What is surface area?

Surface area is the total area of all the outside faces of a three-dimensional object. It is measured in square units and tells you how much material it would take to cover the object, how much paint or coating you need, or how much surface is available for heat to escape.

How do you find the surface area of a cylinder?

Add the two circular ends to the curved side. Each end is pi x r squared, and the curved side unrolls into a rectangle of 2 x pi x r times the height. Total SA = 2 x pi x r x (r + h).

What is the difference between surface area and volume?

Surface area measures the outside of an object in square units, while volume measures the space inside in cubic units. You use surface area for covering, coating or wrapping, and volume for capacity or how much it holds.

Surface Area Calculator

Surface area is the total area of all the outside faces of a solid object, the amount of material it would take to cover it completely. Whenever you need to paint a tank, wrap a parcel, clad a column, line a duct, tile a surface, work out heat loss, or order sheet material, surface area is the number you need. This calculator covers the five shapes that come up most often: the cube, the rectangular box (cuboid), the sphere, the cylinder, and the cone. Choose a shape from the dropdown and the calculator shows only the dimensions that shape needs, then returns the surface area the moment you type. There is no clutter and no need to remember which formula applies to each case. A cube is six identical squares, so its surface area is 6 times the side squared. A cuboid has three pairs of rectangles, summed and doubled. A sphere's surface is four times the area of its great circle, a result that surprised mathematicians. A cylinder is two circular ends plus a curved side that unrolls into a rectangle. A cone is its circular base plus a curved surface that depends on the slant height, which is automatically calculated from the radius and height. The default shows a cube with side 4, giving surface area 96 square units. You can switch to any other shape and the inputs update to match. Use this tool for geometry study, material estimates in construction and manufacturing, and any practical sizing task. The formulas for every shape are explained below.

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Shape

Side length

Width

Height

surface area (square units)

How it works

Cube (side a): SA = 6a². Rectangular box (L, W, H): SA = 2(LW + LH + WH). Sphere (radius r): SA = 4πr². Cylinder (radius r, height h): SA = 2πr(r + h). Cone (radius r, height h): slant l = √(r² + h²), SA = πr(r + l). Each formula follows directly from adding up the areas of all the faces for that shape.

Worked example

The default is a cube with side 4: SA = 6 × 4² = 6 × 16 = 96 square units. Switching to a box with L=4, W=3, H=5: SA = 2 × (12 + 20 + 15) = 2 × 47 = 94. A cylinder with r=5 and h=10: SA = 2 × π × 5 × 15 ≈ 471.24 square units.

Related calculators

Cube Calculator: volume, surface area and diagonals of a cube.
Cylinder Surface Area Calculator: lateral and total SA of a cylinder.
Sphere Surface Area Calculator: surface area and volume of a sphere.
Cone Surface Area Calculator: slant height and surface area of a cone.

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