Rectangular prism (cuboid): properties & formulas
A rectangular prism, also called a cuboid or rectangular box, has six rectangular faces. Opposite faces match, making it useful for understanding packaging, storage, and three-dimensional measurement.
- 6 rectangular faces
- 12 edges
- 8 vertices
- 4 space diagonals
Properties of a rectangular prism (cuboid)
| Faces | 6 rectangles in 3 pairs of equal, opposite faces |
|---|---|
| Edges | 12, in 3 groups of 4 equal, parallel edges |
| Vertices | 8; three edges meet at right angles at each |
| Euler check | Faces − edges + vertices = 6 − 12 + 8 = 2 |
| Space diagonals | 4, all the same length |
| Special case | A cube has all 12 edges equal |
Rectangular prism (cuboid) formulas
| Volume | V = whd (length × width × height) |
|---|---|
| Surface area | S = 2(wh + wd + hd) |
| Space diagonal | D = √(w² + h² + d²) |
| Face diagonal | √(w² + h²) |
Rectangular prism (cuboid) volume & surface area calculator
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Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
A worked example
A 6 × 4 × 3 prism has volume 72 cubic units, surface area 108 square units, and space diagonal √61 ≈ 7.810 units.
Rectangular prism (cuboid): common questions
Wondering about the why? Start here.
Is a rectangular prism the same as a cuboid?
Yes. Rectangular prism is the usual name in the United States; cuboid is common in the United Kingdom and elsewhere. Both describe a solid with six rectangular faces meeting at right angles.
How many faces, edges, and vertices does a rectangular prism have?
It has 6 faces, 12 edges, and 8 vertices. Euler’s formula checks it: 6 − 12 + 8 = 2. A cube is the special rectangular prism whose 12 edges are all equal.
How do I calculate a rectangular prism’s volume?
Multiply width, height, and depth: V = whd. A box measuring 6 cm by 4 cm by 3 cm holds 72 cm³ of space. To estimate internal capacity, use its inside dimensions.
Read about volumeWhy does the surface area formula have a factor of two?
A closed rectangular prism has three pairs of equal opposite faces. Add the areas wh, wd, and hd, then double the sum: S = 2(wh + wd + hd). Subtract any missing face separately for an open box.
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