Piping
Pipe bending calculator
In short
A bend joins two straight legs with an arc of radius R and angle θ. Tangent T = R tan(θ / 2), arc A = R × θ (rad), gain G = 2T − A: the cut length is L = a + b − G, with a and b the end-to-vertex dimensions, and the bend starts d = a − T from end 1.
Calculation
Example calculated with the tool’s default values.
Inputs
- Pipe
- DN25 · 33.7 × 3.2 mm
- Bend radius (centreline)
- 100 mm
- Bend angle
- 90°
- End to vertex (leg 1)
- 300 mm
- Vertex to end (leg 2)
- 300 mm
- Springback
- Not included
Results
- Cut length
- 557.1 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Bend start mark (from end 1)
- 200.0 mm
- Bend end mark (from end 1)
- 357.1 mm
- Developed arc length
- 157.1 mm
- Take-out (tangent)
- 100.0 mm
- Gain
- 42.9 mm
- Approx. wall at extrados
- 2.78 mm
- Approx. wall at intrados
- 3.78 mm
- Extrados thinning
- 13.2%
- Intrados I factor (B31.3)
- 1.101divides S E W in the required thickness
- Extrados I factor (B31.3)
- 0.928
- Ovality not computed: check it (ASME B31.3 § 332.2.1: diameter difference ≤ 8 % for internal pressure, 3 % for external).
- Springback not included: measure it on a test bend (“Springback” option).
Step-by-step calculation
Tangent
T = R tan(θ / 2)
100.0 × tan 45.0° = 100.0 mm
Arc
A = R × θ (rad)
100.0 × 1.5708 = 157.1 mm
Gain
G = 2T − A
200.0 − 157.1 = 42.9 mm
Bend start
d = a − T
300.0 − 100.0 = 200.0 mm
Cut length
L = a + b − G
300.0 + 300.0 − 42.9 = 557.1 mm
Extrados
t_ext = t R / (R + D/2 − t/2)
3.20 × 100.0 / 115.25 = 2.78 mm
Intrados
t_int = t R / (R − D/2 + t/2)
3.20 × 100.0 / 84.75 = 3.78 mm
I factors
I = (4R/D ∓ 1) / (4R/D ∓ 2)
int 1.101 ; ext 0.928
How to use it
- Pick the pipe: outside diameter and wall thickness.
- Enter the bend radius, measured on the centreline, and the bend angle (1° to 179°).
- Enter the end to vertex (leg 1) and vertex to end (leg 2) dimensions: the vertex is where the axes intersect.
- To allow for springback, enter the angle set on the machine for a test bend and the angle measured after springback.
- Read the cut length.
Frequently asked questions
What is the pipe bending formula?
The pipe centreline follows two straight legs joined by an arc of radius R and angle θ. Tangent from vertex to arc start: T = R tan(θ / 2). Arc: A = R × θ, θ in radians. Gain: G = 2T − A. Cut length: L = a + b − G. Bend start mark from end 1: d = a − T; the bend ends at d + A.
What is the bend allowance and cut length for a 90° tube bend?
33.7 × 3.2 pipe, 100 mm radius, 90° angle, 300 and 300 mm to the vertex: tangent 100.0 × tan 45.0° = 100.0 mm, developed arc length (bend allowance) 100.0 × 1.5708 = 157.1 mm, gain 200.0 − 157.1 = 42.9 mm. Cut length: 300.0 + 300.0 − 42.9 = 557.1 mm. Bend starts 300.0 − 100.0 = 200.0 mm from end 1.
How do I work out wall thinning on a pipe bend?
The approximate calculation keeps the cross-section, with no stretch of the centreline: extrados t_ext = t R / (R + D/2 − t/2), intrados t_int = t R / (R − D/2 + t/2). In the example: 3.20 × 100.0 / 115.25 = 2.78 mm at the extrados and 3.20 × 100.0 / 84.75 = 3.78 mm at the intrados. ASME B31.3 § 304.2.1 I factors are I = (4R/D ∓ 1) / (4R/D ∓ 2): 1.101 at the intrados, 0.928 at the extrados.
How do I allow for springback when bending pipe?
No published general value is reliable: measure springback on a test bend. The piece bent to θm on the machine springs back to θr; with a ratio K = θr / θm constant for the same pipe, radius and tooling, the machine angle needed for θ is θ / K. Sample entry: 90° on the machine, 87° measured after springback.
Limits
Indicative results. Neutral axis assumed at the middle of the pipe. Ovality not computed: check it (ASME B31.3 § 332.2.1: diameter difference ≤ 8 % for internal pressure, 3 % for external). Below 1.5 D, mandrel bending advised; intrados I factor unreliable for R ≤ D. The radius must exceed half the diameter.
Sources
- Géométrie du cintrage : Tangente R tan(θ/2), arc R θ, gain 2T − A
- Amincissement / épaississement : Stressman Engineering, mémo 100103-TM-001 rév. 2 « Induction bends », § 2.2 (link)
- Facteurs I intrados / extrados: ASME B31.3, § 304.2.1
- Ovalisation admise: ASME B31.3, § 332.2.1 (8 % / 3 %)