This surface area calculator covers cube, sphere, cylinder, and rectangular box. Choose a shape, enter the labeled dimensions, and read total outer area. The default is a cube with side 4, so 6 × 4² = 96.
Packaging, paint estimates, and geometry homework all need surface area. For circle area alone, use the circle calculator. For triangle area from three sides, use the triangle calculator.
How the formula works
Cube: six equal faces, 6a². Sphere: 4πa² with a as radius. Cylinder: 2πa(a+b) with radius a and height b. Box: 2(ab + ac + bc) for length, width, and height.
Worked example
Shape cube, a = 4. Each face has area 16. Six faces total 96.
| Input | Value |
|---|---|
| Shape | Cube |
| Side a | 4 |
| Surface area | 96 |
How to use the fields
- Shape selects cube, sphere, cylinder, or box.
- a is side, radius, or length depending on shape.
- b is width or cylinder height when needed.
- c is box height when the box shape is selected.
Paint and wrap estimates
Surface area tells you how much skin a solid has. Paint coverage charts use area per can. Add a waste factor yourself for edges and texture; the calculator returns geometric area only.
Common mistakes
- Using volume formulas by accident
- Entering diameter in a radius field
- Forgetting both bases on a closed cylinder
- Mixing units across length, width, and height
Sphere and cylinder checks
For a sphere, only radius a matters. For a cylinder, radius a and height b both matter. Doubling radius grows sphere area by four because of the a² term. That scaling surprise shows up in material planning.
Open tops and nets
If a container has no lid, subtract one face from the closed formula by hand. Classroom nets (unfolded faces) should sum to the same total when all faces are included.
Box packing intuition
A 4×3×2 box has surface area 2(12 + 8 + 6) = 52. Compare that with the default cube of side 4 at 96 to see how shape changes wrap needs even when one dimension matches.
Always label which edge is a, b, and c so teammates can repeat the entry.
Classroom practice
Start with the default cube, then switch to sphere with the same a = 4 and compare. Next try cylinder with a = 4 and b = 3. Writing each formula beside the result builds memory better than memorizing numbers alone.
Ask students whether surface area can stay the same while volume changes. Different shapes prove that covering and capacity are separate ideas.
Choosing among the four shapes
Pick cube when all edges match. Pick sphere when you have a radius only. Pick cylinder when you have radius and height for a closed can style solid. Pick box when three rectangular edge lengths differ.
Wrong shape selection is the fastest way to get a confident but useless number.
Paint coverage math
Divide surface area by the coverage rate on your paint can to estimate how many cans you need, then add waste for texture and cutting in. The calculator stops at geometric area.
Recheck units so you do not mix square feet of wall with coverage listed per square meter.
Open containers
An open top box needs five faces, not six. Start from the closed box formula and subtract the missing face area by hand. Note that change beside your result so teammates do not assume a sealed solid.
Cylinders without lids subtract one circular base the same way.
Comparing cube and box defaults
The default cube of side 4 has area 96. A box using a=4, b=3, and c=2 has area 52. Same length a can wrap very differently once the other edges shrink. Run both shapes when a packaging choice is not obviously cubic.
Keep a one line note of shape plus dimensions beside every quote you send to a vendor.
Limitations
Only the four listed solids are supported. Cones, pyramids, and irregular meshes need other tools. Results assume smooth closed surfaces with the standard formulas above.