Cuboid Calculator

A cuboid is the most ordinary shape in the room: a box. Six rectangular faces, twelve edges, eight corners, with a length, a width, and a height that can all differ. Cardboard cartons, bricks, fish tanks, shipping containers, and most rooms are cuboids. When the three dimensions happen to be equal you have a cube, which is just the special case.

From those three measurements every other property follows. Volume is length times width times height, the space inside, measured in cubic units. Surface area is 2(lw + lh + wh), the total skin of all six faces, which is what you need for wrapping, painting, or working out material. The space diagonal, the straight line from one corner to the opposite corner through the middle, is the square root of (l squared plus w squared plus h squared). That one tells you the longest straight object that can fit inside, which is why it matters when you are packing a box.

There are smaller numbers worth having too. The three face diagonals are the diagonals across each pair of faces. The total edge length, 4(l + w + h), is how much framing or trim you would need to outline the box, useful for everything from aquarium bracing to picture-frame style builds.

Enter the length, width, and height in the same unit and the calculator returns all of these at once. Keep the units consistent: feed it centimetres and you get cubic centimetres of volume and square centimetres of surface area. Mixing inches and centimetres is the one mistake that quietly wrecks the answer.

Worked example: a 12 by 8 by 6 cm box

Volume: 12 × 8 × 6 = 576 cm³, which is 0.576 litres.

Surface area: 2(12×8 + 12×6 + 8×6) = 2(96 + 72 + 48) = 2 × 216 = 432 cm².

Space diagonal: √(144 + 64 + 36) = √244 ≈ 15.62 cm. So a 15 cm ruler slides in corner to corner; a 16 cm one does not go in at all, at any angle.

Total edge length: 4(12 + 8 + 6) = 104 cm of framing.

Face diagonals: √(144+64) ≈ 14.42, √(144+36) ≈ 13.42, √(64+36) = 10 cm exactly, that last one because 6, 8, 10 is a Pythagorean triple.

A cheap sanity check

Surface area should always land between two numbers you can work out in your head: six times the smallest face, and six times the largest. For the box above, the faces are 48, 72 and 96 cm², so the surface has to sit between 288 and 576. It came out 432. If your answer falls outside that window, you have transposed a dimension somewhere.