which you would. That is the whole argument for keeping the exact figure to hand.
18" (457 mm) at 45° — the shop rule is not
A run has to drop 18" (457 mm) to get under a beam, in a short space, so it is a 45. Exact: 18 × 1.414 = 25.46 → 25 7/16" (647 mm) between marks. Shop rule: 18 × 1.4 = 25.2 → 25 3/16" (640 mm). 1/4" (6.4 mm) short between the marks means the offset comes out a bit under 18" (457 mm) of rise, and under a beam a bit under is the difference between clearing it and not. Use 1.414.
A 300 mm drop at 45°, metric job
A run drops 11 13/16" (300 mm) under a beam at 45°. Exact: 300 × 1.414 = 424.3 → 16 11/16" (424 mm) between marks. The shop ×1.4 gives 16 9/16" (420 mm), 3/16" (4 mm) short — the offset comes out that much under a full drop. The shrink is 300 × 0.414 = 124.3 → 4 7/8" (124 mm), on the overall length. The multiplier is the same number in millimetres as in inches; only the rise changes.
A 37° offset — an angle with no shop rule
The bender's shoe has a mark you have been asked to use that is neither 30 nor 45. There is no shop rule for 37°, and there does not need to be: type 37 in the calculator above and the multiplier is 1.662, the shrink 0.335 × the rise. A 9" (229 mm) rise then wants marks 9 × 1.662 = 14.96 → 14 15/16" (380 mm) apart and takes 9 × 0.335 = 3.0 → 3" (76 mm) out of the run. Any angle on the shoe works the same way.
At a glance — how far the shop rule drifts
The difference between rise × shop rule and rise × exact multiplier — to the nearest sixteenth in the inch table, to the millimetre in the metric one. Heavy means the rule lays the jog out long, light means short; ×2 at 30° is exact, so its row is all zeros.
| Ángulo | Shop rule | 5" rise | 10" rise | 20" rise | 40" rise |
|---|---|---|---|---|---|
| 10° | ×6 (heavy) | 1 3/16 | 2 7/16 | 4 13/16 | 9 5/8 |
| 15° | ×3.9 (heavy) | 3/16 | 3/8 | 3/4 | 1 7/16 |
| 22.5° | ×2.6 (light) | 1/16 | 1/8 | 1/4 | 1/2 |
| 30° | ×2 (exact) | 0 | 0 | 0 | 0 |
| 45° | ×1.4 (light) | 1/16 | 1/8 | 5/16 | 9/16 |
| 60° | ×1.15 (light) | 0 | 1/16 | 1/8 | 3/16 |
| Ángulo | Shop rule | 100 mm rise | 250 mm rise | 500 mm rise | 1000 mm rise |
|---|---|---|---|---|---|
| 10° | ×6 (heavy) | 24 | 60 | 121 | 241 |
| 15° | ×3.9 (heavy) | 3.6 | 9.1 | 18 | 36 |
| 22.5° | ×2.6 (light) | 1.3 | 3.3 | 6.6 | 13 |
| 30° | ×2 (exact) | 0 | 0 | 0 | 0 |
| 45° | ×1.4 (light) | 1.4 | 3.6 | 7.1 | 14 |
| 60° | ×1.15 (light) | 0.5 | 1.2 | 2.4 | 4.7 |
Under 1/16" (1.6 mm), the tape cannot tell the difference. 1/8" (3.2 mm) is a sloppy joint. 1/4" (6.4 mm) and up is a bend that misses. So: shop rule for anything under about 10" (254 mm) of rise at 22.5° and 45°, exact above that, and ×2 at 30° all day long. The ×6 at 10° is the odd one out — it runs heavy by about 0.24 × the rise, so it is 1/8" (3 mm) out on the 1/2" (13 mm) jog of a box offset and 2 7/16" (61 mm) out on a 10" (254 mm) rise. Treat it as a box-offset rule and nothing else.
Which angle, when
| Ángulo | Reach for it when | Watch out for |
|---|---|---|
| 10° | Box offsets and tiny corrections on a long tail. | The jog is nearly six times the rise — it needs room. |
| 22.5° | A shallow, easy pull with plenty of run; parallel racks. | Long between-marks distances; check the stick length. |
| 30° | Almost everything. ×2 in your head, moderate shrink. | Nothing much — it is the default for a reason. |
| 45° | Deep offsets in a short run; going under something close. | Shrink is 0.414 × the rise and the shop rule drifts fast. |
| 60° | The obstruction is right on top of the fitting. | A hard pull, big shrink, and a tight bend to fish wire round. |
What went wrong
Multiplier mistakes are quiet ones: the arithmetic is fine and the pipe is still wrong. These are the three that do it.
The multiplier was never applied
What you see: the offset is far too steep — nearly a Z — and the run does not lie flat when you set it in place.
Why: the marks were spaced by the rise instead of by rise × multiplier. It is an easy slip when the two numbers are both sitting on the tape at once.
Fix: say it out loud as you mark: "six inch rise, thirty degrees, twelve between marks" (or "150 rise, thirty, 300 between"). The rise never goes on the pipe — only the distance between marks does.
The shop rule used on a big rise
What you see: a deep offset that is out by 1/2" (13 mm) or more, on a rise where 1/4" (6.4 mm) would not have mattered.
Why: the shop rules are rounded multipliers. The error is proportional to the rise: at 22.5° the rounded 2.6 is 0.013 × the rise light, which is nothing on a 5" (127 mm) rise and over 1/2" (13 mm) on a 40" (1016 mm). The drift table above puts numbers on it.
Fix: shop rule for small rises, exact multiplier for anything deep. The calculator at the top of this page gives the exact figure for any angle, including the ones with no rule of thumb at all.
The multiplier was right and the shrink was forgotten
What you see: the two bends are perfect, the jog is the right height, and the far end of the stick is 1" (25 mm) short of the box.
Why: the multiplier spaces the marks; it says nothing about the length the bends consume. That is the second number in the same row of the table, and it is the one people read past.
Fix: the shrink ratio × rise, added to the overall length before you cut — not to mark 1. The shrink calculator does it on its own page, and every offset result on the site carries it.
The formula
The multiplier is one over the sine of the angle; the shrink ratio is that less one over the tangent:
multiplier = 1 ÷ sin θ
shrink ratio = 1 ÷ sin θ − 1 ÷ tan θ
The offset is the rise of a right triangle and the pipe between the marks is the hypotenuse, so the hypotenuse is rise ÷ sin θ — that is the multiplier. The horizontal run the pipe covers is rise ÷ tan θ, and the difference between the hypotenuse and that run is what the pipe pulls back: the shrink.
Which bender these numbers assume — and how to adjust
The geometry belongs to the angle, not the tool. What the tool changes — its reference marks, its take-up and gain, its springback — is yours to read off the shoe or prove on scrap, never a table here (the four test bends). For this bend:
A multiplier is one over the sine of the angle and a bender has no say in it. The shop rules are rounded so the arithmetic can be done in your head, not because any bender bends that way. What a bender does change is which angles it offers a line for, which is why the chips on every calculator here are the five common ones and there is an “Other angle” box beside them for whatever your shoe actually carries.
Preguntas
- What is the multiplier for a 30° offset?
- Exactly 2. The multiplier is 1 ÷ sin(angle), and sin 30° is 0.5, so 1 ÷ 0.5 = 2. Multiply your rise by 2 to get the distance between the two marks. Most benders learn 30° first for exactly this reason — the mental math is trivial.
- Why are there two numbers for each angle?
- The first is the exact multiplier from the trigonometry; the second is the rounded figure the trade carries in its head. The shop rule for 22.5° is 2.6, the exact value is 2.613 — close enough for a small offset, off by enough to matter on a long one.
- Does the multiplier depend on the conduit size?
- No. The multiplier comes only from the angle, so 30° is ×2 whether you are bending half-inch EMT or two-inch rigid. Take-up and gain change with the bender and the pipe; the offset multiplier and the shrink ratio do not.
- When does the rounding start to matter?
- On large offsets and tight runs, because the drift is proportional to the rise. At 22.5° the shop ×2.6 is about 0.013 × the rise light: nothing on a 3" (76 mm) offset, 1/4" (6.4 mm) on a 20" (508 mm) one, and over 1/2" (13 mm) on a 40" (1016 mm). At 10° the shop ×6 is the worst of them, about 0.24 × the rise heavy. Use the exact figure when the offset is big or the run is short enough that the far end has no slack — the drift table on this page has the numbers.