Surface area measures how much material covers the outside of a 3D object — paint for a tank, sheet metal for a duct, paper for a gift box, or tile for a dome.
About this calculator
Surface area measures how much material covers the outside of a 3D object — paint for a tank, sheet metal for a duct, paper for a gift box, or tile for a dome. This calculator handles the five shapes you meet most often in school geometry and practical trades: cube, rectangular prism, cylinder, sphere, and cone.
Pick a shape, enter the dimensions, and read the total outer area in square units. The result card shows which formula was applied — for example 6s² for a cube or 2πr(r + h) for a cylinder. Switch shapes anytime; input groups show only the fields that matter for the selected solid.
Surface area is different from volume — a tall thin box can have large volume but modest surface area, or vice versa. For enclosed space use the [[volume]] calculator. For flat figures use the [[area]] calculator. Shape-specific tools like [[cone]], [[cylinder]], and [[sphere]] calculators also show volume alongside surface area if you need both numbers.
Common uses
- Paint or wallpaper coverage for boxes, tanks, and rooms modeled as prisms
- Sheet metal or fabric needed to wrap cylindrical or conical objects
- School geometry homework — verify hand calculations for each solid
- Packaging design — compare material cost for different box sizes
- Engineering rough estimates for heat exchange or coating area on pipes and spheres
Frequently asked questions
What is the surface area of a cube with side 4 cm?
A cube has six equal square faces. Each face is 4 × 4 = 16 cm². Total surface area = 6 × 16 = 96 cm². Enter shape Cube and side 4 to confirm.
How do you find the surface area of a cylinder?
A cylinder has two circular bases plus a curved side. Total area = 2πr(r + h), where r is base radius and h is height. The term 2πr² covers both bases; 2πrh is the lateral wrap-around area.
Why does the cone formula use slant height?
The curved side of a cone is a sector when unrolled — its area is πrℓ, where ℓ is the slant height from base edge to apex. Vertical height h alone is shorter than ℓ unless the cone is flat. The calculator computes ℓ = √(r² + h²) from your inputs.
What units should I enter?
Use any consistent unit — cm, m, inches, feet. The result is in square units of that measure (cm², m², etc.). All dimensions for one calculation must share the same unit.
Is surface area the same as lateral area?
No. Lateral area counts only the curved or side faces, not top and bottom bases. This calculator returns total surface area including all outer faces. For a closed cylinder that means both circular ends plus the curved wall.