Bender deduct and gain
The deduct puts the mark in the right place: for a 90, the mark goes at the leg length minus the deduct, measured from the end. The gain sizes the stick: a bent 90 uses less pipe than its two legs added up, so the cut length is leg A plus leg B minus the gain. Type your own bender's figures above and you get both — the mark and the cut — in inches or millimetres.
Two numbers, two jobs
Most hand benders carry two figures per pipe size. They answer different questions, and mixing them up is how a stick ends up a couple of inches wrong with a perfect bend in it.
- Deduct (take-up): where the bend starts. A 90 does not turn on a point; it sweeps round a radius, so the leg ends up longer than the distance from the end to the mark. Subtract the deduct from the leg you want and put the arrow on that. The stub-up calculator is this and nothing else.
- Gain: how much pipe the curve saves. Two legs measured to the back of a square corner add up to more than the pipe it takes to make them, because the bend cuts the corner. The gain is that difference. It only matters when the length of the stick matters — a pre-cut piece, a 90 between two boxes, a take-off.
Both depend on the bender and the pipe size, and both drift with wear and with the pipe you are bending. The figures in the examples below are examples — "say your bender is stamped …" — not anybody's chart. Use yours.
On the bender
A 90 that has to land on two measurements, from a stick cut to size first:
- Measure. Both legs to the back of the 90 — the outside of the bend, where the two outside surfaces would meet if the corner were square.
- Cut. Cut the stick to leg A plus leg B minus your gain. Ream it before you bend, not after.
- Mark. From the end of leg A, measure leg A minus your deduct and mark all the way round the pipe.
- Bend. Arrow on the mark, leg A toward the hook side as you would for any stub, and bend to 90°.
- Check. Measure both legs to the back. If both are long by the same amount, your gain is small; if leg A is right and leg B is off, the gain is the figure to change.
Worked examples
A 90 between a box and a ceiling run
You need a leg of 14" (356 mm) down to a box and 30" (762 mm) along the ceiling to the next fitting, both to the back of the bend. Say your bender is stamped with a deduct of 5" (127 mm) and a gain of 2 5/8" (67 mm) for this pipe. Cut the stick at 14 + 30 − 2 5/8 = 41 3/8" (1051 mm). Mark at 14 − 5 = 9" (229 mm) from the end of the short leg, arrow on the mark, bend 90°. Both legs land without a trim.
A metric job, 400 mm and 900 mm
Legs of 15 3/4" (400 mm) and 35 7/16" (900 mm), and you have measured your bender at a deduct of 125 mm and a gain of 65 mm for this pipe. Cut at 400 + 900 − 65 = 1235 mm. Mark at 400 − 125 = 275 mm from the end of the 15 3/4" leg. No fractions anywhere — the metric version of this job is the easy one.
No gain to hand: the estimate
The gain is not on this bender and there is no time for a test bend. The pipe measures 3/4" (19 mm) across, and the deduct is 5" (127 mm). By geometry alone the gain is about 0.429 × 5 + 0.785 × 0.75 ≈ 2 3/4" (69 mm). Good enough to count sticks for a take-off; for cutting a finished piece, cut 1/4" (6.4 mm) long and trim, then measure the real gain off that bend.
Voir le calcul derrière l’estimation
Mesurée jusqu’au dos du coude, chaque branche est sa partie droite plus le rayon à l’axe R plus la moitié du diamètre extérieur (DE). Le conduit lui-même, ce sont les deux parties droites plus l’arc, πR/2. Donc gain = 2R + DE − πR/2 = 0,429R + DE. Un coude qui commence sur sa marque a une déduction de R + DE/2, donc R = déduction − DE/2, ce qui donne gain ≈ 0,429 × déduction + 0,785 × DE.
Measure your gain in two minutes
One test bend gives you both numbers for that bender and that pipe size — the measure your bender page has the full procedure and a table to keep them in.
- Cut. A scrap piece to a round length — 24" (610 mm) or 23 5/8" — square and reamed.
- Mark. A line all the way round at the middle.
- Bend. Arrow on the line, a clean 90, checked with a square or level.
- Measure. Both legs to the back of the bend. Gain = leg A + leg B − the length you cut. Deduct = the leg on the arrow side − the distance from that end to your mark.
- Write it down. On the bender in paint pen, and on the take-up page so the calculators here fill it in for you.
What went wrong
Leg A right, leg B short
What you see: the mark was right, the stick was cut short, the far leg does not reach.
Why: the gain was used as the deduct, or the gain for a bigger pipe size was used — a bigger shoe has a bigger radius and a bigger gain.
Fix: the deduct only ever moves the mark; the gain only ever changes the cut length. Read both off the same row for the pipe in your hand.
Both legs long by the same amount
What you see: a tidy 90, both legs a little over.
Why: the legs were measured to the inside of the bend, or to the centreline, not to the back.
Fix: deduct and gain are both figures for legs measured to the back of the bend. Measure every leg the same way — see measuring and marking.
Right on one bender, wrong on the next
What you see: the same numbers that worked all week come out off by a quarter.
Why: a different bender, or a worn shoe. Deduct and gain belong to one bender and one pipe size.
Fix: a test bend on the bender you are using. Two minutes against a stick of scrap.
Questions
- What is the difference between deduct and gain?
- The deduct (take-up) tells you where to put the mark: stub height minus the deduct, measured from the end. The gain tells you how long to cut the stick: a 90 with two legs measured to the back of the bend uses less pipe than the two legs added together, and the gain is how much less. One places the bend, the other sizes the stick.
- Is take-up the same as deduct?
- Yes. Take-up, deduct and deduction are three names for the same figure: the amount you subtract from the stub height to find the mark for a 90. Different benders and different shops use different words for it.
- Where do I find the gain for my bender?
- Many benders have it stamped or printed on the shoe or handle beside the deduct, per pipe size. If yours does not, measure it: cut a piece to a known length, bend a 90 in the middle, measure both legs to the back of the bend and subtract the stick length from their sum. A 24" (610 mm) stick marked at 12" (305 mm) and bent there, with legs of 17" (432 mm) and 9 1/2" (241 mm), has a gain of 2 1/2" (64 mm) (17 + 9 1/2 − 24) and a deduct of 5" (127 mm) (17 − 12).
- Why does the estimate from the outside diameter not match my bender exactly?
- The estimate assumes the bend starts exactly on the mark and follows a perfect radius. Real pipe stretches and springs back a little, and the stamped figures are measured off real bends. The estimate is good for planning a take-off; for cutting, use the figure on your bender or one you measured.
- Does gain matter on a single stub-up?
- Not for the mark — the deduct does that. It matters when both legs have to land on a figure: a 90 between two boxes, a pre-cut piece, or a take-off where you are counting sticks. Then the cut length is leg A plus leg B minus the gain, and cutting to it first means leg B comes out right with nothing to trim.