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Calculator Answers

Surface Area Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A surface area calculator is a geometric tool that computes the total area of the outer faces of three-dimensional shapes. It calculates surface area using standard formulas for shapes such as spheres, cylinders, cones, cubes, rectangular prisms, and pyramids. The calculator sums the areas of all flat and curved surfaces that bound the solid object. It is widely used in packaging design, manufacturing, and house renovation. Contractors and DIY enthusiasts use this tool to estimate material quantities like paint, wrapping, or protective coatings needed to cover physical objects.

Pick a shape, enter its dimensions, and the calculator returns the total surface area (and lateral surface area where applicable) along with the formula used.

Quick Answer

Calculate the outer surface area of 3D geometric shapes. Select your shape and enter the dimensions to find the area in square units.

Shape

e.g. 4

e.g. 3

e.g. 5

Surface area is in squared units. Pair with the volume calculator for the same shapes.

Rectangular prism surface area

Total surface area

94

2 × (12 + 20 + 15) = 94

ShapeRectangular prism
FormulaSA = 2(lw + lh + wh)
Total surface area94
Lateral surface area70

Pair with the volume calculator for the corresponding 3D volume formulas.

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Examples

Cube side 4

SA = 96 (= 6 × 16)

Sphere r = 5

SA ≈ 314.159

Cylinder r = 3, h = 5

SA ≈ 150.796 · lateral ≈ 94.248

Cone r = 3, h = 4

SA ≈ 75.398 · lateral ≈ 47.124

How it works

Each 3D shape has its own surface area formula. The calculator picks the right one based on the shape you select, runs the arithmetic, and shows the total along with the lateral surface area when it differs from the total.

Rectangular prism · SA = 2(lw + lh + wh)

Cube · SA = 6s²

Cylinder · SA = 2πr² + 2πrh

Sphere · SA = 4πr²

Cone · SA = πr(r + √(h² + r²))

Square pyramid · SA = base² + 2 × base × slant height

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Volume Calculator – Rectangular Prism, Cylinder, Sphere & ConeCalculate the volume of common 3D shapes including rectangular prism volume, cylinder volume, sphere, cone, and pyramid. Round shapes accept a radius or a diameter. Includes formulas and cubic unit conversions.

Frequently asked questions

Surface area is the total area covering the outside of a 3D shape. It is measured in squared units (square inches, square meters, etc.), the same as 2D area. A cube of side 4 has a surface area of 6 × 4² = 96 square units.

Surface area measures the outside skin of a 3D shape (squared units). Volume measures how much 3D space the shape contains (cubed units). A balloon's surface area is the rubber's coverage; its volume is the air inside. Same shape, different measurements.

Lateral surface area is the side surface only, excluding the top and bottom (the bases). For a cylinder, the lateral surface is 2πrh (the curved part) and the total surface adds 2πr² for the two end caps. For a cube, the lateral surface is the four side faces (4s²) and the total is six faces (6s²).

Use SA = 4πr². For a sphere with radius 5, the surface area is 4π × 25 ≈ 314.159 square units. A sphere has no distinct lateral vs total: it is a single curved surface.

The cone's curved side is not a flat circle; if you unroll it, it forms a sector of a circle with radius equal to the slant height ℓ = √(h² + r²). The lateral surface area is πrℓ, not πrh. The calculator computes the slant height from the vertical height you enter, so you only need to provide r and h.

Yes. Use the volume calculator for the corresponding 3D volume formulas with the same shape set. They are designed to be used together.