Estimates only. Check measurements, product labels and local building codes before you buy or build.
How the Mitered Elbow Calculator works
A mitered (segmented) elbow is a turn built from straight pipe: pieces with angled ends welded together. Give the elbow angle, the centerline radius, the pipe's outside diameter and the number of welds, and the calculator gives the cut angle, the length of every piece on the centerline, the long side (heel) and the short side (throat), and the elbow's take-out.
Each weld turns the pipe by the elbow angle ÷ the number of welds, so every cut face is angled θ ÷ (2N) off square. N welds make N + 1 pieces: two end pieces and N − 1 middle segments. A middle segment is 2R × tan(cut angle) on the centerline, 2(R + OD/2) × tan(cut angle) on the long side and 2(R − OD/2) × tan(cut angle) on the short side; an end piece is half of each. The take-out is R × tan(θ ÷ 2), like any elbow.
Example: a 90° elbow with 2 welds (3 pieces), 12" radius, 4.5" OD (4" pipe). Cut angle = 90 ÷ 4 = 22.5°, and tan 22.5° = 0.4142. Middle segment: centerline 2 × 12 × 0.4142 = 9.94" (9 15/16"), long side 2 × 14.25 × 0.4142 = 11.81" (11 13/16"), short side 2 × 9.75 × 0.4142 = 8.08" (8 1/16"). Each end piece is half: 4.97" (5"), 5.90" (5 7/8") and 4.04" (4 1/16"). Take-out = 12 × tan 45° = 12".
Lengths are along the pipe wall between cut lines, and end pieces are measured from the square line at the tangent point, so add any straight length you want past it. Fit-up gaps and wrap-around layout are not included. The radius has to be more than half the OD, or the throat would have no length. More welds give a smoother turn with shorter pieces.
Frequently asked questions
How do you calculate the cut angle of a mitered elbow?
Cut angle = elbow angle ÷ (2 × number of welds). A 90° with 2 welds: 90 ÷ 4 = 22.5° off square on every cut face. With 1 weld it is 45°, with 3 welds 15° and with 4 welds 11.25°.
What is the cut angle for a 3-piece 90 degree mitered elbow?
22½°. Three pieces means two welds, so 90 ÷ (2 × 2) = 22.5°. A 4-piece 90 (3 welds) uses 15° cuts and a 5-piece 90 (4 welds) 11¼° cuts.
How long is each segment of a mitered elbow?
On the centerline, a middle segment is 2 × radius × tan(cut angle) and each end piece half that. For the long and short sides, use radius + half the OD and radius − half the OD instead of the radius. A 90° with 2 welds, 12" radius and 4.5" OD: middle segment 9 15/16" on the centerline, 11 13/16" on the long side, 8 1/16" on the short side.
What is the take-out of a mitered elbow?
Radius × tan(elbow angle ÷ 2), the same as a bent or forged elbow of that radius. For a 90° that is the radius itself, 12" for a 12" radius; for a 45° it is 0.414 × the radius.