Three bends cover almost everything
Watch an electrician run EMT for a day and you will see the same three moves over and over: the 90-degree stub-up that turns a horizontal run vertical, the two-bend offset that jogs the conduit sideways to clear an obstruction, and the 3-point saddle that humps over a pipe crossing the path. Everything else is a combination or a special case. Each bend is placed with pencil marks measured before the bender ever touches the tube, and every one of those marks comes from a small piece of right-triangle trigonometry that the trade long ago compressed into memorized multipliers.
The code adds a quiet constraint that makes clean layout matter: NEC 358.26 allows no more than 360 degrees of total bend between pull points, so every unnecessary or botched bend spends part of a fixed budget — four 90s and the run is done, box to box. Bends also cannot crowd each other; when two bends land closer together than about twice the conduit’s outside diameter, they start to overlap on the bender shoe and the pair becomes impractical to form cleanly. Good conduit math is therefore not just about hitting the obstruction — it is about spending degrees and inches deliberately.
The offset multiplier is just 1/sin(angle)
An offset is two equal, opposite bends that shift the conduit sideways by some height h while it keeps traveling forward. Between the bends, the tube runs along the hypotenuse of a right triangle whose opposite side is the rise — so the distance between the two bend marks is exactly h/sin(a). That single identity is the entire secret behind the numbers every apprentice memorizes: 1/sin(10°) = 5.76, 1/sin(22.5°) = 2.613, 1/sin(30°) = 2.000 exactly, 1/sin(45°) = 1.414, and 1/sin(60°) = 1.15. The trade multipliers are cosecants, rounded for field use — nothing more mystical than that.
The angle choice is a real trade-off, and the multiplier table shows why. A shallow 10-degree offset spreads its bends 5.76 times the rise apart — gentle on the wire pull, stingy with shrink, greedy for room. A steep 60 fits where nothing else will but costs pulling friction and shortens the run the most. The 30-degree bend is the trade’s default for an honest reason: its multiplier is exactly 2, which turns layout into doubling the rise in your head, and it sits in the comfortable middle of the space-versus-pull compromise.
Shrink: the run gets shorter
Bend an offset into a straight tube and the far end pulls back toward you, because the conduit now travels the hypotenuse where the straight line used to be. The difference is the shrink: h·(1 − cos a)/sin a, which simplifies to the tidy h·tan(a/2). Per inch of rise that comes to 0.087 in at 10 degrees, 0.199 at 22.5, 0.268 at 30, 0.414 at 45, and 0.577 at 60 — the field versions being roughly a quarter inch per inch of rise at 30 degrees and three-eighths at 45.
Shrink is where offset layouts actually go wrong, because it changes where the first mark belongs. Measure to the obstruction, then add the shrink before placing the first bend mark — otherwise the finished offset lands short of the thing it was supposed to clear by exactly the shrink. It also accumulates: every offset and saddle in a run steals length, so a conduit cut to the straight-line measurement between boxes arrives too short after bending. Tally the shrink of every planned bend and add it to the stick before cutting.
The 3-point saddle as two half-offsets
The 3-point saddle looks like its own species — one center bend, two return bends, a hump over a pipe — but the math treats it as two back-to-back offsets, each at half the center angle. A 45-degree-center saddle is really a pair of 22.5-degree offsets sharing their apex, which is why its outer marks sit at the obstruction depth times 2.61 on either side of the center mark: that 2.61 is the same cosecant of 22.5 degrees from the offset table. A 60-degree-center saddle uses two 30-degree halves and the familiar multiplier 2.0.
The shrink logic halves along with the angle. A saddle’s shrink is d·tan(a/4) — the half-offset’s half-angle — which for the 45-degree saddle gives 0.199 per inch of depth, the exact value behind the trade’s "3/16 in per inch" rule. Layout order: measure to the center of the obstruction, add the shrink, place the center mark there, then set the outer marks at the multiplier spacing to each side. The center bend is made first at the full 45 or 60 degrees; the conduit is then flipped for the two return bends at half that angle.
Stub-ups and take-up deducts
The 90-degree stub-up trades trigonometry for one calibrated constant. A 90 consumes conduit through its curved section — you cannot bend a sharp corner, and the arc uses up length that a square corner would not — and the amount consumed is fixed by the bender shoe’s radius. That amount is the take-up, or deduct: 5 in for 1/2-inch EMT, 6 in for 3/4, 8 in for 1, and 11 in for 1-1/4. The radius, and with it the take-up, grows with trade size because larger conduit must be bent to a larger radius per NEC Chapter 9, Table 2, to avoid flattening the tube and pinching the wire path.
Using it is a one-line calculation: mark = stub height − take-up, with the mark aligned to the bender’s arrow. A second 90 bent back-to-back skips the deduct entirely — the outside-to-outside distance is marked from the back of the first 90 and aligned to the bender’s back-of-90 reference point instead of the arrow. The deduct numbers are worth committing to memory for the sizes you bend daily; they are the difference between a stub that lands flush at the box and one that needs a coupling and a confession.
One obstruction course, marked out end to end
The running example: a single stick of 3/4-inch EMT (take-up 6 in) leaves the slab, crosses a mechanical room, and meets three problems in a row. First the stub-up: the run needs an 18-in stub out of the deck, so the bend mark goes at 18 − 6 = 12 in from the conduit end — arrow on the mark, bend, done. Second, a water line 40 in downstream demands a 5-in rise, bent as a 30-degree offset: distance between bends = 5 × 2.0 = 10 in, shrink = 5 × 0.268 = 1.34 in. Add the shrink to the measurement: first offset mark at 40 + 1.34 = 41.34 in from the last bend, second mark 10 in beyond it at 51.34 in.
Third, a 3-in-deep pipe crosses the path with its centerline measured 30 in past the offset. Lay out a 45-degree saddle: shrink = 3 × 0.199 = 0.60 in, so the center mark lands at 30 + 0.60 = 30.60 in, with outer marks 3 × 2.61 = 7.83 in to each side. Total shrink so far: 1.34 + 0.60 = 1.94 in — the stick is now almost 2 in shorter than its straight-line path, which is exactly the allowance to add before cutting the next length. The conduit bending calculator produces this whole mark sheet from the measurements — multiplier, shrink, and mark positions for offsets, saddle spacing, stub deducts by EMT size — and flags bends placed too close together to form cleanly on the shoe.
The layout in one pass
Recap the run: stub mark at 12 in (height minus the 3/4-inch take-up of 6); offset marks at 41.34 and 51.34 in (measure 40, add 1.34 of shrink, spread the marks by twice the 5-in rise at 30 degrees); saddle center at 30.60 in past the offset with wings at ±7.83 (depth times 2.61, shrink at the 22.5-degree half-angle rate); nearly 2 in of accumulated shrink owed back to the cut length. Three identities carried the whole job: the multiplier is 1/sin(a), the shrink is h·tan(a/2), and the saddle is two offsets at half the center angle — plus one memorized constant per trade size for the 90s. Keep the degree budget of NEC 358.26 in the back of your mind, add shrink before marking rather than after cursing, and the bender becomes the easy part.