Case 1
- Length
- 4
- Width
- 3
- Height
- 2
52.00
Open with these valuesCuboid Surface Area Calculator
52.00units²
Result: 52.00 units²A cuboid has six rectangular faces in three matching pairs, so the surface area is twice the sum of the three different face areas. A 4 × 3 × 2 box gives 2 × (12 + 8 + 6) = 52 square units. The volume and the space diagonal of every example box stand in the table below.
The numbers at a glance
Held fixed: Length 4.000, Width 3.000.
| Height | Result |
|---|---|
| 0.500 | 31.00 |
| 1.000 | 38.00 |
| 1.500 | 45.00 |
| 2.000Your value | 52.00 |
| 2.500 | 59.00 |
| 3.000 | 66.00 |
| 3.500 | 73.00 |
| 4.000 | 80.00 |
Worked examples
Case 2
- Length
- 1
- Width
- 1
- Height
- 1
6.00
Open with these valuesCase 3
- Length
- 10
- Width
- 2
- Height
- 3
112.00
Open with these valuesHow it's calculated
A = 2 × (l×w + l×h + w×h)
- StepMeasure length, width and height in one and the same unit.
- StepWork out the three different face areas: l×w, l×h and w×h.
- ResultAdd them and double the sum — that is the whole outside.
Reference table
| Length, width, height | Volume | Space diagonal | Surface area |
|---|---|---|---|
| 1, 1, 1 | 1 | 1.732051 | 6 |
| 4, 3, 2 | 24 | 5.385165 | 52 |
| 2, 2, 8 | 32 | 8.485281 | 72 |
| 10, 2, 3 | 60 | 10.630146 | 112 |
| 5, 5, 5 | 125 | 8.660254 | 150 |
Questions
How do I calculate the surface area of a cuboid?
A cuboid has six rectangular faces in three matching pairs, so the total is 2 × (length×width + length×height + width×height). For a box of 4 × 3 × 2 that is 2 × (12 + 8 + 6) = 52 square units. Work out the three face areas, add them, then double the total.
What is a cuboid?
A cuboid is a rectangular box: six flat rectangular faces, every corner a right angle. Length, width and height can all be different, and a cube is the special case where all three are equal. Bricks, shipping boxes, rooms and aquariums are everyday cuboids.
What is the difference between surface area and volume?
Surface area is the outside of all six faces in square units — how much paint, wrapping paper or sheet material the box needs. Volume is the space inside, length × width × height in cubic units. For a 4 × 3 × 2 box the surface area is 52 and the volume is 24.
What is the space diagonal of a cuboid?
It is the longest straight line inside the box, running corner to opposite corner, and by the Pythagorean theorem in space it is √(l² + w² + h²). For a 4 × 3 × 2 box that is √29 ≈ 5.385165, the value listed in the table above. It is the longest rod that still fits diagonally inside.
Which units does the answer use?
Whatever you entered, squared. Length, width and height in centimetres give square centimetres, in inches square inches. All three inputs must use the same unit.
Sources and last check
Information, not professional advice.