Surface Area Calculator
Calculate the total and lateral surface area of common 3D shapes with step-by-step solutions.
About Surface Area
Surface area is the total area of all the outer faces of a three-dimensional object. It is measured in square units (cm², m², in²). Surface area calculations are essential in engineering, manufacturing, and science — from determining how much paint is needed to coat an object to calculating heat exchange rates in chemical reactors.
Surface area is often split into lateral surface area (the side faces, excluding bases) and base surface area. For example, a cylinder's lateral surface area is the curved side wall, while the base area includes both circular ends. Understanding this distinction matters in real-world applications like labeling cans or lining cylindrical tanks.
For curved shapes like cones and pyramids, a key intermediate value is the slant height— the distance along the sloped face from the base edge to the apex. It is calculated using the Pythagorean theorem: l = √(r² + h²) for a cone. The slant height always exceeds the vertical height for any non-zero base radius or width.
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For a related calculation, use Area Calculator to calculate the area of circles, triangles, rectangles, trapezoids, ellipses, parallelograms, and sectors. Alternatively, use Volume Calculator to calculate the volume of spheres, cylinders, cones, cubes, prisms, pyramids, and more with unit conversion.