Surface Area Calculator

Surface Area Calculator

This surface area calculator estimates the total surface area occupied by common 3D shapes. To find the dimensions of these shapes, our tool applies different equations. Furthermore, surface area calculations can help across various fields like aerodynamics, education, engineering, architecture, and design.

How to Find the Surface Area of 3D Shapes?

Surface area is determined by adding the areas of every face or surface of an object. In geometric shapes, the surface area can be computed using specific formulas tailored for each shape.

➥ Surface Area of Capsule 

The formula used to find the surface area of a capsule is:

SA = 4πr² + 2πrh

Where:

• r = radius 
• h = height

➥ Surface Area of Cone 

• base SA = πr²
• lateral SA = πr√r² + h²

Total SA = πr² + πr√(r² + h²)

➥ Surface Area of Conical Frustum 

The formula for the Surface area Conical Frustum is given below:

Area of the Conical Frustum  = Circle Top + Circular Bottom 

Circle top = π r² 

Circular bottom = π R²

So,

• Area of Circular end SA = π(R² + r²)
• lateral SA = π(R+r)√(R-r)² + h²

SA = π(R + r) * l + πR² + πr²

Where:  

• R and r = radii of the ends  
• h = height

➥ Surface Area of Cube 

SA = 6a²

Where:  

• a = edge length

➥ Surface Area of Cylinder 

• base SA = 2πr²
• lateral SA = 2πrh

total SA = 2πr(r + h) 

➥ Surface Area of Hemisphere

Surface area of the Hemisphere = Curved surface area of hemisphere + circular base area

• Curved surface area of the hemisphere = 2πr²
• Circular base area = πr²

Then;

Surface area of the Hemisphere = 2πr² + πr² = 3πr² square units

➥ Surface Area of Rectangular Prism (cuboid)

S = 2 ( lh + lw + wh )

Where: 

• l = length 
• w = width 
• h = height of the prism

➥ Surface Area of Sphere 

The surface area (SA) of a sphere can be calculated using the equation:

SA = 4πr² = π * d²

➥ Surface Area of Spherical Cap 

Spherical cap SA = 2πRh

➥ Surface Area of Triangular Prisms

Surface area = bh + (a + b + c) H

Where:

• a, b, and c = Side lengths of the triangular bases 
• b and h = Base and height of the triangular faces 
• H = Height of the prism

➥ Surface Area of Pyramids 

Surface Area = l × √(l² + 4 × h²) + l²

Where:

• l = Length of one side of the base of the pyramid
• l² = Area of the square base

➥ Ball Surface Area 

A ball is a spherical object, so its surface area can be calculated using this formula.

Surface Area = 4πr²

➥ Ellipsoid Surface Area

S = 4π * [(ab)^1.6 + (ac)^1.6 + (bc)^1.6]^(1/1.6) / 3

Where: 

• a, b, and c = axes of the ellipsoid

Table of Common Shapes Formulas:

How is surface area different from volume?

The surface area is the total area of the outer side of the 3D objects while the volume is the measure of space inside that object. 

What are the units of measurement for surface area?

Surface area is measured in the following units including square centimeters (cm²), square millimeters (mm)², square meters (m²), square inches (in²), square feet (ft²), and square yards (yd²).