Cuboid Calculator: Volume, Surface Area and Diagonal
Enter the three dimensions of the box and a unit. You get the volume, surface areas, the longest diagonal and the capacity.
- Nothing you type is stored
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Volume
144cm³
- Total surface area (TSA)
- 192 cm²
- Lateral surface area (LSA)
- 96 cm²
- Space diagonal
- 13 cm
- Capacity in litres
- 0.144 L
Show working
- V = l × b × h = 12 × 4 × 3 = 144 cm³
- TSA = 2(lb + bh + hl) = 2 × (48 + 12 + 36) = 192 cm²
- LSA = 2h(l + b) = 96 cm²
- d = √(l² + b² + h²) = √(144 + 16 + 9) = 13 cm
How to use
- Enter length, breadth and height.
- Choose a length unit.
- Read the volume, TSA, LSA, diagonal and litres.
Good to know
Volume = l × b × h, total surface area = 2(lb + bh + hl), lateral surface area (four walls) = 2h(l + b), and the space diagonal = √(l² + b² + h²). These are in NCERT Class 8 and 9.
The diagonal tells you the longest straight rod that fits inside the box, a common textbook question. A 12 × 4 × 3 box fits a 13-unit rod.
For a room: LSA is the wall area to paint (minus doors and windows), l × b the floor, and volume the air space. For tanks and boxes, litres = volume in cm³ ÷ 1,000.
Questions
What is the volume of a cuboid?
Length × breadth × height.
What is the diagonal of a cuboid?
√(l² + b² + h²), the longest straight line from one corner to the opposite corner.
What is the lateral surface area?
The area of the four side faces, 2h(l + b), not counting the top and bottom.
How many bricks fit in a wall?
Wall volume ÷ one brick's volume gives a rough count. Allow for mortar and use a brick calculator for real orders.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.