Surface Area Calculator

Calculate surface area of various 3D shapes including spheres, cubes, cylinders, cones, and prisms

Calculate Surface Area

units

Surface Area Formulas

Sphere:
A = 4πr²
Cube:
A = 6a²
Cylinder:
A = 2πr² + 2πrh
Cone:
A = πr² + πr√(r² + h²)
Rectangular Prism:
A = 2(lw + wh + lh)
Square Pyramid:
A = l² + l√(l² + 4h²)

Surface Area Tips

Surface area is always measured in square units

Lateral area excludes the base and top surfaces

For hollow shapes, calculate inner and outer surfaces

Double-check units are consistent across all dimensions

Understanding Surface Area

What is Surface Area?

Surface area is the total area that the surface of a 3D object occupies. It represents the sum of all the areas of the faces or surfaces that bound the solid. Surface area is measured in square units (cm², m², ft², etc.).

Types of Surface Area

  • Total Surface Area: Sum of all surface areas
  • Lateral Surface Area: Area of sides (excluding bases)
  • Base Area: Area of the base(s) only

Common Applications

  • Material estimation for manufacturing
  • Paint coverage calculations
  • Heat transfer analysis
  • Packaging design
  • Architecture and construction

Pro Tip: When dealing with composite shapes, break them down into simpler geometric forms and calculate each surface area separately.

Shape-Specific Formulas

Sphere

A perfectly round 3D object

A = 4πr²

r = radius

Cube

6 equal square faces

A = 6a²

a = side length

Cylinder

Circular bases with curved side

A = 2πr² + 2πrh

r = radius, h = height

Cone

Circular base with pointed top

A = πr² + πr√(r² + h²)

r = radius, h = height

Rectangular Prism

Box with rectangular faces

A = 2(lw + wh + lh)

l = length, w = width, h = height

Square Pyramid

Square base with triangular faces

A = l² + l√(l² + 4h²)

l = base side, h = height