# Surface Area Calculator

> Total, lateral and base surface area of a sphere, hemisphere, cube, rectangular box, cylinder, cone or square pyramid, with the volume too.

Category: Algebra, geometry & advanced math · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/surface-area-calculator

Surface area is the total area of every face or curved surface of a solid: the amount of paint, wrapping or sheet material needed to cover it.

Also called: Total surface area calculator, Lateral area calculator.

## Inputs
- Shape (options: Sphere, Hemisphere (closed), Cube, Rectangular box (cuboid), Cylinder (closed), Cone (with base), Square pyramid; default cylinder)
- Radius (default 3)
- Radius (default 3)
- Edge length (default 3)
- Length (default 4)
- Width (default 3)
- Height (default 2)
- Radius (default 3)
- Height (default 10)
- Base radius (default 3)
- Perpendicular height (default 4)
- Base edge (default 6)
- Perpendicular height (default 4)

## Results
- Total surface area
- Lateral (side or curved) area
- Base area (all bases)
- Volume

## Formula

```
Sphere 4πr²;  hemisphere 3πr²;  cube 6a²;  box 2(lw + lh + wh);  cylinder 2πr(r + h);  cone πr(r + s), s = √(r² + h²);  square pyramid a² + 2a√(h² + (a/2)²)
```

Where:
- r: radius
- h: perpendicular height
- a: edge length
- l, w: length and width
- s: slant height

## Worked example
1. Curved side: 2π × 3 × 10 = 60π ≈ 188.4956.
2. Two ends: 2 × π × 3² = 18π ≈ 56.5487.
3. Total: 78π ≈ 245.0442.

**Result:** A closed cylinder of radius 3 and height 10 has a surface area of about 245.04 square units.

## What the result means

Use the lateral area for open shapes, such as a pipe or a tube without ends, and the total for closed containers. Units are the square of the length unit you entered.

## Assumptions and limits
- Ideal solids with straight sides; the cone and pyramid are right (apex above the centre of the base).
- Heights are perpendicular heights, not slant heights.
- Material estimates need extra for seams, overlaps and waste.

## Questions

### What is the difference between lateral and total surface area?

Lateral area excludes the base or bases; total area includes them. For a can, the label covers the lateral area.

### I only know the slant height of a cone. What now?

Perpendicular height h = √(s² − r²). Enter that value as the height.

## Related calculators
- [Circle Calculator](https://calculators.geekmidst.com/calculators/circle-calculator)
- [Concrete Calculator](https://calculators.geekmidst.com/calculators/concrete-calculator)
- [Pythagorean Theorem Calculator](https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/surface-area-calculator