What is the formula for the volume of a cuboid?

Volume = Length x Width x Height. For a box measuring 4 x 3 x 5 units, the volume is 4 x 3 x 5 = 60 cubic units.

How do you calculate the surface area of a rectangular box?

A cuboid has three pairs of opposite rectangular faces. Total surface area = 2 x (LW + LH + WH). For L=4, W=3, H=5: SA = 2 x (12 + 20 + 15) = 2 x 47 = 94 square units.

What is the space diagonal of a cuboid?

The space diagonal is the straight-line distance from one corner of the box to the opposite corner through the interior. It equals the square root of (L squared + W squared + H squared). For L=4, W=3, H=5: diagonal = sqrt(16 + 9 + 25) = sqrt(50) = 7.07 units.

Rectangular Box (Cuboid) Calculator

A cuboid, also called a rectangular prism or rectangular box, is a three-dimensional shape with six rectangular faces where opposite faces are equal. It is the most common shape in everyday objects: boxes, rooms, bricks, books, and crates are all cuboids. Unlike a cube, a cuboid can have three different dimensions: length, width, and height. This calculator takes those three measurements and returns the volume, the total surface area, and the space diagonal. Volume tells you the capacity of the box and is used in shipping, storage, and fluid calculations. Surface area tells you how much material you need to cover the outside, which is relevant for wrapping, painting, or insulating. The space diagonal is the longest straight line that fits inside the box, running from one corner to the opposite corner through the interior, and it determines whether a long object such as a pipe or a rod will fit inside. Enter length, width, and height in any consistent unit and the calculator returns results instantly. All dimensions must be positive. The result labels say cubic units and square units, so just substitute the unit you used. For example, if your dimensions are in centimetres, volume will be in cubic centimetres and surface area in square centimetres. Use the tool for homework, packing calculations, or any practical sizing problem where you need all three measurements at once.

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Length (L)

units

Width (W)

units

Height (H)

units

volume (cubic units)

Surface area94

Space diagonal7.07

How it works

Volume is the product of all three dimensions: V = L × W × H. Surface area sums the areas of all six faces, which come in three pairs: 2 × (L×W + L×H + W×H). The space diagonal is the square root of (L² + W² + H²), which comes from applying Pythagoras in three dimensions: first across the base to get the face diagonal, then from that to the opposite top corner.

Worked example

A box with L=4, W=3, H=5: volume = 4 × 3 × 5 = 60 cubic units. Surface area = 2 × (4×3 + 4×5 + 3×5) = 2 × (12 + 20 + 15) = 2 × 47 = 94 square units. Space diagonal = √(16 + 9 + 25) = √50 = 7.07 units. These match the defaults pre-filled above.

Related calculators

Cube Calculator: volume, surface area and diagonals when all three sides are equal.
Triangular Prism Calculator: volume and surface area of a prism with a triangular cross-section.
Surface Area Calculator: multi-solid chooser covering cube, cuboid, cylinder, cone and sphere.
Pyramid Calculator: square-base pyramid volume and surface area.

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