# 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≈ 0.0491 (d_{o}^{4}- d_{i}^{4}) / 64_{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 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_{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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