Surface Area Calculator
Calculate total surface area for common three-dimensional shapes
Cube: use Length only. Sphere: Length is radius. Cylinder: Length is radius and Height is height.
Total surface area
How we calculated it
About the Surface Area Calculator
Surface area measures the total outside area of a three-dimensional solid. It is useful for paint, wrapping, heat-transfer and geometry problems where every exposed face or curved surface matters.
The correct formula depends on the solid. A rectangular box is handled by adding face areas, while cylinders, spheres and cones include curved surfaces.
How to Use the Surface Area Calculator
- Choose the solid that matches the object.
- Enter the required dimensions using consistent length units.
- Decide whether all faces are included or whether the real task excludes a base or opening.
- Calculate the total and convert to the square unit needed.
How the Calculation Works
A rectangular prism uses SA = 2(lw + lh + wh). A sphere uses SA = 4πr². A closed cylinder uses SA = 2πr² + 2πrh.
Other supported solids use their corresponding geometric relationships. Because the output is area, the final units are squared.
Worked example
Surface Area Calculator Worked Example
Box 4×3×2
Surface area = 2(4×3 + 4×2 + 3×2) = 2(12+8+6) = 52 square units.
Result guide
Understanding Your Surface Area Calculator Result
Surface area is not the same as volume. Two objects can hold the same volume while having very different outside surface area.
Before you rely on the answer
Assumptions and Limitations
- The chosen geometric solid represents the object.
- Dimensions use compatible units.
- Openings or excluded faces are handled according to the selected mode.
Practical tip
Using This Result in Practice
For a real container, decide whether the top, bottom or internal surfaces should be included before calculating. Many practical mistakes come from using the formula for a closed solid when the object is open.
Related calculations
Useful Calculations to Continue With
If you also need the space contained inside the solid, use the Volume Calculator.
If the object can be broken into flat faces you want to calculate individually, use the Area Calculator for those sections.
Common questions
Surface Area Calculator FAQ
What is the difference between surface area and volume?
Surface area measures the outside covering of a solid, while volume measures the three-dimensional space it occupies or contains.
Why are surface-area units squared?
Each surface is two-dimensional, so its area is measured in square units.
Do I include the base of a cylinder?
Use the closed-cylinder formula when both circular ends are included. An open container needs the omitted surface removed.