# Tube Calculator

## Tube Shape

r_{1} = outer radius

C_{1} = outer circumference

L_{1} = outer surface area

V_{1} = volume within C_{1}

r_{2} = inner radius

C_{2} = inner circumference

L_{2} = inner surface area

V_{2} = volume within C_{2}

h = height

t = wall thickness

V = volume of solid

A = end surface area

π = pi = 3.1415926535898

√ = square root

## Calculator Use

This calculator will calculate the various properties of a tube, also called a pipe or hollow cylinder, given 3 known 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, ft^{2} or ft^{3}. For example, if you are starting with mm and you know r and h in mm, your calculations will result with C in mm, V in mm^{3}, L in mm^{2}, and A in mm^{2}.

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,
- C
_{1}= 2πr_{1} - C
_{2}= 2πr_{2}

- Lateral Surface Area, L, for a
cylinder:
- generally L = C * h = 2πrh, therefore,
- L
_{1}= 2πr_{1}h, the external surface area - L
_{2}= 2πr_{2}h, the internal surface area

- Area, A, for the end cross section of the tube:
- generally A = πr
^{2}, for a circle, therefore, - A
_{1}= πr_{1}^{2}for the area enclosed by C_{1} - A
_{2}= πr_{2}^{2}for the area enclosed by C_{2} - A = A
_{1}- A_{2}for the area of the solid cross section of the tube, the end. - A =
π(r
_{1}^{2}- r_{2}^{2})

- generally A = πr
- Volume, V, for a
cylinder:
- generally V = A * h = πr
^{2}h, therefore, - V
_{1}= πr_{1}^{2}h for the volume enclosed by C_{1} - V
_{2}= πr_{2}^{2}h for the volume enclosed by C_{2} - V = V
_{1}- V_{2}for the volume of the solid, the tube. - V =
π(r
_{1}^{2}- r_{2}^{2})h

- generally V = A * h = πr
- Thickness of the tube wall, t:
- t = r
_{1}- r_{2}

- t = r

## References

CalculatorSoup: Cylinder Calculator and Annulus Calculator