Surface Area Calculator
Calculate the total surface area of common 3D geometric shapes including cubes, cylinders, spheres, cones, and rectangular prisms.
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Surface Area Formulas
Surface area is the total area of the outer surfaces of a 3D object. Understanding how to calculate it is useful for painting, packaging, and construction.
- Cube: SA = 6 × a² (where a is the side length)
- Rectangular Prism (Box): SA = 2(lw + lh + wh)
- Cylinder: SA = 2πr² + 2πrh
- Sphere: SA = 4πr²
- Cone: SA = πr(r + √(h² + r²))
- Capsule: SA = 4πr² + 2πrl (combination of sphere and cylinder body)
Real World Uses
- Painting: Calculating the surface area of walls to determine paint gallons needed.
- Wrapping: Determining how much wrapping paper is needed for a box.
- Manufacturing: Estimating material costs for metal sheets or plastic molds.
If you need to calculate the space inside these shapes, check out our Volume Calculator.
? Frequently Asked Questions
Surface area is the sum of all the areas of all the shapes that cover the surface of the object. Think of it as the amount of wrapping paper needed to cover the object exactly.
Yes, total surface area includes all faces (top, bottom, and sides). If you only need the sides (like a label on a can), that is called 'Lateral Surface Area'.
If your measurements are in feet, the formula gives square feet directly. If in inches, calculate the area in square inches and divide by 144.