MITER BEND Formula to Calculate Length, Angle of Cut, Weight, and Cut-back of the Miters?

In the Piping and Pipeline Engineering field, Miter Bend plays an important role because standard Elbows are not easily available and economical for larger pipe sizes. Site Engineer or the Fabrication supervisor is responsible for the perfect delivery of the joints made for the miter bend.
This article will provide detailed calculation procedures for finding out the required dimensions, angles of cut, and weight of the pipe.

What is a Miter Bend?

A Miter Bend or Miter Elbow is prepared by mitering (angle cutting) and welding pipe ends of the cut-pieces, usually at a 45° and 90° to form a corner. There are two types of miter bend, one non-perpendicular bend & another is 3-D bend. Miter Elbow/Bend is made from miter cut pieces of pipe. The Miter pieces also called gores, There are two end gores and two middle gores in a 4-piece Miter bend.

Miter Bend/Elbow
Fig. 1: Miter Bend/Elbow

Standards Associated with Miter Bend

AWWS (American Water Work Association)

For sizing and number of cuts/miter.

ASME B16.9

For end preparation of the miters

Note: according to ASME B 31.3, the number of the miters is restricted to a maximum of 5.

Important Points about Miter Bend

  • Miter bends are not standard fittings.
  • It is also called fabricated bend.
  • Highly skilled welders and fitters are required for perfect miter bend preparation.
  • Used mainly in general services (category “D” fluid).
  • If used in process lines then above 14” pipe size.
  • Used above 6” for utility lines.
  • Miter bend can be fabricated with 2, 3, 4, & 5 miters.
  • The numbers of cut will be a maximum of 5.

The numbers of miters will be decided according to the pressure and temperature of the line.
2. Application size range can vary from company to company.

Limitations of Miter Bend

  • Poor strength because of the more number of joints.
  • Higher pressure drop.
  • Higher turbulence.
  • Higher risk of corrosion because of more numbers of weld joints.
  • Less strength.
  • Not suitable for pigging.
  • High skilled manpower required.

Advantages of Miter Bend

  • Low cost.
  • No thinning required
  • It can be made at the site or in the workshop.

Inputs Required for Calculation

Pipe/Line SizeSchedule NumberMaterial TypeBend AngleNumber of CutRadius of Bend
8″SCH 120CS (Carbon Steel)9032.5 D
Table No. 1
Note: D = Pipe/Line size

Steps for Calculation

Step-1: Write down the available data(refer to Table No. 1)

We have,

D = 8”,     OD (Outer Diameter) of pipe =  219 mm
Schedule- SCH120
Material- CS (Carbon Steel)
Bend Angle = 90°
No. of cuts = 4
R = 2.5 D = 2.5*8*25.4 = 508 mm

Step-2: As per the number of cuts, Sketch the drawing as below (refer to Fig. 2)

Sketch of Miter Bend for Calculation
Fig. 2: Sketch of Miter Bend for Calculation

Step-3: Find the Angle of Cut (refer to Fig. 2 for all the steps)

We know,

Step-4: Find the Center Line Length (CL1) of the First Miter

We know from Pythagoras formula,

Important Note:

  1. The first and last miter always will be of the same length at each point.
  2. Except for the last miter, all the miter’s length will be double of the first miter at every point.


            CL2 = CL1 * 2 = 272 mm
= CL1 * 2 = 272 mm
            CL4 = CL1 = 136 mm

Step-5: Calculate Inside and Outside Radius (IR & OR) of the bend.

We know from fig. 2,

Step-6: Calculate the Inside Length (IL1) of the First Miter.

We know from Pythagoras formula,


            IL2 = IL1 * 2 = 214 mm
= IL1 * 2 = 214 mm
            IL4 = IL1 = 107 mm

Step-7: Find out the Outside Length (OL1) of the First Miter

We know from Pythagoras formula,


            OL2 = OL1 * 2 = 330 mm
= OL1 * 2 = 330 mm
            OL4 = OL1 = 165 mm

Step-8: Find the “Length of Pipe required” for the Miter Bend.

Length of pipe required = CL1 + Cutting allowance + CL2 + Cutting allowance + CL3 + Cutting allowance + CL4
Note- Cutting allowance depends upon the cutting method used, we are assuming 5 mm, refer to Fig. 3.

         L = 136+5+272+5+272+5+136
        L = 831 mm

Calculated Dimensions for Miter Bend
Fig. 3: Calculated Dimensions for Miter Bend

Step-9: Calculate the Weight of the Pipe.

Check the Plain End Mass in the code-book under the code “ASME B 36.10 for 8” SCH 120 Pipe (refer to Fig. 4).

Part of Table 1 of ASME B 36.10M-2015
Fig. 4: Part of Table 1 of ASME B 36.10M-2015

Plain End mass is given 90.44 kg/m as per ASME B 36.10 M
find the weight using the following formula-

Weight of the Pipe = Plain End Mass * Length of Pipe ( in meter)

Weight (W) = 90.44 * 0.831 = 75 kg.

Step-10: Get the Cut-back (optional).

Cut-back = CL1 – IL1

Cut-back = 136 – 107 = 29 mm

Few more useful resources for you.

Piping Elbows vs Bends: A useful literature for piping engineers
Piping Elbow or Bend SIF (Stress Intensification Factor)
Tee Connection: A short literature for piping engineers
Technical requirements for Pipes & Fittings for preparation of Purchase Requisition
“Pipe Coupling”-A short Introduction for the piping professionals
Comparison of Pipe and Tube (Pipe Vs Tube)
Details about Spectacle Blind and Spacers

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Rehan Ahmad Khan

I am a graduate in Mechanical Engineering and have worked in automotive aftermarket industry as a Service Engineer before. But there was a spark in me to do creative work which led me to explore opportunities in design world. So, i left my previous job where I had great experience, and decided to enter the energy industry. Later on, enrolled for the “Post Graduation Diploma in Piping Engineering” and through which I got the skills that were required to meet the gap between the industry and my technical skills. I am still exploring this industry and having a great experience. In the process felt to share my knowledge with the other Piping Engineers and as a result, I am here with you.

3 thoughts on “MITER BEND Formula to Calculate Length, Angle of Cut, Weight, and Cut-back of the Miters?

  1. I am Mechanical Piping & Pipeline Supervisor Engineer with more than 13 years experience relevant in Oil & Gas Indusry EPC Projects.
    I am also Hydraulic Engineer.

  2. Hello, i Wanna ask about number of cut and number of cuts what a different ?
    if i wanna make Elbow 90deg 1200mm for 5 pcs segmented is meaning how many number of cut and cuts ?
    Thanks ,

  3. How to do this calculation below

    The length of pipe to be cut of 3/4″ pipe that has a 90 and a 45 at each end is _______.

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