Concentric bend calculator
Concentric bends carry several conduits around one corner on shared centres, each a fixed distance outside the last, so the group stays parallel and evenly spaced. Enter the inner radius, the spacing between runs, how many there are, and the angle of the turn; the calculator lists each run's radius, its developed length, and how much longer it is than the innermost.
Worked examples
Three conduits round a 90, 3" (76 mm) apart
Say three conduits turn 90°, the inner one on a 12" (305 mm) radius, spaced 3" (76 mm) apart. The inner run is 12 × (90° in radians) ≈ 18 7/8" (479 mm) of pipe (18.85 in). The middle run sits on a 15" (381 mm) radius, 15 × the same angle ≈ 23.56 in (23 9/16" (598 mm)); the outer on 18" (457 mm) ≈ 28.27 in (28 1/4" (718 mm)). Each step out adds 3 × (90° in radians) ≈ 4 11/16" (120 mm) of pipe — that constant gain is the same for every step because the spacing is constant.
A word of warning about the word: on a single 90, gain is the pipe you save by rounding the corner, and you subtract it. On a concentric group, "gain per run" is the extra pipe each run further out needs, and you add it. Opposite signs, same word — it is the trade's term for both, so this page uses it and says which one it means.
Three runs round a 90, 75 mm apart, metric job
The same group on a metric drawing: inner radius 11 13/16" (300 mm), runs 2 15/16" (75 mm) apart, a 90° turn (1.5708 radians). The inner run is 300 × 1.5708 = 18 9/16" (471 mm) of pipe; the middle, on 14 3/4" (375 mm), is 23 3/16" (589 mm); the outer, on 17 11/16" (450 mm), is 27 13/16" (707 mm). The gain per run is 75 × 1.5708 = 117.8 → 4 5/8" (118 mm), so the outer stick needs 9 5/16" (236 mm) more than the inner one.
Five runs round a 45, 2" (51 mm) apart, on a tight inner radius
A rack of five turns 45° round a column. The inner run is on an 8" (203 mm) radius and the runs are 2" (51 mm) apart. 45° is 0.785 radians, so the inner arc is 8 × 0.785 ≈ 6 5/16" (160 mm) and the gain per step out is 2 × 0.785 ≈ 1 9/16" (40 mm). The outer run, four steps out on a 16" (406 mm) radius, uses 16 × 0.785 ≈ 12 9/16" (319 mm) through the turn — twice the inner one, because its radius is twice as big. When you cut the five sticks, the outer one needs 4 × 1.571 = 6.28 → 6 5/16" (160 mm) more than the inner one just to get round the corner.
Where the runs start their turn
The part people miss: the runs do not all start bending at the same place along the rack. Concentric arcs share a centre, so each run's arc begins on the same radial line from that centre — which means the start of the bend is at the same position along the straight run for every pipe. Mark that line across the whole rack with a square before you bend anything, then work each pipe as its own segmented bend from that mark, on its own radius. Same bend count for all of them, wider spacing for each one further out.
Doing it
- Measure. The inner radius (the tightest the inside pipe can take, or what the drawing wants), the centre-to-centre spacing, how many runs, and the angle of the turn.
- Mark. A start-of-bend line across the whole rack. Then for each run, its own segmented layout from that line: same number of bends, its own spacing from the calculator's radius for that run.
- Line up. Inner run first. Each bend on its own mark.
- Bend. The same small angle at each mark, all in one plane. Then the next run out, on its wider spacing, the same number of times.
- Check. Lay them nested on the floor. The gaps should be the spacing all the way round. A gap that closes toward the outside means the outer run was bent on too tight a radius.
What went wrong
The gaps close up on the outside of the turn
What you see: even spacing going in, the outer runs crowding or touching the inner ones through the bend, even spacing again coming out.
Why: every run was bent on the same radius — usually the bender's own — instead of each on its own larger radius.
Fix: each run out needs the spacing added to its radius. On a hand bender that means a segmented bend for each run at a wider spacing between the small bends; a one-shot shoe radius cannot do it.
The outer run is short at the far end
What you see: all the sticks were cut the same length and the outer ones do not reach.
Why: the gain per run was ignored. A bigger radius over the same angle is more pipe, and that pipe has to come from somewhere.
Fix: cut each run longer than the one inside it by the gain the calculator lists, or bend from full sticks and trim after.
The turns start at different places
What you see: the runs are evenly spaced but the bends are staggered along the rack, so the group looks like it is peeling apart.
Why: each run's first mark was measured separately and they drifted, or a parallel-offset stagger was applied where none belongs.
Fix: one start-of-bend line squared across every pipe at once. Concentric bends share a centre and start together; the stagger is a parallel-offset thing.
The formula
Each run's radius grows by the spacing; its developed length is radius times the angle in radians:
radiusₙ = inner + n × spacing · developedₙ = radiusₙ × angle(rad) · gain = spacing × angle(rad)
Developed length is just how far you travel along a circle of that radius through the turn, which is radius times the angle in radians. Step the radius out by the spacing and the length grows by the spacing times that same angle — a fixed gain per run. Bend the inner one, then add the gain for each run further out.
Spacing and count only — no capacity
This tool lays out the geometry of the group: radii, lengths, and the gain between runs. It says nothing about how many conductors a raceway may carry or how a rack should be supported — those are code and engineering questions, not trigonometry, and they are not what this is for. Keep every run in the same plane so the group turns flat.
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:
The radii here are centreline radii you choose, so the bender only enters when it cannot make one of them: a hand bender bends at one fixed radius per shoe, so the inner run is at that radius and the outer runs are segmented to their larger radii. The developed lengths assume the pipe follows the arc; a shoe-radius 90 with straight tangents does not, so for the innermost run use the shoe's own gain and take-up (your own figures, from a test bend) rather than the arc length.
Preguntas
- What are concentric bends?
- Several conduits bent around the same corner on shared centres, so they stay parallel and evenly spaced the whole way round. Each run sits a fixed distance outside the last, which means each has a larger radius and takes a bit more pipe than the one inside it.
- Why is the outer conduit longer?
- Because it follows a bigger radius. Developed length is radius times the angle, so a larger radius over the same turn is more pipe. Each step out adds the spacing to the radius, which adds spacing times the angle in radians to the length — the gain the calculator lists per run.
- Which conduit do I bend first?
- The innermost, on the tightest radius, then work outward. Each successive run is the same shape on a larger radius, so once you have the inner one set, the rest follow by adding the spacing to the radius and the gain to the pipe length.
- Is a concentric bend the same as a parallel offset?
- They are cousins. A parallel offset keeps runs even through a step; a concentric bend keeps them even around a sweep. The offset uses a stagger along the pipe; the concentric bend uses a growing radius. Use the parallel offset calculator for the step and this one for the corner.