Conduit-Bend Constants
An offset bend is a right triangle laid into a stick of pipe, and two identities from that triangle govern every mark you make: mark spacing is rise / sin theta, and shrink is rise × (1 − cos theta) / sin theta. Those two are the whole trade for offsets and 3-point saddles. Pick one of the five standard trade angles, read its constants off the table below, and multiply by your rise for the mark spacing and the length to add back.
The two constants every bend reduces to
Every offset resolves to two fixed numbers per angle. The mark multiplier, 1 / sin theta, sets how far apart to space your two bend marks. The shrink-per-inch, (1 − cos theta) / sin theta, is how much length the bend pulls back toward you; add that shrink to your measurement before the first bend so the run lands on the box.
Both constants depend only on the angle, not on conduit size, bender brand, or rise. That is what makes a five-row table sufficient: a 6-inch and a 12-inch rise at 30 degrees share the same multipliers, and you scale by the rise. The five trade angles are the detents cast into a standard hand bender for EMT sized to ANSI C80.3, so the table holds across brands.
The 3-point saddle adds one wrinkle. A saddle is two offset bends sharing a center, so its total shrink is exactly twice the single-offset shrink for the same angle and rise. The mark multiplier is unchanged; the shrink doubles.
Trade-angle reference table
The five angles Bendmark supports, their mark-spacing multiplier (1 / sin theta) and shrink per inch of rise ((1 − cos theta) / sin theta). These are the exact values the calculator uses.
The 30-degree row is the everyday default for a reason: sin 30 degrees is exactly 0.5, so the mark multiplier is exactly 2.0 and the arithmetic is mental. A 6-inch offset at 30 degrees puts your marks 12 inches apart and shrinks 6 × 0.2679 = 1.61 inches, which lands on 1 5/8" on the tape. Shallow angles like 10 degrees barely deflect the pipe, so shrink stays low (0.0876 per inch) while the marks spread wide (5.759 per inch). Steep angles like 60 degrees do the opposite: high shrink (0.5774 per inch), tight marks (1.155 per inch). Picking an angle is picking that trade-off.
Derivation footnote: mark spacing is the hypotenuse of the bend triangle, rise / sin theta; shrink is that hypotenuse minus its horizontal projection, which factors to rise × (1 − cos theta) / sin theta.
What the shrink figure corrects, and what it does not
Shrink corrects for the horizontal length the bend steals. Kick the pipe up and the far end travels toward you, so the straight-line distance from box to fitting comes in shorter than the pipe you fed. Add the shrink back and the run lands on the print.
Shrink does not correct for take-up, and this is where marks go wrong. Take-up (also called deduct) is the fixed offset between your bender's arrow and the actual bend, and it depends on the bender and the conduit size, not the angle. Keep take-up separate from the shrink math: the common mistake is folding one into the other and double-counting. Take-up shifts where marks land on the pipe; shrink changes how much pipe you need. They stay independent.
One note on rounding. Decimal-inch results round to the nearest 1/16 inch for the tape, because 1/16" is the finest gradation you read in the field and 1.607" is precision no tape can honor. The math holds full precision; only the reading rounds.
Why shrink gets left out of most references
Many printed field guides publish the mark multipliers and the classic 3-point saddle procedure but drop the shrink figure. A saddle how-to that walks the marks and leaves out the shrink step lands offsets short, and they get recut. That is why the shrink value belongs next to the multiplier: it is the number the marks alone do not give you.
The rule for checking any source is simple. For a known rise and angle, the mark spacing is rise / sin theta and the shrink is rise × (1 − cos theta) / sin theta. A single wrong shrink value at any angle sends every offset at that angle short, so a reference that omits it is not a shortcut, it is a gap you fill by hand.
Common questions
What is conduit shrink and why does it matter?
When you bend an offset into a run of conduit, the two bends pull the far end of the pipe closer to you. The straight-line length between your box and your fitting comes in shorter than the pipe you fed in. That lost length is the shrink. Ignore it and your conduit lands short of the box, so you cut a fresh stick. Add the shrink back to your measurement before the first bend and the pipe lands dead on.
How do I calculate offset shrink?
Shrink equals the rise times the shrink-per-inch constant for your angle: shrink = rise × (1 − cos θ) / sin θ. For a 6-inch rise at 30°, that is 6 × 0.2679 ≈ 1.61 inches, which lands on 1 5/8" on the tape. Look up the shrink-per-inch value for your angle in the reference table and multiply it by the rise.
How is 3-point saddle shrink different from offset shrink?
A 3-point saddle is two offsets sharing a center bend: you bend up and then back down to clear an obstruction. Because there are two bends pulling the pipe, the total saddle shrink is exactly twice the single-bend shrink for the same angle and rise. If a single 30° bend over a 3-inch obstruction shrinks 0.80", the full saddle shrinks about 1.61".
Why does a shallower angle produce less shrink?
A shallow bend, like 10°, barely deflects the pipe, so the far end moves very little toward you and the shrink-per-inch is only 0.0876. A steep 60° bend deflects hard and pulls a lot of length, at 0.5774 per inch of rise. Less angle means less shrink but longer, more gradual marks. That is the trade-off you pick when you choose an angle.
Does the take-up or deduct affect the shrink number?
No. Take-up (also called deduct) is the fixed distance your bender's arrow sits back from the actual bend, and it depends on your bender and conduit size, not the angle. It shifts where you place your marks on the pipe, but the shrink you add back is purely a function of angle and rise. Keep the two separate: the common mistake is folding one into the other and double-counting.
Are these constants exact?
They come straight from trigonometry, rounded for the tape. The mark multiplier is 1 / sin θ and the shrink-per-inch is (1 − cos θ) / sin θ. The 30° multiplier is exactly 2.0 because sin 30° is exactly 0.5; the others carry three decimals, which is finer than any tape measure can resolve. You can verify any value yourself: for a given rise and angle, mark spacing is rise / sin θ and shrink is rise × (1 − cos θ) / sin θ.