What Is a Rectangular Prism?
A rectangular prism is a three-dimensional solid
with six rectangular faces. It has three primary
dimensions: length, width, and height.
A rectangular box, shipping package, storage
container, and many building components are common
real-world examples of rectangular prisms.
A rectangular prism has 6 faces, 12 edges, and
8 vertices. Opposite faces have the same dimensions
and are parallel to each other.
This calculator can determine the volume, total
surface area, total edge length, space diagonal,
base area, and lateral surface area from the three
dimensions.
How to Use the Rectangular Prism Calculator
Enter the length, width, and height of your
rectangular prism. The calculator will automatically
calculate several useful measurements.
1
Enter Length
Enter the length of the rectangular prism
in your preferred measurement unit.
2
Enter Width & Height
Add the width and height using the same
measurement unit as the length.
3
View the Results
Click calculate to instantly see volume,
surface area, diagonal, and more.
Rectangular Prism Formulas
Volume
The volume measures the amount of three-dimensional
space inside the rectangular prism.
V = l × w × h
Surface Area
Surface area is the total area of all six
rectangular faces.
SA = 2(lw + lh + wh)
Space Diagonal
The space diagonal is the straight-line distance
from one vertex to the opposite vertex through
the interior of the prism.
d = √(l² + w² + h²)
Total Edge Length
A rectangular prism has four edges of each
dimension, giving the total edge length:
E = 4(l + w + h)
Rectangular Prism Calculation Example
Suppose a rectangular prism has a length of
10 units, a width of
6 units, and a height of
4 units.
Volume Calculation
V = l × w × h
V = 10 × 6 × 4
V = 240 cubic units
Surface Area Calculation
SA = 2(lw + lh + wh)
SA = 2(60 + 40 + 24)
SA = 248 square units
Space Diagonal
d = √(10² + 6² + 4²)
d = √152
d ≈ 12.33 units
Therefore, the prism has a volume of
240 cubic units, a surface area
of 248 square units, and a space
diagonal of approximately 12.33 units.
Volume vs. Surface Area
Volume and surface area describe different
properties of a rectangular prism.
Volume
Volume measures the amount of space contained
inside the prism. It is measured in cubic units,
such as cm³, m³, or ft³.
Surface Area
Surface area measures the total area covering
the outside of the prism. It is measured in
square units, such as cm², m², or ft².
Volume = l × w × h
Surface Area = 2(lw + lh + wh)
Where Are Rectangular Prisms Used?
Rectangular prisms appear in many everyday
objects and practical applications. Boxes,
books, bricks, cabinets, rooms, containers,
packages, and storage units can often be
approximated as rectangular prisms.
Their volume can help determine storage capacity,
while surface area can be useful for estimating
materials needed to cover or manufacture the object.
In mathematics and engineering, rectangular prisms
are also commonly used to study three-dimensional
geometry, dimensions, volume, area, and diagonal
relationships.
Frequently Asked Questions
What is a rectangular prism?
A rectangular prism is a three-dimensional shape
with six rectangular faces, 12 edges, and 8 vertices.
What is the formula for the volume of a rectangular prism?
The volume formula is V = l × w × h, where l is
length, w is width, and h is height.
What is the surface area formula?
The surface area is SA = 2(lw + lh + wh).
It adds the areas of all six rectangular faces.
How do you calculate the diagonal of a rectangular prism?
Use d = √(l² + w² + h²) to calculate the
space diagonal between opposite vertices.
How many faces does a rectangular prism have?
A rectangular prism has six rectangular faces.
Opposite faces have equal dimensions.
How many edges does a rectangular prism have?
A rectangular prism has 12 edges. There are four
edges corresponding to each of its three dimensions.
How many vertices does a rectangular prism have?
A rectangular prism has eight vertices, where
three edges meet at each vertex.
What is the difference between a rectangular prism and a cube?
A cube is a special type of rectangular prism in
which length, width, and height are all equal.
What units are used for rectangular prism volume?
Volume is expressed in cubic units. For example,
dimensions measured in centimeters produce volume
in cubic centimeters (cm³).
Can this calculator calculate surface area too?
Yes. The calculator provides volume, total surface
area, total edge length, space diagonal, base area,
and lateral surface area.