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Cuboid Calculator

Calculate cuboid (rectangular prism) volume, total surface area, lateral area, and space diagonal from length, width, and height.

Cuboid Results
Volume
120
Total Surface Area
148
Lateral Surface Area
100
Space Diagonal
8.775
Deduction Steps:
Dimensions: length = 6, width = 4, height = 5
Volume: V = l × w × h = 6 × 4 × 5 = 120
Total Surface Area: A = 2(lw + lh + wh) = 2(24 + 30 + 20) = 148
Lateral Surface Area: A_lat = 2h(l + w) = 2 × 5 × (6 + 4) = 100
Space Diagonal: d = √(l² + w² + h²) = √(36 + 16 + 25) = 8.775
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What Is a Cuboid Calculator?

A cuboid (or rectangular prism) is a convex polyhedron bounded by six rectangular faces. Opposite faces are congruent rectangles, meeting at right angles (90°).

How to Use This Calculator

  1. Enter length (l), width (w), and height (h).
  2. View the calculated Volume, Total Surface Area, Lateral Area, and Space Diagonal.
  3. Review the step-by-step geometric calculations.

Cuboid Volume and Surface Area Formulas

V = lwh, \quad A_{\text{total}} = 2(lw + lh + wh), \quad d = \sqrt{l^2 + w^2 + h^2}

Volume is the product of length, width, and height. Total surface area is the sum of the areas of the three pairs of opposing rectangular faces.

Worked Example

Scenario: Calculate cuboid with length l = 8 m, width w = 5 m, height h = 3 m

Volume: V = 8 × 5 × 3 = 120 m³

Surface Area: A = 2 × (8×5 + 8×3 + 5×3) = 2 × (40 + 24 + 15) = 2 × 79 = 158 m²

Lateral Area: A_lat = 2 × 3 × (8 + 5) = 6 × 13 = 78 m²

Space Diagonal: d = √(8² + 5² + 3²) = √(64 + 25 + 9) = √98 ≈ 9.8995 m

Result: Volume = 120 m³, Surface Area = 158 m², Space Diagonal ≈ 9.90 m

Tips & Key Notes

  • If length, width, and height are all equal, the cuboid is a cube.
  • The space diagonal is the longest straight line segment that fits inside the cuboid.
  • Lateral surface area represents the four vertical walls of a room: 2h(l + w).

Frequently Asked Questions

What is the difference between a cuboid and a cube?

A cube is a special cuboid where length, width, and height are identical (all 6 faces are squares).

How do you find the space diagonal of a cuboid?

Apply 3D Pythagorean theorem: d = √(length² + width² + height²).

What is lateral surface area of a cuboid?

It is the area of the four side faces: A_lat = 2h(l + w), excluding the top and bottom faces.

How many edges and vertices does a cuboid have?

A cuboid has 6 faces, 12 edges (4 lengths, 4 widths, 4 heights), and 8 vertices.

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