# Cross-Sectional Area Calculator

URL: https://speedycalculator.com/calculators/math/cross-sectional-area/
Last updated: 2026-10-30

> The cross-sectional area calculator finds the area of common structural profiles: solid and hollow rectangles, I-beams, C-channels, T-sections, L-angles, triangles, solid circles and round tubes.

## Inputs

- Profile
- Width W (cm, m, mm, in, ft, yd, km, mi)
- Height H (cm, m, mm, in, ft, yd, km, mi)
- Thickness t (wall or flange) (cm, m, mm, in, ft, yd, km, mi)
- Web thickness t_w (cm, m, mm, in, ft, yd, km, mi)
- Outer diameter D (cm, m, mm, in, ft, yd, km, mi)

## Results

- Cross-sectional area
- Outer perimeter

## Formula

```
Rectangle W·H · Hollow rectangle W·H − (W − 2t)(H − 2t) · I-beam / C-channel 2W·t + (H − 2t)·t_w
T-section W·t + (H − t)·t_w · L-angle W·t + (H − t)·t_w · Tube π(D² − (D − 2t)²)/4
```

## Explanation

The cross-sectional area of a beam or bar sets its weight per metre, its axial strength (stress = force ÷ area) and how much material it uses. It is the first number an engineer needs when choosing a steel profile or timber.

### How to use the Cross-Sectional Area Calculator

- **Profile**
- **Width W**
- **Height H**
- **Thickness t (wall or flange)**
- **Web thickness t_w**
- **Outer diameter D**

Results update as you type, and everything is calculated in your browser.

### How it works

Choose the profile. W is the overall width (flange width), H the overall height, t the wall or flange thickness and t_w the web thickness. Multiply the area by the length and density to get the weight.

### Inputs explained

FieldWhat to enterProfileChoose one: Rectangle, Hollow rectangle, I-beam, C-channel …Width WUnits: cm, m, mm, in, ft, yd …Height HUnits: cm, m, mm, in, ft, yd …Thickness t (wall or flange)Units: cm, m, mm, in, ft, yd …Web thickness t_wUnits: cm, m, mm, in, ft, yd …Outer diameter DUnits: cm, m, mm, in, ft, yd …

### Example values

How the main result changes when **Width W** changes and everything else stays at the example values above:

Width W (cm)Cross-sectional area (cm²)526.087.532.081038.0812.544.081550.082062.08

## Worked example

Inputs — Profile: I-beam; Width W: 10 cm; Height H: 20 cm; Thickness t (wall or flange): 1.2 cm; Web thickness t_w: 0.8 cm.

Results — **Cross-sectional area = 38.08 cm²**.

## Key terms

- **Flange**: The horizontal plate of an I, C or T profile.
- **Web**: The vertical plate connecting the flanges.

## FAQ

**Why does cross-sectional area matter?**
Stress equals force divided by area, and weight equals area × length × density.

**Is a bigger area always stronger in bending?**
Not necessarily – bending depends on the moment of inertia, i.e. how far material is from the axis.

**How do I get the weight of a steel beam?**
Area × length × 7,850 kg/m³.

**What is the web of a beam?**
The vertical plate joining the flanges.


## Sources

- [Wolfram MathWorld – Cross-section](https://mathworld.wolfram.com/Cross-Section.html)
- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)