Surface Area Calculator
MathCalculate the surface area and volume of cubes, spheres, cylinders, cones, and rectangular prisms. Enter dimensions for precise 3D shape measurements.
Surface Area
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Volume
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What is a Surface Area?
A Surface Area Calculator works out the total area covering the outside of a 3D shape — cube, sphere, cylinder, cone, or rectangular prism — based on its dimensions, along with the shape's enclosed volume. Surface area calculations come up whenever a real-world task involves covering, painting, or wrapping a three-dimensional object, where simply knowing how much space something occupies (its volume) isn't the figure you actually need.
This calculator handles five common 3D shapes in one place, applying the correct surface area formula for whichever you select. It's the surface-area-focused companion to the Volume Calculator, which covers the same shapes but highlights volume as the primary result.
How to use this Surface Area calculator
- Select the Shape you want to calculate — Cube, Sphere, Cylinder, Cone, or Rectangular Prism.
- Enter Dimension 1 — the side length for a cube, or the radius for a sphere, cylinder, or cone.
- For cylinders and cones, enter Dimension 2 as the height.
- For a rectangular prism, enter all three dimensions — length, width, and depth.
- Read the Surface Area result, the primary figure for most covering or painting tasks.
- Check the Volume result if you also need to know the shape's capacity.
Formula & Methodology
Each shape uses its own standard surface area formula: - Cube: SA = 6s², Volume = s³ - Sphere: SA = 4πr², Volume = (4/3)πr³ - Cylinder: SA = 2πr² + 2πrh, Volume = πr²h - Cone: SA = πr² + πr × slant height (slant height = √(r² + h²)), Volume = (1/3)πr²h - Rectangular Prism: SA = 2(lw + lh + wh), Volume = l × w × h Worked example: for a cone with radius 3 and height 4: - Slant height = √(3² + 4²) = √25 = 5 - Surface Area = π × 3² + π × 3 × 5 = 28.3 + 47.1 ≈ 75.4 square units - Volume = (1/3) × π × 3² × 4 ≈ 37.7 cubic units
Frequently Asked Questions
The surface area of a cube is calculated as SA = 6s², where s is the length of one side, since a cube has six identical square faces. For a cube with a 4 cm side, the surface area is 6 × 4² = 96 square centimetres.
A sphere's surface area is calculated as SA = 4πr², where r is the radius. This represents the total area of the sphere's curved outer surface, with no flat faces or edges.
A cylinder's total surface area is SA = 2πr² + 2πrh, combining the area of its two circular ends (2πr²) with the area of its curved side (2πrh), where r is the radius and h is the height.
A cone's surface area is SA = πr² + πr × slant height, combining the circular base (πr²) with the curved lateral surface (πr × slant height). The slant height is calculated separately as √(r² + h²), using the radius and vertical height.
Surface area measures the total area covering the outside of a 3D shape (in square units), while volume measures the space enclosed inside it (in cubic units). This calculator shows both together, since many tasks — like painting a tank that also needs a capacity check — need both figures.
A rectangular prism's (box's) total surface area is 2(lw + lh + wh), where l, w, and h are the length, width, and height. Select 'Rectangular Prism' and enter all three dimensions to get the result.
A cone's volume only depends on its base radius and vertical height, but its surface area depends on the slant height — the distance along the cone's slanted side from the base edge to the apex — since that's the dimension that actually forms the curved surface. The calculator computes the slant height automatically from the radius and height you enter.
Both tools cover the same five shapes and calculate the same two figures, but this Surface Area Calculator highlights surface area as the primary result, while the [Volume Calculator](/volume-calculator/) highlights volume instead. Use whichever matches what you're primarily trying to find.
Surface area calculations come up whenever you're covering, painting, wrapping, or coating a 3D object — for example, working out how much paint a cylindrical tank needs, or how much wrapping paper covers a box. Volume, by contrast, matters when you're filling the shape rather than covering it.
Yes — surface area results are in square units matching whatever unit you used for the dimensions (for example, entering centimetres gives a result in square centimetres). Make sure all dimensions use the same unit before calculating for an accurate result.
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