Surface Area Calculator

Ask how much skin wraps a cube, box, sphere, closed cylinder or cone — paint, foil, plating or gift paper — which is a squared length, not the cubic capacity inside.

How to use

Select the solid whose outside you will coat or wrap. There is no pyramid mode here; a rectangular pyramid is not implemented.
Enter the lengths in one unit. For a cone, type the base radius and the perpendicular height; the page builds slant height ℓ = √(r² + h²) for you.
Read total surface area in unit². On a cylinder or cone, the lateral (side-only) area is listed as a detail beside that closed total.
If you meant how much the solid holds, switch to the volume calculator. If you meant a flat cut-out on the plane, use the area calculator.

How it works

Surface area is the sum of the faces, the “skin.” A cube of side 2 has six faces of 4, total 24 unit² — enough wrap to cover the box, not enough to say how much fits inside (that interior is 8 unit³). A rectangular carton is 2(lw + lh + wh), the three pair of opposite faces. A sphere is 4πr²: radius 2 gives 16π ≈ 50.265 unit² of balloon or globe surface.

A closed cylinder includes the tube and both lids: 2πrh + 2πr². If you are labelling only the curved wall (a soup-can wrap, not the metal of the lids), the lateral area 2πrh is the detail under the total. A cone likewise reports a closed total πrℓ + πr² and a lateral πrℓ, with slant height computed from the radius and the perpendicular height you typed — do not enter a pre-measured slant unless you are checking that identity by hand.

This is not volume. Filling the can is πr²h on the volume page. It is also not the 2-D area of a room or a circular rug: those plane figures have no “inside a solid.” People see both answers labelled in “squares” and treat a tank’s paint estimate as its capacity; the dimensions differ.

A pyramid is absent on purpose. Volume can still do a rectangular pyramid’s interior, but this form does not unfold its four triangles plus base. Hemispheres, open pipes (lateral only as the primary result), frustums and irregular tanks are also out of scope.

Every input is a positive length in one unit. Mixing a millimetre radius with a metre height produces a meaningless square. π is Math.PI, so a hand 3.14 will drift from the displayed digits.

Formula

Cube: SA = 6s²
Box: SA = 2(lw + lh + wh)
Sphere: SA = 4πr²
Cylinder: SA = 2πrh + 2πr²
Cone: ℓ = √(r² + h²),  SA = πrℓ + πr²

Worked examples

A cube of side 2
cube, s = 2 → 24 unit²
A sphere of radius 2
r = 2 → 16π ≈ 50.265 unit²

Useful notes

Cylinder and cone include the base(s). Lateral area is shown as a detail where it differs.
Cone height is vertical; slant length is derived, not a separate input.
There is no pyramid, frustum or hemisphere mode on this page.
A cube of side 2 is 24 unit² of skin and 8 unit³ of interior — different pages.

FAQ

How do I find the surface area of a sphere?: SA = 4πr². Radius 2 gives 16π.
Does the cylinder include the lids?: Yes, the primary result is the closed cylinder. Lateral area (the tube only) is listed as a detail.
Is surface area the same as volume?: No. Surface area is a wrapping (unit²). Volume is the interior (unit³).
Do I enter a cone’s slant height or its vertical height?: Enter the perpendicular height and the base radius. The page computes slant height ℓ = √(r² + h²) and then the closed surface πrℓ + πr².
Why is there no pyramid option?: This form covers cube, box, sphere, cylinder and cone. A rectangular pyramid’s interior is on the volume page; its unfolded skin is not calculated here.

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