Surface Area Calculator
Calculate the total surface area of common 3D shapes — sphere, cylinder, cube, rectangular prism, cone and pyramid.
How to use the Surface Area Calculator
- Enter your inputs into the Surface Area Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
Common surface area formulas
Sphere: 4πr² · · · Cylinder: 2πr² + 2πrh · · · Cube: 6s² · · · Cone: πr² + πrl (l = slant height)
Surface area measures the total external 2D area of a 3D shape. Useful for material estimation (painting, wrapping, packaging) and heat transfer calculations.
Worked example
A cylinder with radius 5 cm and height 12 cm: SA = 2π(25) + 2π(5)(12) = 50π + 120π = 170π ≈ 534 cm². A sphere of the same radius: 4π(25) = 100π ≈ 314 cm².
Frequently asked questions
What's the difference between lateral and total surface area?
Lateral surface area excludes the top and bottom (the "side"). Total includes everything. A cylinder's lateral SA is 2πrh; total is 2πrh + 2πr².
Why does the sphere have minimal surface area?
For a given volume, a sphere has the smallest possible surface area. This is why bubbles and drops naturally form spherical shapes — surface tension minimizes surface area.
How is this useful?
Construction (paint, siding), heat loss (insulation), packaging, biology (cell surface-to-volume ratios), and any application involving material covering a 3D object.