Surface Area Calculator
• Cube: SA = 6s²
• Rectangular Prism: SA = 2(lw + lh + wh)
• Sphere: SA = 4πr²
• Cylinder: SA = 2πr² + 2πrh
• Cone: SA = πr² + πr√(r² + h²)
Surface area = 6 × 5²
= 6 × 25
= 150 cm²
(6 faces, each 25 cm²)
🔗 Related Calculators
📐 Formula
• Cube: SA = 6s²
• Rectangular Prism: SA = 2(lw + lh + wh)
• Sphere: SA = 4πr²
• Cylinder: SA = 2πr² + 2πrh
• Cone: SA = πr² + πr√(r² + h²)
📝 Example Calculation
Surface area = 6 × 5²
= 6 × 25
= 150 cm²
(6 faces, each 25 cm²)
About Surface Area
Surface area is the total area of all the faces or surfaces that enclose a three-dimensional solid. Understanding surface area is essential for applications ranging from packaging design to heat transfer calculations. This calculator provides surface area and volume for common 3D shapes.
Surface Area Formulas by Shape
- Cube: SA = 6a^2 (where a is the side length)
- Rectangular Prism: SA = 2(lw + lh + wh)
- Sphere: SA = 4PIr^2
- Cylinder: SA = 2PIrh + 2PIr^2 (lateral + 2 bases)
- Cone: SA = PIrs + PIr^2 (lateral + base, s = slant height)
- Square Pyramid: SA = a^2 + 2as (base + lateral)
- Hemisphere: SA = 3PIr^2 (curved surface + base)
How to Use This Calculator
- Select the 3D shape from the dropdown menu
- Enter the required dimensions for that shape
- Click "Calculate" to get the surface area
- View detailed results including volume and component areas
Lateral vs Total Surface Area
Total surface area includes all faces of the solid, including bases. Lateral surface area includes only the side surfaces, excluding top and bottom bases. For example, a cylinder's total surface area includes the curved side and both circular ends, while the lateral surface area includes only the curved side.
Frequently Asked Questions
What is surface area?
Surface area is the total area of all the outer surfaces of a three-dimensional object. It represents the amount of material needed to cover the entire outside of the object. Surface area is measured in square units (like square meters or square feet).
What is the difference between surface area and volume?
Surface area measures the total area of the outer surfaces of a 3D object (measured in square units), while volume measures the amount of space inside the object (measured in cubic units). For example, surface area tells you how much paint you need to cover a box, while volume tells you how much the box can hold.
How do you calculate the surface area of a cube?
The surface area of a cube is calculated using the formula SA = 6a^2, where a is the length of one side. Since a cube has 6 identical square faces, you multiply the area of one face (a^2) by 6.
What is the surface area formula for a sphere?
The surface area of a sphere is SA = 4PIr^2, where r is the radius. This formula represents the area of the curved surface that completely encloses the sphere. It is exactly four times the area of a circle with the same radius.
What is lateral surface area?
Lateral surface area is the area of the sides of a 3D object, excluding the top and bottom bases. For example, a cylinder's lateral surface area is the area of the curved side (2PIrh), not including the circular top and bottom.
What are real-world applications of surface area?
Surface area calculations are used for determining paint or wallpaper needed, calculating material for packaging, designing heat exchangers, estimating drug dosages based on body surface area, sizing HVAC systems, calculating solar panel coverage, and determining coating requirements in manufacturing.