Enter values to see results
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units²
Enter values to see results
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units²
The Surface Area Calculator determines the total outer surface area of common three-dimensional solids—cubes, spheres, cylinders, cones, and rectangular pyramids. Surface area is the sum of the areas of all faces or curved surfaces that enclose a solid, measured in square units.
Knowing the surface area is essential in numerous real-world contexts: calculating how much paint is needed to cover a tank, determining the amount of wrapping paper for a gift box, estimating heat loss through a building’s exterior, or sizing the material required to fabricate a metal container.
Cube with edge $$a$$:
$$SA_{\text{cube}} = 6a^2$$
Sphere with radius $$r$$:
$$SA_{\text{sphere}} = 4\pi r^2$$
Cylinder with radius $$r$$ and height $$h$$:
$$SA_{\text{cylinder}} = 2\pi r(r + h)$$
This includes two circular bases ($$2\pi r^2$$) plus the lateral surface ($$2\pi r h$$).
Cone with radius $$r$$ and height $$h$$, slant height $$l = \sqrt{r^2 + h^2}$$:
$$SA_{\text{cone}} = \pi r(r + l)$$
Rectangular Pyramid with base $$l \times w$$ and height $$h$$:
$$SA_{\text{pyramid}} = lw + l\sqrt{h^2 + (w/2)^2} + w\sqrt{h^2 + (l/2)^2}$$
The pyramid formula sums the rectangular base area with the four triangular lateral faces, computed via their respective slant heights.
Surface area and volume measure fundamentally different properties. Volume quantifies the space inside a solid; surface area quantifies the extent of its boundary. For a given volume, the sphere has the minimum possible surface area—a principle known as the isoperimetric inequality. This is why bubbles are spherical: surface tension minimizes area for a trapped volume of air.
In engineering, surface area determines material costs for fabrication, coating requirements, and thermal transfer rates. In biology, the surface-area-to-volume ratio governs diffusion rates in cells. In architecture, the building envelope’s surface area affects energy efficiency. In cooking, a larger surface area means faster heat transfer and crispier results when frying.
Select your shape, enter dimensions, and obtain the total surface area instantly.
Choose a shape and enter the relevant dimensions. For a cube, only edge length is needed. For a sphere, enter the radius. For a cylinder or cone, provide radius and height. For a rectangular pyramid, supply length, width, and height. The calculator computes slant heights internally and returns the total surface area.
The result is the total surface area in square units matching your input. If dimensions are in meters, the output is in m². This includes all faces—base(s) and lateral surfaces. For a cylinder, both circular ends are included; for a cone, the circular base is included.
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A cylinder with radius 2 m and height 6 m: SA = 2π(2)(2+6) = 32π ≈ 100.53 m². At 5 m² per liter of paint, you need about 20.1 liters.
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A cube with edge 15 cm: SA = 6(15)² = 1350 cm². You need at least 1350 cm² of wrapping paper, plus extra for overlaps.
Yes. The formula $$SA = \pi r(r + l)$$ includes the circular base ($$\pi r^2$$) and the lateral surface ($$\pi r l$$). For the lateral area only, subtract $$\pi r^2$$.
Slant height is the distance from the apex of a cone or pyramid to a point on the edge of the base, measured along the surface. For a cone: $$l = \sqrt{r^2 + h^2}$$.
The sphere. This is the isoperimetric inequality in three dimensions. Among all solids of equal volume, the sphere minimizes surface area.
Subtract the base area(s) from the total. For a cylinder, lateral area = total − 2πr². For a cone, lateral area = total − πr².
This calculator handles rectangular-base pyramids. For triangular or hexagonal bases, decompose the lateral faces into individual triangles and sum their areas with the base area.
Surface area determines material usage for fabrication, heat dissipation rates (Newton’s law of cooling), aerodynamic drag, chemical reaction rates, and coating/painting requirements.
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The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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