Use our online volume of cuboid calculator to calculate the volume of a cuboid, also known as a rectangular prism or rectangular box.
This three-dimensional shape has six rectangular faces, with each pair of opposite faces being identical. The calculator takes the measurements of the cuboid’s length, width, and height as inputs and calculates its volume.
The volume of an object is the amount of three-dimensional space it occupies. For a cuboid, this represents the amount of space or material contained within its boundaries.
- A moving box measures 2 feet in length, 1.5 feet in width, and 2 feet in height. The calculator would determine its volume as 6 cubic feet.
- A storage container has dimensions of 10 meters long, 2.5 meters wide, and 3 meters high. The calculator would compute its volume as 75 cubic meters.
- A small jewelry box measures 5 inches in length, 3 inches in width, and 2 inches in height. The calculator would calculate its volume as 30 cubic inches.
Volume Of Cuboid Calculator
| Length | Width | Height | Volume | Conversion Equation | Converted Volume |
|---|---|---|---|---|---|
| 5 ft | 4 ft | 3 ft | 60 ft³ | 1 ft³ = 0.0283168 m³ | 1.699 m³ |
| 2 m | 1.5 m | 1.8 m | 5.4 m³ | 1 m³ = 1000 L | 5,400 L |
| 10 cm | 8 cm | 6 cm | 480 cm³ | 1 cm³ = 1 mL | 480 mL |
| 3 yd | 2 yd | 2.5 yd | 15 yd³ | 1 yd³ = 0.764555 m³ | 11.468 m³ |
| 20 in | 15 in | 12 in | 3600 in³ | 1 in³ = 16.3871 cm³ | 58,993.56 cm³ |
How do you calculate the volume of a cuboid?
To calculate the volume of a cuboid, follow these steps:
- Measure the dimensions: Determine the length, width, and height of the cuboid using a consistent unit of measurement.
- Apply the formula: Multiply the three dimensions together using the formula V = l × w × h.
- Verify the units: Ensure that the result is expressed in cubic units (e.g., cubic centimeters, cubic feet, cubic meters).
- Round if necessary: Depending on the precision required, round the result to an appropriate number of decimal places.
Example calculation: Let’s calculate the volume of a cuboid with length 7.5 meters, width 3.2 meters, and height 2.8 meters.
- Dimensions: l = 7.5 m, w = 3.2 m, h = 2.8 m
- V = 7.5 m × 3.2 m × 2.8 m
- V = 67.2 cubic meters (m³)
In this case, the volume is already expressed in cubic meters, so no unit conversion is necessary.
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Volume Of Cuboid Formula
The formula for the volume of a cuboid is easy:
V = l × w × h
Where:
- V represents the volume.
- l stands for length.
- w denotes width.
- h indicates height.
This formula calculates the space occupied by the cuboid by multiplying its three dimensions. It’s important to ensure that all measurements are in the same unit before applying the formula.
Examples:
- A cuboid with length 5 cm, width 3 cm, and height 4 cm: V = 5 cm × 3 cm × 4 cm = 60 cubic centimeters (cm³)
- A room measuring 15 feet long, 12 feet wide, and 8 feet high: V = 15 ft × 12 ft × 8 ft = 1,440 cubic feet (ft³)
- A shipping container with length 6 m, width 2.4 m, and height 2.6 m: V = 6 m × 2.4 m × 2.6 m = 37.44 cubic meters (m³)
How to calculate area of cuboid?
The surface area is the total area of all six faces of the cuboid. Here’s how to calculate it:
- Calculate the area of each face: There are three pairs of identical rectangular faces.
- Front/Back face area: length × height
- Left/Right face area: width × height
- Top/Bottom face area: length × width
- Sum up the areas: Add the areas of all six faces.
The formula for the surface area of a cuboid is:
SA = 2(lw + lh + wh)
Where:
- SA is the surface area.
- l is length.
- w is width.
- h is height.
Example calculation: Let’s calculate the surface area of a cuboid with length 5 m, width 3 m, and height 2 m.
- Front/Back face area: 5 m × 2 m = 10 m² (× 2 faces = 20 m²)
- Left/Right face area: 3 m × 2 m = 6 m² (× 2 faces = 12 m²)
- Top/Bottom face area: 5 m × 3 m = 15 m² (× 2 faces = 30 m²)
Total surface area = 20 m² + 12 m² + 30 m² = 62 m²
Alternatively, using the formula: SA = 2(5 × 3 + 5 × 2 + 3 × 2) = 2(15 + 10 + 6) = 2(31) = 62 m².
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