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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

### 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)

where

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)

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

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

where

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)

where

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)

where

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

### Transverse Internal Area

Transverse internal area can be expressed as

Aa  = 0.7854 di2                       (6)

where

Aa = transverse internal area (in2)

### Circumference External

External circumference can be expressed as

Ce  = π do                      (7)

where

Ce =  external circumference (in)

### Circumference Internal

Internal circumference can be expressed as

Ci  = π di                       (8)

where

Ci =  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

## Related Topics

• Dimensions - Sizes and dimensions of pipes and tubes, and their fittings - inside and outside diameter, weight and more

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

9 25