📐 Surface Area Calculator
Calculate surface area for various 3D shapes
How to Use This Calculator
Select Shape Type
Choose the 3D shape from the dropdown menu: Sphere, Cylinder, Cone, Cube, or Rectangular Prism.
Enter Dimensions
Input the required dimensions for your selected shape. The input fields will change based on the shape you choose. Make sure all values are positive numbers.
Get Surface Area
Click "Calculate Surface Area" to get the total surface area of your shape. The result includes step-by-step calculation details.
Formulas
Sphere: A = 4πr²
r = radius
Cylinder: A = 2πr(r + h) = 2πr² + 2πrh
r = radius, h = height
Cone: A = πr(r + s) = πr² + πrs
r = radius, h = height, s = slant height = √(r² + h²)
Cube: A = 6a²
a = edge length
Rectangular Prism: A = 2(lw + lh + wh)
l = length, w = width, h = height
Example 1: Sphere with radius 5 units
A = 4 × π × 5² = 4 × π × 25 = 100π ≈ 314.16 units²
Example 2: Cylinder with radius 3, height 8
A = 2 × π × 3 × (3 + 8) = 2 × π × 3 × 11 = 66π ≈ 207.35 units²
Example 3: Cone with radius 4, height 6
s = √(4² + 6²) = √52 ≈ 7.21
A = π × 4 × (4 + 7.21) = π × 4 × 11.21 ≈ 140.81 units²
Example 4: Cube with edge 7 units
A = 6 × 7² = 6 × 49 = 294 units²
Example 5: Rectangular Prism with l=5, w=4, h=3
A = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2 × 47 = 94 units²
About Surface Area Calculator
Surface area is the total area of all surfaces covering a 3D shape. This calculator finds the surface area for common 3D shapes: spheres, cylinders, cones, cubes, and rectangular prisms. Surface area is important for determining material requirements, heat transfer, and geometric properties.
When to Use This Calculator
- Construction: Calculate paint, tiles, or material needed to cover surfaces
- Engineering: Determine surface area for heat transfer, coating, or finishing calculations
- Packaging: Calculate wrapping material needed for 3D objects
- Architecture: Estimate surface area for building facades or structures
- Mathematics Education: Teach students about 3D geometry and surface area
- Design: Plan surface coverage for 3D models or products
Why Use Our Calculator?
- ✅ Multiple Shapes: Handles spheres, cylinders, cones, cubes, and rectangular prisms
- ✅ Instant Results: Get accurate surface area calculations immediately
- ✅ Step-by-Step Display: See the formulas applied with your values
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand surface area concepts
- ✅ Completely Free: No registration required
Understanding Surface Area
Surface area differs from volume:
- Surface Area: Total area covering the outside (in square units: m², cm², etc.)
- Volume: Space inside the shape (in cubic units: m³, cm³, etc.)
- Units: Surface area is always in square units, volume in cubic units
- Applications: Surface area determines material needed; volume determines capacity
Real-World Applications
Painting: A sphere with radius 2 m needs paint. Surface area = 4π × 4 = 16π ≈ 50.27 m². This determines how much paint is needed.
Packaging: A cylinder with radius 5 cm and height 10 cm needs wrapping. Surface area = 2π × 5 × (5 + 10) = 150π ≈ 471.24 cm² of material.
Construction: A cube building with edge 10 m needs surface area = 6 × 100 = 600 m² for siding or cladding material.
Frequently Asked Questions
What is surface area?
Surface area is the total area of all surfaces covering a 3D object. It's measured in square units (m², cm², etc.) and represents the area you would cover if you wrapped the object with material.
What's the difference between surface area and volume?
Surface area measures the outside covering (square units), while volume measures the space inside (cubic units). For example, a sphere with radius 5 has surface area ≈ 314.16 units² and volume ≈ 523.60 units³.
How do I calculate surface area for irregular shapes?
This calculator handles regular shapes. For irregular shapes, you'd need to break them into regular components, calculate each part's surface area, then sum them. More complex shapes may require calculus or specialized methods.
Does surface area include all faces?
Yes! Total surface area includes all faces of the shape. For a cylinder, this means both circular bases plus the curved side. For a rectangular prism, it means all six rectangular faces.
Can I calculate lateral area instead?
Lateral area excludes the bases. For a cylinder: lateral area = 2πrh (just the curved side). For a cone: lateral area = πrs (just the curved surface). This calculator gives total surface area; subtract base areas if you need lateral area only.
What units should I use?
Use any consistent units (meters, centimeters, inches, feet, etc.). The result will be in square units of whatever you input. For example, if dimensions are in meters, surface area will be in square meters (m²).