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 |
Real-World Applications
Shipping Containers
Logistics companies calculate container volume to maximize cargo space and estimate shipping costs.
Swimming Pools
Pool builders calculate water volume to size pumps, heaters, and determine chemical dosages.
Room Volume
HVAC engineers calculate room volumes to properly size air conditioning and heating systems.
Aquariums
Aquarium enthusiasts calculate tank volume to determine water capacity and appropriate fish stocking levels.
Solved Examples
Example 1: Shipping Container
A standard 20-foot shipping container has internal dimensions of approximately 5.9 m × 2.35 m × 2.39 m. Find its volume.
V = 5.9 × 2.35 × 2.39
V ≈ 33.13 m³
Example 2: Swimming Pool Water Volume
A rectangular swimming pool is 12 m long, 6 m wide, and 1.8 m deep. How many liters of water does it hold?
V = 12 × 6 × 1.8 = 129.6 m³
1 m³ = 1000 L
V = 129,600 liters
Example 3: Aquarium Capacity
A rectangular aquarium measures 80 cm × 40 cm × 50 cm. How many liters of water can it hold?
V = 80 × 40 × 50 = 160,000 cm³
1 L = 1000 cm³
V = 160 liters
Practice Questions
Q1: Find the volume of a box that is 15 cm × 8 cm × 6 cm.
Answer: V = 15 × 8 × 6 = 720 cm³
Q2: A room is 5 m × 4 m × 3 m. What is its volume in cubic meters?
Answer: V = 5 × 4 × 3 = 60 m³
Q3: A rectangular prism has volume 360 cm³, length 12 cm, and width 6 cm. Find its height.
Answer: h = V / (l × w) = 360 / (12 × 6) = 360 / 72 = 5 cm
Q4: What is the surface area of a box measuring 10 × 5 × 3?
Answer: SA = 2(10×5 + 10×3 + 5×3) = 2(50 + 30 + 15) = 2(95) = 190 square units
Q5: How many boxes (20×15×10 cm) fit in a container (200×150×100 cm)?
Answer: Along each dimension: 200/20=10, 150/15=10, 100/10=10; Total = 10×10×10 = 1000 boxes
Key Takeaways
- Rectangular prism volume is simply V = length × width × height.
- The order of multiplication does not matter — l×w×h = w×h×l.
- A cube is a special case where all three dimensions are equal.
- 1 m³ = 1,000 liters = 1,000,000 cm³ — useful for capacity conversions.
- The space diagonal √(l²+w²+h²) is the longest line inside the box.
- Surface area = 2(lw + lh + wh) covers all six rectangular faces.
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.