Surface area is the total area of all outer faces and curved surfaces of a three-dimensional object. It is measured in square units such as cm2, m2, or ft2.
Definition
Surface area answers the question: how much material would you need to completely cover a 3D shape? Think of wrapping a gift box — the wrapping paper you use equals the box's surface area.
Surface Area vs Volume
Surface area measures the outside of a shape (in square units). Volume measures the inside (in cubic units). Doubling the radius of a sphere quadruples its surface area but increases volume eightfold. See surface area vs volume for more.
How to Find Surface Area
- Identify the shape — cube, cylinder, sphere, prism, etc.
- Choose the formula — each shape has a specific equation (see our formulas chart).
- Measure dimensions — radius, height, side lengths.
- Substitute and calculate — plug values into the formula.
- Write the answer in square units — always cm², m², ft², etc.
Common Formulas at a Glance
| Shape | Formula |
|---|---|
| Cube | 6s² |
| Rectangular prism | 2(lw + lh + wh) |
| Cylinder | 2πr² + 2πrh |
| Sphere | 4πr² |
| Cone | πr² + πrl |
| Triangular prism | bh + (a + b + c)H |
Worked Example — Rectangular Prism
SA = 2(lw + lh + wh) = 2(15 + 20 + 12) = 2 × 47 = 94 cm²
Real-World Uses
Surface area matters whenever you cover, coat, or wrap something: painting rooms, sizing packaging, estimating pipe insulation, and calculating drug dosing from body surface area.
Use our Sphere, Cylinder, Cone, Cube, and Rectangular Prism calculators for instant results.