Volume of a Rectangular Prism Calculator
Calculate the volume, surface area, and space diagonal of a rectangular prism (cuboid) from its length, width, and height. See also Volume of Cube Calculator and Volume of Triangular Prism Calculator.
How to Calculate the Volume of a Rectangular Prism
To find the volume of a rectangular prism (also called a cuboid or box), multiply its length by its width by its height. All three measurements must be in the same unit. The surface area is the sum of the areas of all six rectangular faces. This calculator also computes the space diagonal — the longest straight line that fits inside the box.
Rectangular Prism Volume Formula
V = l × w × h
SA = 2 × (l×w + l×h + w×h)
Space Diagonal = √(l² + w² + h²)
Example
Find the volume of a rectangular prism with l=10, w=6, h=4:
V = l × w × h
V = 10 × 6 × 4
V = 240 cubic units
SA = 2 × (60 + 40 + 24) = 2 × 124 = 248 square units
Rectangular Prism Volume Reference Table
| L × W × H | Volume | Surface Area | Space Diagonal |
|---|---|---|---|
| 2 × 2 × 2 | 8 | 24 | 3.4641 |
| 3 × 2 × 1 | 6 | 22 | 3.7417 |
| 4 × 3 × 2 | 24 | 52 | 5.3852 |
| 5 × 4 × 3 | 60 | 94 | 7.0711 |
| 6 × 4 × 3 | 72 | 108 | 7.8102 |
| 8 × 5 × 3 | 120 | 158 | 9.8995 |
| 10 × 5 × 4 | 200 | 220 | 11.8743 |
| 10 × 6 × 4 | 240 | 248 | 12.3288 |
| 10 × 8 × 5 | 400 | 340 | 13.7477 |
| 12 × 8 × 6 | 576 | 432 | 15.6205 |
| 12 × 10 × 8 | 960 | 592 | 17.5499 |
| 15 × 10 × 5 | 750 | 550 | 18.7083 |
| 20 × 10 × 8 | 1600 | 880 | 23.7487 |
| 20 × 15 × 10 | 3000 | 1300 | 26.9258 |
| 30 × 20 × 10 | 6000 | 2200 | 37.4166 |
Frequently Asked Questions
What is a rectangular prism?
A rectangular prism (also called a cuboid) is a 3D shape with six rectangular faces. All angles are right angles. A box, a brick, and a room are everyday examples of rectangular prisms.
What is the difference between a rectangular prism and a cube?
A cube is a special rectangular prism where all three dimensions are equal. In a general rectangular prism, the length, width, and height can all be different.
What is the space diagonal?
The space diagonal is the longest straight line that can be drawn inside the rectangular prism, connecting two opposite corners. It is calculated as √(l² + w² + h²).
Does the order of dimensions matter?
No. Since multiplication is commutative, l × w × h gives the same volume regardless of which dimension you call length, width, or height.