Calculate surface area for common 3D shapes.
The Surface Area Calculator is a geometric tool designed to calculate the total surface area of various three-dimensional solids. Surface area represents the total area of the outer boundary of a three-dimensional object, measured in square units. The shapes supported include cubes, rectangular prisms, cylinders, spheres, cones, and pyramids.
Each shape has a specific mathematical formula for surface area: - **Cube:** A = 6s² (six times the area of one square face) - **Rectangular Prism:** A = 2(lw + lh + wh) (sum of the areas of all six rectangular faces) - **Cylinder:** A = 2πr(r + h) (sum of the two circular bases and the curved lateral surface) - **Sphere:** A = 4πr² (four times the area of a circle with the same radius) - **Cone:** A = πr(r + s) (sum of the circular base and the curved lateral surface using slant height s) - **Pyramid (Square):** A = a² + 2as (base area plus the four triangular faces using slant height s)
Surface area calculations are essential in manufacturing and construction to estimate the amount of raw materials (like sheet metal, glass, or plastic) needed to fabricate containers or covers. In painting and coating industries, it determines the volume of paint required to cover structures. The surface area calculator automates these complex multi-step computations, providing instant, precise results for structural planning.
Surface Area
Surface area computes the total area of all outward-facing boundary surface planes.
How it Works & Formula
Unified surface area calculations for common three-dimensional solid shapes.
Practical Examples
A cube box with side 5cm requires SA = 6 × 5² = 150 cm² of paper.
Frequently Asked Questions
What is surface area?
The total area that the surface of a three-dimensional object occupies.