Bending, from zero

The bender and its marks

Before any arithmetic, learn the tool. A hand bender is a curved shoe on a handle. The pipe lies in the shoe, a hook at the front holds it, you put your foot on the pedal at the back and pull the handle toward you. The pipe follows the curve of the shoe, and how far you pull is the angle you get. Everything else is marks cast into the shoe that tell you where the bend will land.

• Arrow. The mark you use most. For a stub-up and for the first bend of an offset, your pencil mark on the pipe lines up with the arrow.
• Star (or a line on the back). Marks the back of a finished 90. You use it when you need the back of a bend to land somewhere — a back-to-back, mostly.
• Notch (or teardrop). On many shoes it is where the centre of a saddle bend lands. Some benders mark it differently; read yours.
• Degree marks. Along the shoe, showing the angle you have pulled so far: 10°, 22.5°, 30°, 45°, 60° on most. You read the angle against the pipe, not the floor.
• Take-up. A number stamped on the shoe, one per pipe size. It is how much length the sweep of a 90 eats. It belongs to that bender; another make has another figure, and there is no chart that beats reading it off the tool.

Arrow for stubs and offsets. Star for the back of a 90. Notch for the centre of a saddle. Take-up: read it off the shoe.

Next: the 90° stub-up →

The 90° stub-up

The first bend to learn, and the one that teaches you to trust the tool. A stub-up is a single 90 to a set height: the pipe runs along, turns up, and the leg stands to the height you asked for. The catch is that the bend is not a sharp corner — it sweeps a radius, and that sweep uses up some pipe. That used-up length is the take-up. So the mark does not go at the height; it goes at the height less the take-up, measured from the free end.

mark from the end = finished height − take-up

Hook the pipe, slide the arrow to the mark, foot on the pedal, pull until the pipe reads 90° against the shoe. Then measure the finished leg to the back of the bend. If it lands on the height, your take-up is right and everything else on this site will land too. If every stub is off by the same amount, the take-up figure is off by that amount — the take-up page finds the real one from one test bend.

Next: the offset and the multiplier →

The offset and where the multiplier comes from

An offset is a pair of matching bends that jog the run past something and bring it back level. The height it steps is the rise. The two bends are the same angle, pulled in opposite directions, and the question is always the same: how far apart do the two marks go?

Look at the sloped piece of pipe between the two bends. With the rise and the flat run it makes a right triangle, and the sloped pipe is the long side — the hypotenuse. From school: sin θ = opposite ÷ hypotenuse. The opposite side is the rise. Turn it round and the pipe between the marks is rise ÷ sin θ. That is the whole multiplier. It is not a table somebody wrote down; it is one triangle.

between marks = rise ÷ sin θ

At 30°, sin θ is exactly one half, so rise ÷ ½ is rise × 2 — the famous "times two". At 45° it is ×1.414, which the shop rounds to 1.4. At 22.5° it is ×2.613, called 2.6. Those rounded figures are the shop rule; the exact ones come out of the triangle, and the multipliers page has both for every angle. Lay out: mark 1 where the offset should start, mark 2 the multiplied distance further along, arrow on each, bend the same angle each time but flip the pipe between them so the second bend comes back level.

Next: shrink →

Shrink — why the run comes up short

Bend an offset into a pipe and the far end moves back toward you. It has to: the sloped piece between the bends is longer than the flat ground it covers, and that extra length came out of the end. That lost reach is the shrink. It is the second thing every offset needs and the first thing a new apprentice forgets — the bend looks perfect and the coupling is half an inch short of the box.

The arithmetic is the same triangle again: shrink is the hypotenuse minus the run, so per inch of rise it is 1 ÷ sin θ − 1 ÷ tan θ. You do not need to carry that — carry the shop figure: at 30° it is about a quarter inch for every inch of rise. A 6 in offset at 30° shrinks about 1 1/2 in (the exact figure is 1 5/8). What matters more than the decimals is where it goes: measure to where the offset should start, add the shrink, and put mark 1 there. The far end then reaches.

measure → add the shrink → mark 1 → then mark 2

Next: the saddle is two offsets →

The three-point saddle is two offsets

When a pipe crosses your run you go over it, not past it: a hump with a centre bend on the crown and two smaller bends either side that bring the run back down level. That is a three-point saddle. It looks like a new bend; it is not. Cover the right half with your hand and the left half is an offset — a rise (the depth) at the outer angle. The right half is the same offset run backward. So the saddle is two offsets meeting at the centre, and the centre bend is the two outer angles added together.

outer angle = centre ÷ 2 · centre to each outer = depth ÷ sin(outer)

The usual saddle has a 45° centre, so the outers are 22.5° and the multiplier is the 22.5° one, ×2.6. Mark the crown — plus the shrink, same as an offset — then the multiplied distance each side of it. Bend the centre first, on the notch (or the arrow if your shoe says so). Then flip the pipe and pull each outer on the arrow, the opposite way, so the run comes back down flat. Bend the outers before the centre and the crown wanders; centre first keeps it where you marked it. The saddle calculator does the numbers and prints the three lines to follow at the bender.

Next: reading a tape in sixteenths →

Reading a tape in sixteenths

Every number this site gives you ends up on a tape, and a tape does not speak decimals. The inch is cut into sixteenths, and the little lines have heights so you can find your place without counting all sixteen: the tallest inside line is the half, the next two down are quarters, the eighths come next, and the stubby ones are the odd sixteenths.

To turn a decimal into a tape reading, multiply the part after the point by 16 and round: 0.268 × 16 = 4.3, so 4 sixteenths, which is 1/4. 0.49 × 16 = 7.8, so 8 sixteenths, which is 1/2 — 8.49 in is 8 1/2 on the tape. Nobody marks 17/64 on a job; a sixteenth is as fine as a pencil line, which is why every readout on this site rounds to it and shows the decimal small underneath. Adding across a mark is the same game: 5 1/4 + 3/8 is 5 + 4/16 + 6/16 = 5 10/16 = 5 5/8. The tape fractions page has a drill that keeps going until this is reflex.

decimal × 16 → round → that many sixteenths → reduce