What Is the Surface Area of a Cuboid?
A cuboid (also called a rectangular box or rectangular prism) is a 3D shape with six flat rectangular faces meeting at right angles. Its surface area is the total area of all six faces combined. Because opposite faces are identical, the surface area is twice the sum of the three distinct face areas. This calculator finds that total instantly from the length, width and height, and also returns the volume and the internal space diagonal.
How to Use This Calculator
Enter the three dimensions of your box — length (l), width (w) and height (h) — using any consistent unit (cm, m, inches, etc.). The result is given in square units of that same unit. The tool also displays the volume (in cubic units) and the space diagonal, the longest line that fits diagonally inside the box.
The Formula Explained
The surface area formula is $$SA = 2(lw + lh + wh)$$. The cuboid has three pairs of matching faces: two of area \(l\times w\), two of area \(l\times h\), and two of area \(w\times h\). Adding one of each gives \(lw + lh + wh\), and doubling accounts for both faces in each pair.
Worked Example
Suppose a box measures 5 × 4 × 3 units. Then \(lw = 20\), \(lh = 15\), and \(wh = 12\). Their sum is 47, so $$SA = 2 \times 47 = 94 \text{ square units}$$ The volume is \(5 \times 4 \times 3 = 60\) cubic units, and the diagonal is \(\sqrt{25 + 16 + 9} = \sqrt{50} \approx 7.07\) units.
FAQ
Is a cube a special cuboid? Yes. When \(l = w = h = s\), the formula simplifies to \(SA = 6s^2\).
What units should I use? Any unit works as long as all three dimensions share the same unit; the surface area comes out in those units squared.
Does surface area equal the amount of wrapping paper needed? Approximately — it gives the total face area, but real wrapping needs overlap, so add a margin.
