Surface Area Calculator

Calculate the surface area of cubes, spheres, cylinders, cones, and other 3D shapes instantly

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Total Surface Area of

square units

Lateral Surface Area

Curved/Side surfaces

Base Area

Top & bottom surfaces

Slant Height

Calculated: l = √(r² + h²)

Formula Used

Formula:
Values:
Result: SA = square units

Surface Area Formula Reference

Cube SA = 6a²
Rectangular Prism SA = 2(lw+lh+wh)
Sphere SA = 4πr²
Cylinder SA = 2πr(r+h)
Cone SA = πr(r+l)
Square Pyramid SA = a²+2al
Triangular Prism SA = bh+(a+b+c)L
Hemisphere SA = 3πr²

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About Surface Area Calculator

What is a Surface Area Calculator?

A surface area calculator is a mathematical tool that helps you determine the total area of all surfaces on three-dimensional (3D) shapes. Unlike area calculators for 2D shapes, surface area measures the entire outer covering of a solid object—essential for construction, manufacturing, packaging, and scientific applications.

How to Use This Calculator

  1. Select a 3D shape: Choose from 8 common solid shapes (cube, sphere, cylinder, etc.)
  2. Enter measurements: Input the required dimensions for your chosen shape
  3. View results: Instantly see the calculated surface area with the formula used
  4. Compare shapes: Switch between shapes to analyze surface areas for different solids

Supported Shapes and Formulas

Cube

Formula: SA = 6a²

A cube has 6 identical square faces. Multiply the area of one face by 6.

Rectangular Prism (Box)

Formula: SA = 2(lw + lh + wh)

Add the areas of all 6 rectangular faces (3 pairs of identical faces).

Sphere

Formula: SA = 4πr²

Multiply 4 times pi times the square of the radius.

Cylinder

Formula: SA = 2πr(r + h)

The surface includes 2 circular bases plus the curved lateral surface (2πrh).

Cone

Formula: SA = πr(r + l) where l = √(r² + h²)

The surface includes the circular base (πr²) plus the lateral surface (πrl). The slant height (l) is calculated from the radius and height.

Square Pyramid

Formula: SA = a² + 2a√(a²/4 + h²)

The surface includes the square base plus 4 triangular faces. The slant height is calculated from the base half-width and height.

Triangular Prism

Formula: SA = bh + (a + b + c)L

The surface includes 2 triangular bases plus 3 rectangular lateral faces.

Hemisphere

Formula: SA = 3πr²

The surface includes the curved dome (2πr²) plus the flat circular base (πr²).

Real-World Applications

Construction & Architecture

  • Calculating paint or coating needed for walls, domes, and tanks
  • Estimating insulation material for cylindrical pipes or spherical tanks

Manufacturing & Packaging

  • Determining material needed for boxes, cans, and containers
  • Optimizing packaging to minimize material costs

Science & Engineering

  • Calculating heat transfer rates (proportional to surface area)
  • Designing pressure vessels and storage tanks

Frequently Asked Questions

What's the difference between surface area and volume?

Surface area measures the total outer covering of a 3D shape (in square units), while volume measures the space inside the shape (in cubic units).

What units should I use?

You can use any unit (inches, feet, meters, etc.), but be consistent. The resulting surface area will be in square units.

How do I find the slant height?

For cones and pyramids, the slant height (l) is calculated using the Pythagorean theorem: l = √(r² + h²) for cones or l = √((a/2)² + h²) for square pyramids.

Why is surface area important?

Surface area determines how much material is needed to cover or coat an object, affects heat exchange rates, and influences chemical reaction speeds.

Tip: Always measure to the outer edge of objects. For hollow objects, you may need to calculate inner and outer surface areas separately.