Calculate the surface area of common 3D geometric shapes — select your shape from the dropdown, enter the required dimensions (such as radius, height, or edge length), and get the total surface area along with any relevant component areas like lateral and base surfaces.
Total Surface Area
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Lateral Surface Area
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Base Surface Area
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Shape
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Surface area is the total area of all the outer faces or surfaces of a 3D object, measured in square units (e.g. cm²). Volume, on the other hand, measures the space enclosed inside the object in cubic units (e.g. cm³). Think of surface area as the amount of wrapping paper needed to cover a box, while volume is how much it can hold.
The surface area of a sphere is calculated using SA = 4πr², where r is the radius. For example, a sphere with radius 5 cm has a surface area of 4 × π × 5² ≈ 314.16 cm².
The total surface area of a cone is SA = πr² + πrl, where r is the base radius, l is the slant height, and l = √(r² + h²). The first term (πr²) is the base area, and the second term (πrl) is the lateral surface area.
A cube has 6 equal square faces, so its surface area is SA = 6a², where a is the edge length. For a cube with edge length 5 cm, the surface area is 6 × 25 = 150 cm².
A conical frustum is the shape formed when a smaller cone is cut from the top of a larger cone, leaving a truncated cone shape. Its surface area is SA = π(r₁ + r₂)s + πr₁² + πr₂², where r₁ and r₂ are the top and bottom radii, and s = √(h² + (r₂−r₁)²) is the slant height.
A capsule is a cylinder with two hemispherical ends, whereas a cylinder has flat circular ends. The surface area of a capsule is SA = 2πr(2r + h), which includes the cylindrical body and two hemispherical caps. A closed cylinder's surface area is SA = 2πr(r + h), with flat circular ends instead.
You can enter any consistent unit of length (mm, cm, m, km, in, ft, yd) and the result will be in that unit squared. For example, if you enter dimensions in centimeters, the surface area result will be in cm². The calculator does not convert between unit systems — just be sure all inputs use the same unit.
There is no exact closed-form formula for an ellipsoid's surface area, so an approximation by Knud Thomsen is commonly used: SA ≈ 4π × ((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ) / 3)^(1/p), where p ≈ 1.6075 and a, b, c are the three semi-axes. This approximation has an error of at most about 1.061%.