# Surface Area Calculator

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

> The surface area calculator finds the total surface area of ten common solids: sphere, cylinder, cube, cone, rectangular box, triangular prism, square pyramid, hemisphere, capsule and spherical cap.

## Inputs

- Solid
- Radius r (cm, m, mm, in, ft, yd, km, mi)
- Side / length a (cm, m, mm, in, ft, yd, km, mi)
- Width b (cm, m, mm, in, ft, yd, km, mi)
- Height h (cylinder part for a capsule, cap height for a cap) (cm, m, mm, in, ft, yd, km, mi)

## Results

- Surface area

## Formula

```
Sphere 4πr² · Cylinder 2πr(r + h) · Cube 6a² · Cone πr(r + l) · Box 2(ab + ah + bh)
Square pyramid a² + 2a·√(h² + a²/4) · Capsule 2πr(2r + h) · Cap 2πrh
```

## Explanation

Surface area is how much material wraps a solid: wrapping paper, paint, sheet metal, insulation or heat-transfer surface. Each solid has its own formula, gathered here.

### How to use the Surface Area Calculator

- **Solid**
- **Radius r**
- **Side / length a**
- **Width b**
- **Height h (cylinder part for a capsule, cap height for a cap)**

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

### How it works

Choose the solid and enter only the dimensions it needs.

### Inputs explained

FieldWhat to enterSolidChoose one: Sphere, Cylinder, Cube, Cone …Radius rUnits: cm, m, mm, in, ft, yd …Side / length aUnits: cm, m, mm, in, ft, yd …Width bUnits: cm, m, mm, in, ft, yd …Height h (cylinder part for a capsule, cap height for a cap)Units: cm, m, mm, in, ft, yd …

### Example values

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

Radius r (cm)Surface area (cm²)2.578.53983.75176.71465314.15936.25490.87397.5706.8583101,256.6371

## Worked example

Inputs — Solid: Sphere; Radius r: 5 cm.

Results — **Surface area = 314.159265 cm²**.

## Key terms

- **Surface area**: The total area of a solid's boundary.

## FAQ

**What is surface area?**
The total area of all outer faces of a solid.

**How do I find the surface area of a box?**
2(lw + lh + wh).

**Is the lateral area included?**
Yes – this is the total area, sides plus ends.

**Which solid has the smallest surface for its volume?**
The sphere.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)