Cuboids model boxes, rooms and tanks. Enter the length, breadth and height to get the volume, both surface areas and the space diagonal.
Enter length, breadth and height in the same unit.
Read the volume, surface areas and diagonal.
Volume: V = l × b × h
TSA: 2(lb + bh + hl)
Diagonal: √(l² + b² + h²)
A cuboid is a box shape with six rectangular faces, meeting at right angles. Rooms, bricks, almirahs, water tanks, shipping cartons and textbooks are all close to cuboids. Given the length, breadth and height, this calculator returns four things: the volume, the total surface area, the lateral surface area and the space diagonal.
Each result answers a different practical question. Volume tells you how much a tank holds or how much soil a pit needs. Total surface area tells you how much sheet or cardboard covers the whole box. Lateral surface area is the four walls only, which is what a painter quotes for when the floor and ceiling are left out. The diagonal is the longest straight rod or pipe that fits inside. Class 9 surface area and volume chapters test all four.
1. Measure length l, breadth b and height h, and convert them to the same unit.
2. Volume: multiply the three, V = l × b × h. The unit is cubic, such as m³ or cm³.
3. Total surface area: add the three distinct face areas and double the sum, TSA = 2(lb + bh + hl).
4. Lateral surface area: find the perimeter of the base, 2(l + b), and multiply by the height, LSA = 2h(l + b).
5. Space diagonal: D = √(l² + b² + h²).
6. For capacity in litres, use 1 m³ = 1000 litres and 1000 cm³ = 1 litre.
Place unit cubes on the floor of the box. One layer holds l × b of them. Stack h such layers and you have l × b × h cubes, which is the volume. The same idea says volume equals base area × height for any prism, not just a cuboid. It also explains how units behave. If each length doubles, the volume grows eight times, because 2 × 2 × 2 = 8. That scaling is why a slightly bigger water tank holds far more water than you might guess from its measurements.
A cuboid has three pairs of identical opposite faces: top and bottom (l × b), front and back (l × h), and the two sides (b × h). Adding one face from each pair and doubling gives TSA = 2(lb + bh + hl). If you unfold the four walls into one long strip, the strip is as long as the perimeter of the floor, 2(l + b), and as tall as the room, so LSA = 2h(l + b). The difference between TSA and LSA is exactly the floor plus the ceiling, 2lb.
The diagonal of the floor runs from one corner to the opposite corner, and its length is √(l² + b²) by Pythagoras. The space diagonal rises from one end of that floor diagonal to the opposite top corner, forming another right triangle with the floor diagonal and the height as its legs. Applying Pythagoras again gives D² = (l² + b²) + h², so D = √(l² + b² + h²). A cube of side a is the special case where all three are equal, giving D = a√3.
Anjali wants to repaint her bedroom in Bhopal, which is 5 m long, 4 m wide and 3 m high. She also wants to know whether a 7 m curtain rod could fit inside diagonally when it is delivered.
Volume = l × b × h: = 5 × 4 × 3 = 60
Total surface area = 2(lb + bh + hl): = 2(20 + 12 + 15) = 94
Lateral surface area = 2h(l + b): = 2 × 3 × (5 + 4) = 54
Diagonal = √(l² + b² + h²): = √(25 + 16 + 9) = 7.0711
Answer: Volume 60; Total surface area 94; Lateral surface area 54
Quoting total surface area to a painter when only the walls are being painted. Use LSA, and add the ceiling separately if needed.
Not subtracting doors and windows from the wall area before buying paint.
Mixing feet and metres, or centimetres and metres, within one calculation.
Confusing the face diagonal √(l² + b²) with the space diagonal, which also includes the height.
Converting cm³ to litres by dividing by 100 instead of 1000.
Estimating paint, wallpaper or putty for a room from its dimensions.
Finding the capacity of a rectangular overhead or underground water tank in litres.
Working out cardboard or sheet metal for packing boxes and trunks.
Checking whether a long pipe, rod or ladder fits inside a room or vehicle.
Calculating earth to be dug for a foundation trench or soak pit.
How many litres does a cuboid tank hold?
Compute the volume in cubic centimetres and divide by 1000, or in cubic metres and multiply by 1000.
Is a cube a cuboid?
Yes, one with all three dimensions equal.