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Pipe Equations

Calculate cross-sectional areas, weight of empty pipes, weight of pipes filled with water, inside and outside surface areas

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Pipe - diameter and cross sectional area

Cross Sectional inside Pipe Area

Cross-sectional inside area of a pipe can be calculated as

Ai = π (di / 2)2

   = π di 2 / 4                                 (1)


Ai = cross-sectional inside area of pipe (m2, in2)

di = inside diameter (m, in)

Cross Sectional Pipe Wall Area

The cross-sectional wall area - or area of piping material - can be calculated as

Amπ (do / 2)2 - π (di / 2)2

   = π (do 2 - di 2) / 4                               (2)


Am = cross-sectional wall area of pipe (m2, in2)

do = outside diameter (m, in)

Weight of Empty Pipes

Weight of empty pipes per unit length can be calculated as

wpρm Am

    = ρm (π (do / 2)2 - π (di / 2)2

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


wp = weight of empty pipe per unit length (kg/m, lb/in)

ρs = density of pipe material (kg/m3, lb/in3)

Weight of Liquid in Pipes

Weight of liquid in pipes per unit length can be calculated as

wl = ρl A

    = ρl π (di / 2)2 

    = ρl π di2 / 4                                   (4)


wl = weight of liquid in pipe per unit length of pipe (kg, lb)

ρl = density of liquid (kg/m3, lb/in3)

Weight of Pipe filled with Liquid

Weight of pipe filled with liquid per unit length can be calculated as

w = wl + wp                          (5)


w = weight of pipe and liquid per unit length of pipe (kg, lb)  

Outside Surface Area of Pipes

Outside surface area of steel pipes per unit length can be calculated as

Ao = 2 π (do / 2)

     =  π do                            (6)


Ao = outside area of pipe - per unit length of pipe (m2, in2)

Inside Surface Area of Pipes

Inside surface area of steel pipes per unit length can be calculated as

Ai2 π (di / 2)

     =  π di                             (7)


Ai = inside area of pipe - per unit length of pipe (m2, in2)

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  • de: Stahlrohre Gewichtswasserquerschnittsfläche Metalloberfläche
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