Surface Area Calculator
Calculate total, lateral, and base surface area for cubes, prisms, spheres, cylinders, cones, and pyramids.
Surface Area Calculator
Shape Dimensions
Calculate the surface area of a cube using all 6 equal square faces.
Results
Total Surface Area
150.000 cm²
Formula Used
SA = 6s²
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What is Surface Area Calculator?
A surface area calculator computes the total area of all external faces of three-dimensional geometric shapes. Surface area is crucial for applications like material estimation, painting, coating, and packaging design.
Supported 3D Shapes
- Cube: Six equal square faces with surface area = 6s²
- Rectangular Prism: Six rectangular faces with surface area = 2(lw + lh + wh)
- Sphere: Curved surface with surface area = 4πr²
- Cylinder: Two circular bases plus lateral surface = 2πr² + 2πrh
- Cone: Circular base plus lateral surface = πr² + πrs
- Square Pyramid: Square base plus four triangular faces
- Triangular Pyramid: Triangular base plus three triangular faces
Types of Surface Area
- Total Surface Area: Complete external surface including all faces
- Lateral Surface Area: Side surfaces only (excluding bases)
- Base Area: Area of bottom and/or top faces
Key Formulas
- Cube: SA = 6s² (where s is side length)
- Rectangular Prism: SA = 2(lw + lh + wh)
- Sphere: SA = 4πr²
- Cylinder: SA = 2πr(r + h)
- Cone: SA = πr(r + s) where s is slant height
Practical Applications
- Construction: Material estimation for walls, roofs, floors
- Manufacturing: Packaging design and material costs
- Painting/Coating: Calculate required paint or coating amounts
- Architecture: Building envelope calculations
- Engineering: Heat transfer and thermal analysis
Important Notes
- Units: Always ensure consistent units for all dimensions
- Precision: Adjust decimal places based on measurement accuracy
- Waste Factor: Add 10-15% for material waste in practical applications
- Complex Shapes: Break down into simpler geometric components
Worked Surface Area Examples
Cube: A cube with side 4 cm has surface area 6 × 4² = 96 cm².
Rectangular prism: A 5 × 3 × 2 m prism has surface area 2(15 + 10 + 6) = 62 m².
Cylinder: A cylinder with radius 2 m and height 5 m has total surface area 2π × 2(2 + 5) ≈ 87.965 m².
Sphere: A sphere with radius 3 in has surface area 4π × 3² ≈ 113.097 in².
FAQ - Surface Area Calculator
Surface area measures the total area of all external faces of a 3D shape, while volume measures the amount of space inside the shape. Surface area is measured in square units (m²), volume in cubic units (m³).