Tube Calculator (hollow cylinder)

Tube Shape

r₁ = outer radius
C₁ = outer circumference
L₁ = outer surface area
V₁ = volume within C₁
r₂ = inner radius
C₂ = inner circumference
L₂ = inner surface area
V₂ = volume within C₂
h = height
t = wall thickness
V = volume of solid
A = end surface area
π = pi = 3.14159
√ = square root

About this Calculator

This calculator will calculate the various properties of a tube, also called a pipe or hollow cylinder, given 3 know values from variables of radii, circumference, wall thickness and height. A geometric solid tube is generally a cylinder with an end profile represented by an annulus.

* Units: Note that units are shown for convenience but do not affect the calculations.  The units are in place to give an indication of the order of the results such as ft, ft² or ft³.  For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm³, L in mm², and A in mm².

Below are the standard formulas for a tube.  Calculations are based on algebraic manipulation of these standard formulas.

Tube Formulas in terms of radius and height, r and h:

• Circumference, C:
  • generally C = 2πr, therefore,
  • C₁ = 2πr₁
  • C₂ = 2πr₂
• Lateral Surface Area, L, for a cylinder:
  • generally L = C * h = 2πrh, therefore,
  • L₁ = 2πr₁h, the external surface area
  • L₂ = 2πr₂h, the internal surface area
• Area, A, for the end cross section of the tube:
  • generally A = πr², for a circle, therefore,
  • A₁ = πr₁² for the area enclosed by C₁
  • A₂ = πr₂² for the area enclosed by C₂
• A = A₁ - A₂ for the area of the solid cross section of the tube, the end.
• A = π(r₁² - r₂²)
• Volume, V, for a cylinder:
  • generally V = A * h = πr²h, therefore,
  • V₁ = πr₁²h for the volume enclosed by C₁
  • V₂ = πr₂²h for the volume enclosed by C₂
• V = V₁ - V₂ for the volume of the solid, the tube.
• V = π(r₁² - r₂²)h
• Thickness of the tube wall, t:
  • t = r₁ - r₂

References

Calculator Soup: Cylinder Calculator and Annulus Calculator