Surface Area Calculator
Find the surface area of a sphere, cube, cylinder, cone or rectangular box, with its volume shown as a bonus.
How it works
Sphere 4πr² · Cube 6a² · Cylinder 2πr² + 2πrh · Cone πr(r + √(r² + h²)) · Box 2(lw + lh + wh)
Surface area is the total area of the outside skin of a solid — the paint or wrapping it would take — while volume is the space inside. Each shape adds up its faces: a box has three pairs of rectangles, a cylinder has two circles plus a rolled-out rectangle, and a cone has its circular base plus a curved lateral face built on the slant height √(r² + h²).
Worked example
A sphere of radius 5: surface area = 4 × π × 5² = 100π ≈ 314.1593 square units, and its volume = 4⁄3 × π × 5³ ≈ 523.5988 cubic units. A cylinder with the same radius and height 10 would instead be 2π × 25 + 2π × 5 × 10 = 150π ≈ 471.2389.
Sources: Surface area — Wikipedia
Frequently asked questions
What’s the difference between surface area and volume?
Surface area measures the outside boundary in square units — useful for material, paint or heat loss. Volume measures the space enclosed in cubic units — useful for capacity. A shape can have large volume yet modest surface area, which is why bubbles are spheres.
Where does the cone’s slant height come from?
The curved side unrolls into part of a circle whose radius is the slant height ℓ = √(r² + h²), found by the Pythagorean theorem on the radius and vertical height. That’s why the lateral area is πrℓ, added to the base πr².
Why does surface area scale slower than volume?
Scale a shape by k and area grows by k² while volume grows by k³. Doubling a sphere quadruples its surface but multiplies its volume eightfold — the reason large animals overheat less easily than small ones.
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This calculator is for educational purposes. Double-check important results before acting on them.