Surface Area Calculator
Free surface area calculator for cubes, spheres, cylinders, cones, and rectangular prisms. Enter dimensions like side, radius, height, length, and width for instant surface area results.
About This Calculator
Our free Surface Area Calculator helps you compute the total surface area of five common 3D geometric shapes: cube, sphere, cylinder, cone, and rectangular prism. Surface area is the total area that the surface of a 3D object occupies, measured in square units. This calculator is ideal for students studying geometry, teachers preparing lesson materials, architects estimating material coverage, and DIY enthusiasts planning construction or crafting projects.
Each shape uses its specific formula: Cube: SA = 6a^2 where a is side length; Sphere: SA = 4pir^2 where r is radius; Cylinder: SA = 2pir(r + h) where r is radius and h is height (includes top, bottom, and lateral surfaces); Cone: SA = pir(r + l) where l = sqrt(r^2 + h^2) is the slant height; Rectangular Prism: SA = 2(lw + lh + wh) where l is length, w is width, and h is height. The slant height for cones is automatically computed from the radius and height you enter.
All formulas on this page derive from standard Euclidean geometry and are consistent with mathematical textbooks worldwide. Simply select a shape from the dropdown, enter the required dimensions, and click Calculate. The result displays the surface area in square units along with a bar chart comparing the area contribution of each face where applicable. Since the calculator is unit-agnostic, you can work in centimetres, metres, inches, feet, or any consistent unit -- the output will be in the corresponding square units.
Frequently Asked Questions
How do you calculate surface area of a cube?
Surface area of a cube is SA = 6a^2, where a is the side length. For a cube with side length 5 units, the surface area is 6 x 5^2 = 150 square units.
What is the formula for cylinder surface area?
Surface area of a cylinder is SA = 2pir(r + h), where r is the radius and h is the height. This includes the top, bottom, and curved side surface area.
How do you find the surface area of a sphere?
Surface area of a sphere is SA = 4pir^2. For a sphere with radius 5 units, the surface area is 4 x pi x 25 ≈ 314.16 square units.
What is the cone surface area formula?
Surface area of a cone is SA = pir(r + l), where r is the radius and l is the slant height. The slant height is calculated as l = sqrt(r^2 + h^2) where h is the cone height.
How do you calculate surface area of a rectangular prism?
Surface area of a rectangular prism is SA = 2(lw + lh + wh), where l is length, w is width, and h is height. For a prism 6x4x10 units, SA = 2(24 + 60 + 40) = 248 square units.
What is the difference between surface area and volume?
Surface area measures the total area of all outer faces of a 3D shape (in square units), while volume measures the space inside the shape (in cubic units). Both are calculated using different formulas for each shape.
Can I calculate surface area in different units?
Yes, this calculator works with any consistent unit system. Enter dimensions in any unit (cm, m, inches, feet), and the result will be in the corresponding square units (cm^2, m^2, in^2, ft^2).