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Rectangular Prism vs Cube in 3D

A cube is a special rectangular prism: all its edges have the same length. Both shapes have six rectangular faces, twelve edges, and eight vertices. Change the dimensions below to see what stays the same and what makes a cube different.

Explore This Comparison

Rectangular Prism

Three independent dimensions

Complete 3D rectangular prism with accurate faces and edges
Volume72 cm3V = LWH
Surface area108 cm2S = 2(LW + LH + WH)

Cube

One edge length sets every side

Complete 3D cube with accurate faces and edges

Length, width, and height are all a. Moving this slider changes all three together.

a² a
Volume64 cm3V = a³
Surface area96 cm2S = 6a²

Drag to rotate · Scroll or pinch to zoom · Arrow keys rotate the focused model. Turn off Link Rotations to explore one shape at a time.

Numbers stay the same.

This rectangular prism is not a cube: its three dimensions are not all equal.

Same Structure. A Stricter Rule for the Cube.

A rectangle has four right angles. A square is a rectangle with four equal sides, so six square faces still satisfy the definition of a rectangular prism. The extra condition is equality: L = W = H = a.

6rectangular faces
12straight edges
8vertices

Is a Cube a Rectangular Prism?

Yes. Its opposite faces are parallel, every face is a rectangle, and every corner is a right angle. More specifically, all six faces are congruent squares.

Is a Rectangular Prism Always a Cube?

No. It becomes a cube only when length, width, and height are equal. Try Make It a Cube above, then change just one prism dimension to break that equality.

Measure the Space Inside and the Surface Outside

Volume counts cubic units inside the solid. Surface area adds the areas of all six faces. Opposite faces of a rectangular prism come in matching pairs: LW, LH, and WH. In a cube, each pair becomes a², giving 6a².

Rectangular Prism Formulas

VolumeL × W × H
72 cm3
Total surface area2(LW + LH + WH)
108 cm2
One base areaL × W
18 cm2
Lateral surface area2H(L + W)
72 cm2
Space diagonal√(L² + W² + H²)
7.81 cm
Total edge length4(L + W + H)
52 cm

Cube Formulas

Volumea³
64 cm3
Total surface area6a²
96 cm2
One face areaa²
16 cm2
Lateral surface area4a²
64 cm2
Space diagonala√3
6.93 cm
Total edge length12a
48 cm

Lateral area excludes the top and bottom faces, with H used as the prism height. The space diagonal connects opposite vertices through the interior. Select Diagonal on either model to see it. Results are rounded to two decimal places.

Six Faces, Laid Flat

These nets use the dimensions selected above. The prism has three matching pairs of rectangles; the cube has six equal squares. The gold pair marks the chosen parallel bases. Select Net on either model and fold its faces independently.

Shape properties and visible face nets
Property Rectangular prism Cube
Face shapes 6 rectangles in 3 matching pairs 6 congruent squares
Edge lengths L, W, and H; four edges of each length All 12 edges have length a
Right angles Every face corner is 90° Every face corner is 90°
Vertices 8; three edges meet at each 8; three edges meet at each
Bases 2 parallel, congruent rectangles 2 parallel, congruent squares
Flat face nets
Rectangular prism net 1 2 3 4 5 6
6 rectangles. Dashed lines are folds.
Cube net 1 2 3 4 5 6
6 equal squares. Dashed lines are folds.

Common Questions

Is a cuboid the same as a rectangular prism?

In this comparison, yes. A cuboid means a solid with six rectangular faces. Some everyday descriptions use “cuboid” for a box that is not a cube, but a cube satisfies the broader mathematical definition.

Can a rectangular prism have square faces?

Yes. If two dimensions are equal, one pair of opposite faces is square. All six faces are squares only when all three dimensions are equal.

Can a cube and a different rectangular prism have the same volume?

Yes. A cube with edge 4 has volume 64 cubic units. A 8 × 4 × 2 rectangular prism also has volume 64, but their surface areas differ: 96 and 112 square units.

How do I find the diagonal of a cube?

Apply the Pythagorean theorem twice: the square face diagonal is a√2, then the interior diagonal is √((a√2)² + a²) = a√3. This is longer than a face diagonal.