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
The calculator is based on the piping formulas and equations below.
Moment of Inertia
Moment of inertia can be expressed as
I = π (d_{o}^{4}  d_{i}^{4}) / 64
≈ 0.0491 (d_{o}^{4}  d_{i}^{4}) (1)where
I = moment of inertia (in^{4})
d_{o} = outside diameter (in)
d_{i} = inside diameter (in)
Section Modulus
Section modulus can be expressed as
S = 0.0982 (d_{o}^{4}  d_{i}^{4}) / d_{o} (2)
where
S = section modulus (in^{3})
Section modulus is a geometric property for a given crosssection used in the design of beams or flexural members.
Transverse Metal Area
Transverse metal area can be expressed as
A_{m} = π (d_{o}^{2}  d_{i}^{2}) / 4 (3)
where
A_{m} = transverse metal area (in^{2})
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 (ft^{2} 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 (ft^{2} per ft pipe)
Transverse Internal Area
Transverse internal area can be expressed as
A_{a} = 0.7854 d_{i}^{2} (6)
where
A_{a} = transverse internal area (in^{2})
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 
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