Surface Area Calculator
Calculate the total surface area of common 3D shapes — cube, rectangular prism, sphere, cylinder, and cone.
Results
What is it?
Surface area is the total area of all faces (or curved surfaces) of a 3D shape, measured in square units. Formulas: Cube = 6s²; Rectangular Prism = 2(lw + wh + lh); Sphere = 4πr²; Cylinder = 2πr(r + h); Cone = πr(r + l) where l = √(r² + h²) is the slant height.
How to use
Select the 3D shape, enter Dimension 1 (always the primary measurement — side or radius), and fill in Dimension 2 (width) and Dimension 3 (height) where applicable. Only the dimensions needed for the chosen shape affect the result.
Example scenario
Wrapping a gift box (rectangular prism) 30 cm × 20 cm × 10 cm: SA = 2(30×20 + 20×10 + 30×10) = 2(600+200+300) = 2,200 cm². Painting a sphere with radius 5 cm: 4π×25 ≈ 314.16 cm².
Pro tip
Distinguish between Total Surface Area (TSA = all faces) and Lateral Surface Area (LSA = sides only, excluding bases). Cylinder LSA = 2πrh; Cone LSA = πrl. LSA matters when calculating paint for walls (excluding floor/ceiling) or labels on cans. For the cone, the slant height l = √(r² + h²) is crucial — it is the distance along the sloped face, not the vertical height.