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Pipe Formulas

Pipe and Tube Equations - moment of inertia, section modulus, traverse metal area, external pipe surface and traverse internal area - imperial units

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Online Pipe Formula Calculator

outside diameter (in)

inside diameter (in) - (default values: STD 4 inches - Carbon, Alloy and Stainless Steel Pipes - ASME/ANSI B36.10/19

The calculator is based on the piping formulas and equations below.


Moment of Inertia

Moment of inertia can be expressed as

I  = π (do4 - di4) / 64
   ≈ 0.0491 (do4 - di4)                            (1)


I = moment of inertia (in4)

do = outside diameter (in)

di = inside diameter (in)

Section Modulus

Section modulus can be expressed as

S  = 0.0982 (do4 - di4) / do                            (2)


S = section modulus (in3)

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.

Transverse Metal Area

Transverse metal area can be expressed as

Am  = π (do2 - di2) / 4                              (3)


Am = transverse metal area (in2)

External Pipe Surface

External pipe or tube surface per ft of length can be expressed as

Ao  = π do / 12                              (4)


Ao = external  pipe surface area (ft2 per ft pipe)

Internal Pipe Surface

Internal pipe or tube surface per ft of length can be expressed as

Ai  = π di / 12                            (5)


Ai = internal  pipe surface area (ft2 per ft pipe)

Transverse Internal Area

Transverse internal area can be expressed as

Aa  = 0.7854 di2                       (6)


Aa = transverse internal area (in2)

Circumference External

External circumference can be expressed as

Ce  = π do                      (7)


Ce =  external circumference (in)

Circumference Internal

Internal circumference can be expressed as

Ci  = π di                       (8)


Ci =  internal circumference (in)

Estimating Pipe Circumference and Section Area

Nominal Pipe Size
Section Area
1/4 0.785 0.049
3/8 1.178 0.110
1/2 1.571 0.196
3/4 2.356 0.442
1 3.142 0.785
1 1/4 3.927 1.227
1 1/2 4.712 1.767
2 6.283 3.142
2 1/2 7.854 4.909
3 9.425 7.069
3 1/2 11.00 9.621
4 12.57 12.57
5 15.71 19.64
6 18.85 28.27
8 25.13 50.27
10 31.42 78.54
12 37.70 113.1
15 47.12 176.7
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