# Cross-Sectional Area Calculator

The cross-sectional area calculator determines the area for different types of beams. A beam is a very crucial element in construction. The load bearing member of bridges, roofs and floors in buildings are available in different cross-sections. Read on to understand how to calculate cross-sectional area of *I* section, *T* section, *C* beam, *L* beam, round bar, tube, and beams with rectangular and triangular cross-sections.

## What is a cross-section and how to calculate a cross-sectional area?

A cross-section is defined as the common region obtained from the intersection of a plane with a 3D object. For instance, consider a long circular tube cut (intersect) with a plane. You'll see a couple of concentric circles. The concentric circles are the cross-section of a tube. Similarly, the beams — *L*, *I*, *C*, and *T* — are named based on the cross-section shape.

In order to calculate the area of a cross-section, you need to look at them as basic shapes. For instance, a tube is a concentric circle. Therefore, for a tube with inner and outer diameter (`d`

and `D`

) having thickness `t`

, the area of cross-section can be written as:

`A`_{C} = π * (D^{2} - d^{2}) / 4

We also know that the inner diameter `d`

is related to thickness `t`

and outer diameter `D`

as:

` d = D - 2 * t `

Therefore, the area of cross-section becomes:

`A`_{C} = π * (D^{2} - (D - 2 * t)^{2}) / 4

Similarly, the area of cross-section for all other shapes having width `W`

, height `H`

, and thicknesses `t`

and _{1}`t`

are given in the table below._{2}

_{1}) * (W - 2t_{2})) | |

_{1} + (H - 2 * t_{1}) * t_{2} | |

_{1} + (H - 2 * t_{1}) * t_{2} | |

_{1} + (H - t_{1}) * t_{2} | |

^{2} | |

^{2} | |

^{2} - (D - 2 * t)^{2}) |

## How to find cross-sectional area?

Follow the steps below to find the cross-sectional area.

- Step 1: Select the
**shape**of cross-section from the list, say,*Hollow rectangle*. An illustration of the cross-section and the related fields will now be visible. - Step 2: Enter the
**width**of the hollow rectangle,`W`

. - Step 3: Fill in the
**height**of the cross-section,`H`

. - Step 4: Insert the
**thickness**of the hollow rectangle,`t`

. - Step 5: The calculator will return the
**area of the cross-section**.

## Example: Using the cross-sectional area calculator.

Find the cross-sectional area of tube having outer diameter of `10 mm`

and a thickness of `1 mm`

.

- Step 1: Select the
**shape**of cross-section from the list, i.e.,*Tube*. - Step 2: Enter the
**outer diameter**of tube,`D = 10 mm`

. - Step 3: Insert the
**thickness**of the tube,`t = 1 mm`

. - Step 4: The area of cross-section is :

`A`_{C} = π * (D^{2} - (D - 2 * t)^{2}) / 4

`A`_{C} = π * (10^{2} - (10 - 2 * 1)^{2}) / 4 = 28.274 mm^{2}

## Applications of cross-section shapes

*Did you know?*

- An
*I*or*H*beam is used extensively in railway tracks. *T*beams are found in use in early bridges and is used to reinforce structures to withstand large loads on floors of bridges and piers.

## FAQ

### How to calculate cross-sectional area of a pipe?

To calculate cross-section of a pipe:

**Subtract**the squares of inner diameter from the outer diameter.**Multiply**the number with π.**Divide**the product by 4.

### How to calculate area of an I section?

The area of I section with total width `W`

, height `H`

and having thickness `t`

can be calculated as:

`Area = 2 × W × t + (H - 2 × t) × t`

### How to calculate area of an T section?

The area of a T section with total width `W`

, height `H`

and having thickness `t`

can be calculated as:

`Area = W × t + (H - 2 × t) × t`

### What is the cross section of a cube?

The cross-section of a cube is a **square**. Similarly, for a cuboid, it is either a square or a rectangle.