Conduit bending formulas

Every calculation bentright does, written out. It is all trigonometry — the relationship between an angle and the sides of a triangle — with no lookup table behind any of it. θ is the bend angle throughout. Each section links to the calculator that does the arithmetic for you.

The two constants everything rests on

Almost every bend reduces to two figures that depend only on the angle: the offset multiplier and the shrink per unit of rise.

multiplier = 1 ÷ sin θ

shrink per unit = 1 ÷ sin θ − 1 ÷ tan θ = tan(θ ÷ 2)

The multiplier turns a rise into the distance between marks; the shrink turns a rise into the length the run loses. The same shrink constant also sets the stagger on parallel offsets, because it is tan(θ ÷ 2) either way.

Angle	Multiplier (1/sin θ)	Shrink per unit
10°	5.759	0.0875
22.5°	2.613	0.1989
30°	2.000	0.2679
45°	1.414	0.4142
60°	1.155	0.5774

Offset

between marks = rise ÷ sin θ · shrink = rise × (1/sin θ − 1/tan θ)

Two equal bends step a run over by the rise. The pipe between the marks is the hypotenuse of the triangle; the shrink is the difference between that hypotenuse and the flat run it replaces. See the offset calculator and the shrink calculator.

Three-point saddle

outer angle = centre ÷ 2 · centre-to-outer = depth ÷ sin(outer) · shrink = depth × (1/sin(outer) − 1/tan(outer))

A centre bend over the crown of a round obstruction with two outer bends half its angle. Each half is an offset at the outer angle raising the pipe by the depth. See the three-point saddle calculator.

Four-point saddle

offset spacing = depth ÷ sin θ · flat = obstruction width · shrink = 2 × depth × (1/sin θ − 1/tan θ)

Two offsets with a flat run across a flat-topped obstruction. The middle gap is the width; the shrink counts both offsets. See the four-point saddle calculator.

90° stub-up and take-up

mark from end = finished height − take-up

Take-up is the length the 90 sweep consumes; it is stamped on the bender and varies by tool and pipe size. There is no universal chart — find yours on the bender take-up page, and place the stub with the stub-up calculator.

Back-to-back and kick 90

back-to-back second mark = first mark + distance between the backs

kick from 90 = kick rise ÷ sin θ

A back-to-back sets two 90s a fixed distance apart, the second bent off the back-of-bend reference; a kick 90 adds one bend in the tail to lift the run. A kick is a single leg of an offset, so it uses the offset multiplier on its rise. See the back-to-back and kick 90 calculators.

Rolled offset

true offset = √(rise² + roll²) · roll angle = atan(roll ÷ rise)

When the jog rises and rolls sideways at once, the true offset is the hypotenuse of rise and roll, and it is what you bend as an ordinary offset after rolling the pipe to the roll angle. See the rolled offset calculator.

Parallel offset

stagger per conduit = spacing × (1/sin θ − 1/tan θ)

Each conduit in a parallel group starts its offset one stagger further along than the last, so the runs stay even through the jog. The stagger constant is the shrink constant. See the parallel offset calculator.

Segmented bend

per-bend = total ÷ bends · spacing = 2 × radius × tan(per-bend ÷ 2) · developed length = radius × total(rad)

A large-radius sweep made from many small equal bends spaced along the pipe. The developed length is the arc of the ideal curve. See the segmented bend calculator.

Concentric bends

radiusₙ = inner + n × spacing · developed lengthₙ = radiusₙ × angle(rad) · gain = spacing × angle(rad)

Parallel runs around one corner, each on a larger radius. Developed length is radius times the angle; the gain per run is constant when the spacing is. See the concentric bend calculator.

The terms

Shrink, gain, take-up, developed length and the rest are defined plainly in the glossary, and the how-to guide puts the whole set in the order you would actually use them.