# Cross-Sectional Area Calculator

By Rahul Dhari
Last updated: Jun 30, 2021

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:

`AC = π * (D2 - d2) / 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:

`AC = π * (D2 - (D - 2 * t)2) / 4`

Similarly, the area of cross-section for all other shapes having width `W`, height `H`, and thicknesses `t1` and `t2` are given in the table below. Section
Area
Hollow Rectangle
(H * W) - ((W - 2t1) * (W - 2t2))
Rectangle
W * H
I
2 * W * t1 + (H - 2 * t1) * t2
C
2 * W * t1 + (H - 2 * t1) * t2
T
W * t1 + (H - t1) * t2
L
W * t + (H - t) * t
Isosceles Triangle
0.5 * B * H
Equilateral Triangle
0.4330 * L2
Circle
0.25 * π * D2
Tube
0.25 * π *(D2 - (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 :
`AC = π * (D2 - (D - 2 * t)2) / 4`
`AC = π * (102 - (10 - 2 * 1)2) / 4 = 28.274 mm2`

## 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:

1. Subtract the squares of inner diameter from the outer diameter.
2. Multiply the number with π.
3. 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.

Rahul Dhari
Cross section
Hollow rectangle Width (W)
in
Height (H)
in
Thickness (t)
in
Area (A)
in²
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