Segmented bend calculator
A segmented bend fakes a large-radius sweep with a run of small equal bends. Enter the total angle of the sweep, how many bends you want to split it into, and the radius of the curve you are after; the calculator gives the angle to pull at each bend, the spacing between them, and the developed length of the ideal arc.
Worked examples
A 90 on a 24" (610 mm) radius, nine bends
Say you need a 90° sweep on a 24" (610 mm) radius, made from 9 bends. Each bend is 90 ÷ 9 = 10°. The spacing is 2 × 24 × tan(5°) ≈ 4 3/16" (107 mm) between marks. The developed length is 24 × (90° in radians) ≈ 37 11/16" (958 mm) of pipe through the curve (the faceted chain is 37.80, a tenth of an inch or 2 mm over). Mark the first bend, step 4 3/16" (107 mm) for each of the next eight, and pull 10° at every mark in the same plane.
A 90 on a 600 mm radius, metric job
The same sweep drawn in metric: 90° on a 23 5/8" (600 mm) radius, nine bends of 10°. Spacing is 2 × 600 × tan(5°) = 104.99 → 4 1/8" (105 mm) between marks, so the last mark sits 8 × 105 = 33 1/16" (840 mm) from the first. The developed length is 600 × 1.5708 = 37 1/16" (942 mm) (the chain is 945, about 1/8" (2.4 mm) over).
A 45 on a 36" (914 mm) radius, five bends
A run has to sweep 45° round the corner of a tank on a 3' 0" (914 mm) radius so it clears the insulation. Five bends of 45 ÷ 5 = 9°. Spacing is 2 × 36 × tan(4.5°) = 5.67 → 5 11/16" (144 mm) between marks, and the arc uses 36 × 0.785 ≈ 28 1/4" (718 mm) of pipe. Nine degrees is a small pull, and the trap is the total: five bends each a degree over is a 50° sweep. Check the finished angle against a square, not each bend against the shoe.
The same 90, four different counts
How many bends is a judgement — here is what the judgement costs. The same 90° on a 24" (610 mm) radius:
| Bends | Each | Spacing | Pipe used (the chain) | Reads as |
|---|---|---|---|---|
| 3 | 30° | 12 7/8" (327 mm) | 38 9/16" (980 mm) (38,58 in) | Three obvious corners. Fine buried in a wall, ugly on show. |
| 6 | 15° | 6 5/16" (161 mm) | 37 15/16" (963 mm) (37,92 in) | Facets you can see if you look. Common for a rack in a ceiling. |
| 9 | 10° | 4 3/16" (107 mm) | 37 13/16" (960 mm) (37,80 in) | Reads as a curve from a few feet (a metre) away. |
| 18 | 5° | 2 1/8" (53 mm) | 37 3/4" (958 mm) (37,72 in) | Smooth, and eighteen chances to be a degree out. |
The ideal arc is 37.70 in (37 11/16" (958 mm)) of pipe, and that is the figure the calculator reports as the developed length. The faceted chain you actually bend is always a little longer than the arc it approximates — its length is 2 × bends × radius × tan(half the per-bend angle) — and the fewer the bends the longer it gets: nearly an inch (22 mm) over on the three-bend row, two hundredths of an inch (under 1 mm) on the eighteen. So more bends is not only smoother, it is marginally less pipe; below about six bends, lay the marks out from the chain figure rather than the arc.
Laying it out
- Measure. The radius the sweep has to follow, the total angle, and where along the pipe the curve should start.
- Mark. A start mark. Then step the spacing along the pipe for each bend after the first, so a 9-bend sweep has 9 marks over 8 spacings. The last mark should sit (bends − 1) × spacing from the first — if it does not, a step was miscounted.
- Line up. Arrow on the first mark. A pencil line down the pipe to keep the plane.
- Bend. The per-bend angle, gently, at each mark in turn without flipping the pipe. Small angles are easy to over-pull; go to the mark and no further.
- Check. The finished sweep against a square or a template cut to the radius. If the total is over, the shoe was read generously on each bend; if it wanders sideways, one bend left the plane.
What went wrong
The sweep finishes past 90
What you see: each bend looked right on the shoe and the whole thing is 95° or more.
Why: a degree of over-pull per bend, times the count. On small angles the shoe's marks are coarse and springback is small, so every bend tends to come out slightly heavy.
Fix: pull to the mark, not past it. Check the running total every three or four bends against a square, and trim the next ones.
It corkscrews
What you see: a sweep that curves in two directions and will not lie flat.
Why: the pipe rolled a little in the shoe between bends, so the later bends are in a different plane from the first.
Fix: a pencil line along the top of the pipe, checked straight up before every pull. Do not take the pipe out of the bender between bends if you can slide it instead.
The radius is wrong even though the angle is right
What you see: a clean 90 that does not fit the space it was drawn for.
Why: the spacing was measured wrong, or the bend count and spacing came from different radii. Spacing sets the radius; the angle only sets the total turn.
Fix: spacing comes from the calculator for the radius and count together. Change either and the spacing changes.
The formula
The per-bend angle splits the total; the spacing comes from the chord of that small angle on the radius:
per-bend = total ÷ bends · spacing = 2 × radius × tan(per-bend ÷ 2) · developed = radius × total(rad)
Each small bend turns the pipe by the per-bend angle, and the straight length between two adjacent bends is the chord that subtends that angle on the radius, which is 2 × radius × tan of half the angle. String enough of those chords together and they trace the arc; the arc's own length, radius times the angle in radians, is the developed length — the pipe the ideal curve would use. The chain of chords is slightly longer than the arc it cuts, 2 × bends × radius × tan(half the per-bend angle), and it closes on the arc as the count goes up.
Smoothness is a judgement, not a spec
bentright will work any bend count you give it — the right one depends on how the run will be seen and how tight the radius is. Small angles at close spacing read as a clean curve; large angles at wide spacing show the facets. There is no code number here and no single correct answer, only the geometry and your eye. Keep every bend in one plane, or the sweep corkscrews.
Which bender these numbers assume — and how to adjust
The geometry belongs to the angle, not the tool. What the tool changes — its reference marks, its take-up and gain, its springback — is yours to read off the shoe or prove on scrap, never a table here (the four test bends). For this bend:
Each small bend is pulled on the arrow to the same partial angle, so this leans harder on the degree scale than any other bend on the site: ten bends each a degree over is a sweep ten degrees too tight. Most hand-bender scales cannot resolve a 9° pull. In practice a segmented bend is a mechanical-bender or hickey job, with the angle read off a level or a protractor each time; if you must do it on a hand bender, make a test sweep in scrap first and adjust the count.
Questions
- What is a segmented bend?
- A large-radius curve made from many small bends instead of one. A hand bender cannot pull a wide sweep in one shot, so you split the total angle into a series of equal bends spaced evenly along the pipe. Enough of them and the run reads as a smooth arc.
- How many bends should I use?
- More bends give a smoother, truer curve; fewer are quicker but show the facets. It is a trade-off, not a rule — a big-radius sweep in sight might want a bend every few degrees, while one buried in a wall can be coarser. Try a count and read the spacing and per-bend angle the calculator gives, then judge it.
- What is the developed length?
- The length of pipe the ideal curve uses, radius times the total angle in radians. It is the figure to check you have enough pipe. The faceted chain you actually bend is slightly longer — 2 × bends × radius × tan(half the per-bend angle) — and the difference grows as the bend count falls: on a 24" (610 mm) radius, 90 degree sweep it is two hundredths of an inch (under 1 mm) at eighteen bends and nearly an inch (22 mm) at three.
- How do I space the bends?
- Evenly, at the spacing the calculator gives, which is 2 × radius × tan(half the per-bend angle). Mark the first bend, step that spacing along the pipe for the next, and so on, bending the same small angle at each mark. Keep every bend in the same plane or the curve wanders.