Volume of Cuboid Calculator
Enter the length, width, and height of a box-shaped object and instantly get its volume, surface area, base area, and diagonal — useful for storage, shipping, construction, and everyday sizing questions.
Calculate Cuboid Volume
Enter the three dimensions in the same unit — results update instantly.
200 cm³
What Is a Cuboid, and Why Calculate Its Volume?
A cuboid is a three-dimensional shape with six rectangular faces, twelve edges, and eight vertices — think of a shoebox, a shipping carton, a brick, or a standard room. Unlike a cube, where all three dimensions are equal, a cuboid can have a different length, width, and height, making it the more general (and more common) shape in everyday objects.
The volume of a cuboid tells you how much three-dimensional space it occupies — how much it can hold, how much material it's made of, or how much room it takes up. This single number underlies a huge range of practical calculations: how much water a tank holds, how much concrete fills a foundation, how many boxes fit in a container, or how much air a room needs to be ventilated.
The Volume of Cuboid Formula
Cuboid volume is found by multiplying the three dimensions together — one of the most fundamental formulas in geometry.
Volume
V = Length × Width × Height
Multiply all three dimensions together to get the volume, expressed in cubic units (cm³, m³, in³, ft³, and so on).
Example: 10 × 5 × 4 = 200 cm³
Total Surface Area
SA = 2(LW + LH + WH)
Sum the areas of all three pairs of opposite faces, then double the total, since each face has a matching opposite face.
Example: 2(50 + 40 + 20) = 220 cm²
Space Diagonal
d = √(L² + W² + H²)
The diagonal is the straight-line distance from one corner of the cuboid to the opposite corner, found using a 3D version of the Pythagorean theorem.
Example: √(100 + 25 + 16) ≈ 11.87 cm
Lateral Surface Area
LSA = 2H(L + W)
The lateral surface area covers only the four "side" faces, excluding the top and bottom — useful for wrapping or painting the sides of a box-shaped object.
Example: 2 × 4 × (10 + 5) = 120 cm²
Common Cuboid Volume Examples
A ready reference showing volume, surface area, and diagonal for a few commonly encountered box-shaped objects.
| Dimensions (L × W × H) | Volume | Surface Area | Diagonal |
|---|---|---|---|
| 10 × 10 × 10 cm (a cube) | 1,000 cm³ | 600 cm² | 17.32 cm |
| 10 × 5 × 4 cm | 200 cm³ | 220 cm² | 12.85 cm |
| 30 × 20 × 15 cm (shoebox) | 9,000 cm³ | 2,700 cm² | 38.08 cm |
| 60 × 40 × 40 cm (moving box) | 96,000 cm³ | 12,800 cm² | 81.24 cm |
| 2 × 1.5 × 1 m (small room) | 3 m³ | 13 m² | 2.69 m |
| 12 × 8 × 8.5 ft (bedroom) | 816 ft³ | 536 ft² | 17.03 ft |
For a size not listed here, the calculator at the top of this page computes the exact figures instantly, in the unit of your choice.
Worked Examples: Step by Step
Example 1: A storage bin measuring 40 cm × 30 cm × 25 cm
- Formula: V = L × W × H
- 40 × 30 × 25 = 30,000
- Answer: Volume = 30,000 cm³ (or 30 liters, since 1,000 cm³ = 1 liter)
Example 2: A rectangular fish tank measuring 60 cm × 30 cm × 35 cm
- Volume: 60 × 30 × 35 = 63,000 cm³
- Convert to liters: 63,000 ÷ 1,000 = 63 liters
- Answer: The tank holds 63 liters when full
Example 3: A concrete slab 5 m long, 3 m wide, and 0.15 m thick
- Formula: V = L × W × H
- 5 × 3 × 0.15 = 2.25
- Answer: 2.25 cubic meters of concrete needed
Where This Calculation Comes Up
Shipping and Packaging
Calculating a box's volume determines how much product it can hold, how many boxes fit in a container or truck, and how dimensional weight is calculated for shipping costs — a routine part of logistics and e-commerce fulfillment.
Storage and Moving
Knowing the volume of storage bins, moving boxes, or a storage unit helps estimate how much can fit, and how many boxes or trips a move will require.
Aquariums and Tanks
The volume of a rectangular fish tank (in liters or gallons) determines stocking levels, filtration requirements, and water treatment dosing — all derived directly from the cuboid volume formula.
Construction and Concrete
Calculating the volume of a foundation, slab, or wall in cubic meters or cubic yards is the basis for estimating how much concrete, gravel, or fill material a project needs.
HVAC and Room Ventilation
Room volume (length × width × height) is a key input for sizing air conditioning units and calculating required airflow, since ventilation needs scale with the volume of air in a space.
Common Mistakes When Calculating Cuboid Volume
- Mixing units before multiplying. All three dimensions must be in the same unit before multiplying — mixing centimeters and meters, or inches and feet, without converting first produces a meaningless result.
- Confusing volume with surface area. Volume (L × W × H) measures three-dimensional space; surface area (2(LW+LH+WH)) measures the total area of the outer faces — these use different formulas and different units (cubic vs. square).
- Forgetting the cubic unit on the answer. A volume answer should always be labeled in cubic units (cm³, m³, ft³) — writing just "200" without the unit loses essential information about scale.
- Assuming a cuboid is the same as a cube. A cube requires all three dimensions to be equal; a general cuboid does not — using the cube formula (s³) on a non-cube cuboid gives an incorrect result.
Cheat Sheet: Cuboid Formulas
| Quantity | Formula |
|---|---|
| Volume | V = L × W × H |
| Total Surface Area | SA = 2(LW + LH + WH) |
| Lateral Surface Area | LSA = 2H(L + W) |
| Base Area | A = L × W |
| Base Perimeter | P = 2(L + W) |
| Space Diagonal | d = √(L² + W² + H²) |
Frequently Asked Questions
What is the formula for the volume of a cuboid?
Volume = Length × Width × Height. Multiply the three dimensions together, using the same unit for each, to get the volume in cubic units.
What is the difference between a cube and a cuboid?
A cube has all three dimensions equal (length = width = height), while a cuboid can have three different dimensions. Every cube is a cuboid, but not every cuboid is a cube.
How do I find the volume of a cuboid in liters?
Calculate the volume in cubic centimeters (L × W × H, with all dimensions in cm), then divide by 1,000, since 1,000 cm³ equals exactly 1 liter.
What is the surface area formula for a cuboid?
Total Surface Area = 2(LW + LH + WH), which sums the areas of all three pairs of opposite rectangular faces and doubles the total.
How do I calculate the diagonal of a cuboid?
Use the 3D Pythagorean theorem: diagonal = √(L² + W² + H²), where L, W, and H are the cuboid's three dimensions.
Do all three dimensions need to be in the same unit?
Yes. Length, width, and height must all be measured in the same unit before multiplying, or the volume result will be meaningless — convert everything to one unit first if the original measurements differ.
Does this calculator work for a cube as well as a general cuboid?
Yes. Entering the same value for length, width, and height calculates the volume and surface area of a cube, since a cube is simply a cuboid with all equal sides.