Education
Surface Area Calculator
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.
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.
Total surface area
94
2 × (12 + 20 + 15) = 94
Pair with the volume calculator for the corresponding 3D volume formulas.
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
Related calculators
- Volume calculator for the same shape set with the volume formulas.
- Area calculator hub for 2D shapes.
- Rectangle calculator for area, perimeter, diagonal of a flat rectangle.
- Circle calculator for area, circumference, and radius of a flat circle.
- Scientific calculator for general arithmetic with π and square root.
- All education calculators.
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.
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