Pipe Formulas

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

Online Pipe Formula Calculator

Make Shortcut to this Calculator on Your Home Screen?

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

Pipes

Moment of Inertia

Moment of inertia can be expressed as

I = π (d_o⁴ - d_i⁴) / 64
≈ 0.0491 (d_o⁴ - d_i⁴) (1)

where

I = moment of inertia (in⁴)

d_o = outside diameter (in)

d_i = inside diameter (in)

Section Modulus

Section modulus can be expressed as

S = 0.0982 (d_o⁴ - d_i⁴) / d_o (2)

where

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

A_m = π (d_o² - d_i²) / 4 (3)

where

A_m = transverse metal area (in²)

External Pipe Surface

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

A_o = π d_o / 12 (4)

where

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

Internal Pipe Surface

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

A_i = π d_i / 12 (5)

where

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

Transverse Internal Area

Transverse internal area can be expressed as

A_a = 0.7854 d_i² (6)

where

A_a = transverse internal area (in²)

Circumference External

External circumference can be expressed as

C_e = π d_o (7)

where

C_e = external circumference (in)

Circumference Internal

Internal circumference can be expressed as

C_i = π d_i (8)

where

C_i = internal circumference (in)

Estimating Pipe Circumference and Section Area

Nominal Pipe Size (in)	Circumference (in)	Section Area (sq.in.)
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