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.
Tips
- Volume units are cubed: 1 m³ = 1,000,000 cm³ = 1,000 L.
- Use the perpendicular height, not the slant height, for volumes.
- Check whether a question wants the lateral surface or the total surface area.
- Type a volume or area into a result field to work backwards.
Common mistakes to avoid
- Using the diameter instead of the radius.
- Forgetting the 1/3 in pyramid and cone volumes.
- Counting only one end of a cylinder in the total surface area.
Inputs explained
| Field | What to enter |
|---|---|
| Solid | Choose one: Sphere, Cylinder, Cube, Cone … |
| Radius r | Units: cm, m, mm, in, ft, yd … |
| Side / length a | Units: cm, m, mm, in, ft, yd … |
| Width b | Units: 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) |
|---|---|
| 2.5 | 78.5398 |
| 3.75 | 176.7146 |
| 5 | 314.1593 |
| 6.25 | 490.8739 |
| 7.5 | 706.8583 |
| 10 | 1,256.6371 |
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 2πrhWorked 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.
Frequently asked questions
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.
What formula does the Surface Area Calculator use?
Sphere 4πr² · Cylinder 2πr(r + h) · Cube 6a² · Cone πr(r + l) · Box 2(ab + ah + bh).