Surface Area Calculator

Calculate the total surface area of standard geometric 3D shapes with step-by-step substitution steps, unrolled 2D nets, and components breakdown.

Measurement Unit
Radius (r)5 cm
cm
Calculated Surface Area (Sphere)
314.1593 cm²

The total outer boundary surface area enclosing the 3D shape.

2D Unrolled Net Diagramr=5
Surface ComponentFormulaArea (cm²)
Curved Surface4πr²314.1593
Total Surface Area-314.1593
How is this calculated?
SA = 4 × π × r²
SA = 4 × π × (5)²
SA = 4 × π × 25.0000
SA = 314.1593 cm²

About the Surface Area Calculator

Quickly calculate the total surface area of standard geometric 3D solids. Select your shape, adjust inputs in real time, and visualize the unrolled 2D flat nets of the shapes.

Mathematical Formula & Logic

Surface area is calculated using shape-specific formulas: 1. Sphere: SA = 4 * π * r² 2. Cylinder: SA = 2 * π * r² + 2 * π * r * h 3. Cone: SA = π * r² + π * r * s (where slant height s = √(r² + h²)) 4. Rectangular Prism: SA = 2 * (l*w + l*h + w*h) 5. Cube: SA = 6 * s²

Step-by-Step Example

Worked Examples: 1. Sphere: For a radius of 5, the surface area is: SA = 4 * π * 5² = 100 * π ≈ 314.16 2. Cylinder: For a radius of 3 and height of 7, the surface area is: SA = 2 * π * 3² + 2 * π * 3 * 7 = 18 * π + 42 * π = 60 * π ≈ 188.50

Reference Data & Values

shapeinputssurface area
Spherer = 5314.1593
Cylinderr = 3, h = 7188.4956
Coner = 3, h = 475.3982
Rectangular Prisml = 2, w = 3, h = 452.0000
Cubes = 496.0000

Frequently Asked Questions

Surface area is the total measure of the outer face boundaries of a three-dimensional object, expressed in square units (e.g., cm², m²).
The surface area of a sphere is found using the formula: SA = 4πr², where r is the radius of the sphere.
The surface area of a right cylinder is calculated as: SA = 2πr² + 2πrh, which sums the area of the two circular bases (2πr²) and the lateral rectangle face (2πrh).
For a right circular cone, the surface area is: SA = πr² + πrs, where s is the slant height, calculated using the Pythagorean theorem as s = √(r² + h²).
The surface area of a rectangular prism is: SA = 2(lw + lh + wh), where l is length, w is width, and h is height.
A cube has 6 identical square faces. Its surface area is: SA = 6s², where s is the edge/side length of the cube.
Surface area calculations are crucial in construction and painting (determining material coverage), thermodynamics (heat dissipation rates), biochemistry (cell membrane rates of diffusion), and packaging design.
No. Scaling all linear dimensions of a 3D solid by a factor of k scales its total surface area by k². For example, doubling all dimensions increases the surface area by a factor of 4 (2²).