Calculate the volume, surface area, face diagonals, space diagonal, and all face areas of a cuboid (rectangular prism). Cube detection, unit selector, and real-world presets.
A cuboid — also called a rectangular prism or rectangular box — is one of the most common three-dimensional shapes in everyday life. Shoe boxes, shipping containers, rooms, bricks, and refrigerators are all cuboids. The shape is defined by three perpendicular edge lengths: length (l), width (w), and height (h).
The volume of a cuboid is simply l × w × h, representing how much space it occupies. The surface area is 2(lw + lh + wh), which tells you how much material you need to wrap or paint it. These formulas are essential in packaging, construction, logistics, and manufacturing.
Beyond volume and surface area, a cuboid has rich geometry. Each of its six rectangular faces has its own diagonal, and the cuboid itself has a space diagonal — the longest possible straight line through the interior — given by √(l² + w² + h²). When all three dimensions are equal, the cuboid becomes a cube, the most symmetrical of all rectangular prisms.
This calculator computes every property of a cuboid from its three dimensions: volume, total surface area, all three face areas, all three face diagonals, and the space diagonal. It automatically detects cubes and offers real-world presets (shoe box, shipping container, room) for quick exploration. A visual breakdown of face areas and a reference table of common objects make comparing cuboid dimensions easy and practical.
The Cuboid (Rectangular Box) Calculator is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Volume, Surface Area, Space Diagonal in one pass, with conversions and derived values shown together.
Volume: V = l × w × h
Surface Area: SA = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Face Diagonal (l×w): √(l² + w²)
Face Diagonal (l×h): √(l² + h²)
Face Diagonal (w×h): √(w² + h²)
Face Areas: lw, lh, wh
Cube condition: l = w = hResult: Volume = 7,920 cm³, Surface Area = 2,632 cm², Space Diagonal ≈ 40.31 cm
For a shoe box with l = 33, w = 20, h = 12 cm: Volume = 33 × 20 × 12 = 7,920 cm³. Surface Area = 2(660 + 396 + 240) = 2,592 cm². Space Diagonal = √(1089 + 400 + 144) = √1633 ≈ 40.41 cm.
Cuboid (Rectangular Box) Calculator calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
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A cuboid (rectangular prism) is a 3D shape with six rectangular faces, where opposite faces are identical. It is defined by three perpendicular edge lengths: length, width, and height.
Volume = l × w × h. Multiply the three perpendicular dimensions together. For a box 33 × 20 × 12 cm, volume = 7,920 cm³.
Surface Area = 2(lw + lh + wh). Compute the area of each unique face pair and double the sum. This gives the total area of all six faces.
The space diagonal runs from one corner to the opposite corner through the interior: d = √(l² + w² + h²). It is the longest straight line inside the box.
A cube is a special cuboid where all three dimensions are equal (l = w = h). Every face is a square, and all edges have the same length.
Face diagonals lie on one face and use only two dimensions (e.g., √(l² + w²)). The space diagonal passes through the interior and uses all three dimensions (√(l² + w² + h²)).
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