Cuboid Surface Area Calculator
From a length, a width, and a height, get the surface area, the volume, and the space diagonal — the three numbers that describe any rectangular box.
Three inputs, three answers
Enter the length, width, and height and the calculator returns the surface area (2(lw+lh+wh)), the volume (lwh), and the space diagonal (√(l²+w²+h²)) at once.
Keep units consistent
The dimensions are unit-agnostic — your answers come back in the same unit (squared for the surface, cubed for the volume), so don't mix centimetres with inches.
What is a cuboid surface area calculator?
Length, width, and height in, full box out
A cuboid surface area calculator turns three measurements — the length, the width, and the height — into the numbers that describe a whole rectangular box: the total outside area of its six faces (surface area), how much it holds (volume), and the longest straight line that fits inside it (space diagonal). Each one is fixed once you know the three edge lengths, because a cuboid has right angles at every corner. That makes those three inputs all you need for shipping boxes, aquariums, rooms, bricks, and any geometry homework where a rectangular box shows up.
Enter the length, width, and height in any length unit to get the surface area, volume, and space diagonal instantly.
Three short formulas, all built from the three edge lengths — length (l), width (w), and height (h).
surface area = 2 × (l×w + l×h + w×h)A cuboid has six rectangular faces in three matching pairs, so the surface area doubles the sum of the three distinct face areas: 2 × (lw + lh + wh). The volume — the space inside — is simply l × w × h. The space diagonal, the longest straight line from one corner to the opposite corner through the interior, comes from the 3D Pythagorean theorem: √(l² + w² + h²).
Suppose you have a box with a length of 4, a width of 3, and a height of 2.
Volume
4 × 3 × 2 = 24 cubic units — the space inside.
Surface area
2 × (4×3 + 4×2 + 3×2) = 2 × (12 + 8 + 6) = 2 × 26 = 52 square units — the total outside area.
Space diagonal
√(4² + 3² + 2²) = √(16 + 9 + 4) = √29 ≈ 5.385165 — the longest line inside.
The three outputs answer three different everyday questions. The surface area (52 square units for 4 × 3 × 2) is the total area of all six faces — the figure you need when buying paint, wrapping paper, or sheet material to cover the box, because every face has to be coated. The volume (24 cubic units) is the space inside — how much the box holds, whether that is water in an aquarium, sand in a crate, or air in a room. The space diagonal (about 5.385165) is the longest straight line that fits inside, running corner to opposite corner; it tells you the longest rigid item — a pole, a rod, a poster tube — that you can slot diagonally into the box even when it is too long to lie flat. Read together, surface area drives material cost, volume drives capacity, and the diagonal drives what fits.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Right-angled boxes and consistent units
These formulas describe a perfect cuboid — six rectangular faces meeting at right angles. A box with sloping sides, rounded corners, or a non-rectangular base will differ from the computed value. The dimensions are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a length, width, and height in centimetres give a volume in cubic centimetres and a surface area in square centimetres, never a mix.