Do these formulas work in millimetres?

Yes, unchanged. None of them has a unit in it: the multiplier and the shrink factor are ratios, so a rise in inches gives marks in inches and a rise in millimetres gives marks in millimetres. A 250 mm rise at 30° needs marks 500 mm apart, exactly as a 10" rise needs them 20" apart.

Why does the shop say ×6 for 10° when the formula gives 5.759?

The shop figures are the numbers the trade says out loud, not a rounding rule. ×6 is a shade heavy at 10°; ×2.6, ×1.4 and ×1.15 are a shade light at 22.5°, 45° and 60°. For a mark that has to land, use the exact multiplier — every calculator on the site does.

Where is the take-up formula for my bender?

There is no formula for it. Take-up and gain come from the radius your shoe bends to, so they are stamped on the bender or measured with one test bend. The formula on this page only runs the stub-up both ways: mark = height − take-up, and take-up = height − mark.

Fórmulas para doblar conduit

The conduit bending formulas come down to two: between marks = rise ÷ sin θ, and shrink = rise × (1 ÷ sin θ − 1 ÷ tan θ). Here is 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, and the notation is the same everywhere on the site: rise ÷ sin θ, never a multiplier you have to look up. Each section links to the calculator that does the arithmetic for you. The formulas have no units in them: put the rise in inches and the marks come out in inches, put it in millimetres and they come out in millimetres.

The two constants everything rests on

Almost every bend on the site reduces to those two figures, and both depend only on the angle:

multiplier = 1 ÷ sin θ

shrink factor = 1 ÷ sin θ − 1 ÷ tan θ

(the same thing) shrink factor = tan(θ ÷ 2)

The multiplier turns a rise into the distance between marks; the shrink constant turns a rise into the length the run loses — which goes on the overall length of the run, not on the first mark. The shrink constant also sets the stagger on parallel offsets, because it is tan(θ ÷ 2) either way. The shop carries rounded versions of both. The shop shrink column below is the inch figure per inch of rise, rounded up to the next sixteenth so a mental layout errs long rather than short; in millimetres, use the exact factor and round the answer up to the next millimetre. The shop multipliers are not one rounding rule at all — they are the figures the trade says out loud, and the ×6 at 10° below is a shade heavy while ×2.6, ×1.4 and ×1.15 are a shade light:

Ángulo	Multiplier	Shop rule	Shrink factor	Shop shrink (in per in)
10°	5.759	6	0.0875	1/8
22.5°	2.613	2.6	0.1989	1/4
30°	2.000	2	0.2679	5/16
45°	1.414	1.4	0.4142	7/16
60°	1.155	1.15	0.5774	5/8

Derive your own for any angle

Type any angle and the two constants come straight out of the triangle. Nothing is looked up.

Bend by bend

Nine bends, each one a rearrangement of the two constants above. The card is the whole formula; the link is the calculator that runs it.

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.

Silla de tres puntos

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, so it is the offset formula with the outer angle in it. See the three-point saddle calculator.

Silla de cuatro puntos

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 = finished height − mark from end

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 from a test bend on the bender take-up page (the second line, the first one run backward), and place the stub with the stub-up calculator.

Back-to-back and kick 90

second mark = back-to-back distance, measured from the back of the first 90 (pre-marked: height + distance − gain)

kick from the 90 = kick rise ÷ sin θ

A back-to-back sets two 90s a fixed distance apart, the second bent off the star; 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.

Offset rodado

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.

Doblez segmentado

per-bend angle = total ÷ number of bends

spacing = 2 × radius × tan(per-bend ÷ 2)

developed length = radius × total (in radians)

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.

Dobleces concéntricos

radiusₙ = inner radius + n × spacing

developed lengthₙ = radiusₙ × angle (in radians)

gain per run = spacing × angle (in radians)

Gain here is pipe each outer run needs — the opposite of a 90's gain, which is pipe saved.

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.

Preguntas

Do these formulas work in millimetres?: Yes, unchanged. None of them has a unit in it: the multiplier and the shrink factor are ratios, so a rise in inches gives marks in inches and a rise in millimetres gives marks in millimetres. A 250 mm rise at 30° needs marks 500 mm apart, exactly as a 10" rise needs them 20" apart.
Why does the shop say ×6 for 10° when the formula gives 5.759?: The shop figures are the numbers the trade says out loud, not a rounding rule. ×6 is a shade heavy at 10°; ×2.6, ×1.4 and ×1.15 are a shade light at 22.5°, 45° and 60°. For a mark that has to land, use the exact multiplier — every calculator on the site does.
Where is the take-up formula for my bender?: There is no formula for it. Take-up and gain come from the radius your shoe bends to, so they are stamped on the bender or measured with one test bend. The formula on this page only runs the stub-up both ways: mark = height − take-up, and take-up = height − mark.