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Rectangular Prism Calculator

Calculate properties of a rectangular prism (cuboid) including volume, surface area, space diagonal, and lateral surface area. Enter length, width, and height.

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What is a Rectangular Prism?

A rectangular prism (also known as a cuboid) is a three-dimensional geometric shape with six rectangular faces, twelve edges, and eight vertices. It is one of the most fundamental shapes in geometry and appears everywhere in everyday life - from bricks and books to rooms and shipping containers.

A cube is a special case of a rectangular prism where all three dimensions (length, width, height) are equal. This calculator helps you compute all essential properties of a rectangular prism: volume (V), total surface area (S), lateral surface area, top and bottom surface areas, space diagonal (d), and face diagonals.

Rectangular Prism Formulas

For a rectangular prism with length l, width w, and height h:

Volume: V = l × w × h

The volume is simply the product of all three dimensions. This formula works for any rectangular prism regardless of whether it is a cube or not.

Total Surface Area: S = 2(lw + lh + wh)

The total surface area is the sum of the areas of all six rectangular faces. The formula accounts for the three pairs of opposite faces, each pair having the same area.

Lateral Surface Area: L = 2h(l + w)

The lateral surface area excludes the top and bottom faces, covering only the four side faces.

Space Diagonal: d = √(l² + w² + h²)

The space diagonal is the longest diagonal connecting opposite vertices of the prism, passing through the interior.

Face Diagonals:

  • l-w face: d_lw = √(l² + w²)
  • l-h face: d_lh = √(l² + h²)
  • w-h face: d_wh = √(w² + h²)

Each face diagonal connects opposite corners on a single rectangular face.

How to Use the Calculator

  1. Enter Length (l): The longest dimension of the prism.
  2. Enter Width (w): The second dimension of the base.
  3. Enter Height (h): The vertical dimension.

The calculator instantly computes all properties including volume, surface areas, space diagonal, and all three face diagonals. All calculations are performed in real-time in your browser.

Example Calculation

Example: Find the volume, total surface area, and space diagonal of a rectangular prism with length l = 6 cm, width w = 4 cm, and height h = 10 cm.

  • Volume: V = 6 × 4 × 10 = 240 cm³
  • Total Surface Area: S = 2(6×4 + 6×10 + 4×10) = 2(24 + 60 + 40) = 2 × 124 = 248 cm²
  • Space Diagonal: d = √(36 + 16 + 100) = √152 = 12.329 cm

Also check: Rectangle Calculator, Cube Calculator, Volume Calculator, Surface Area Calculator, Tank Volume Calculator, and Cylinder Calculator.

Frequently Asked Questions

What is the difference between a rectangular prism and a cube?

A cube is a special case of a rectangular prism where all three dimensions (length, width, height) are equal. While a rectangular prism can have different values for each dimension, a cube has l = w = h. Every cube is a rectangular prism, but not every rectangular prism is a cube.

What is the difference between total surface area and lateral surface area?

The total surface area includes all six faces of the rectangular prism. The lateral surface area includes only the four side faces, excluding the top and bottom faces. The lateral surface area formula is L = 2h(l + w), while the total surface area is S = 2(lw + lh + wh).

What is the space diagonal of a rectangular prism?

The space diagonal is the longest line segment that connects two opposite vertices (corners) of the prism, passing through its interior. It is calculated using the 3D Pythagorean theorem: d = √(l² + w² + h²). This is different from face diagonals which lie on the surface of individual faces.

Can a rectangular prism have square faces?

Yes, a rectangular prism can have square faces if two of the three dimensions are equal. For example, if l = w but h is different, then the prism has square top and bottom faces with rectangular side faces. When all three dimensions are equal, it becomes a cube.

Where are rectangular prisms used in real life?

Rectangular prisms are everywhere: bricks, books, packages, shipping containers, rooms, buildings, furniture (tables, cabinets), electronic devices (phones, laptops), and many other everyday objects. They are fundamental in construction, packaging, architecture, and manufacturing.

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