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Cube Calculator

Calculate cube volume, total surface area, lateral surface area, space diagonal, and inradius from side length with step-by-step steps.

Cube Calculations
Volume (V)
64
Total Surface Area
96
Lateral Surface Area
64
Space Diagonal
6.9282
Deduction Steps:
Side length: s = 4
Volume: V = s³ = 4³ = 64
Total Surface Area: A = 6s² = 6 × (4)² = 96
Lateral Surface Area: A_lat = 4s² = 4 × (4)² = 64
Space Diagonal: d = s√3 = 4 × 1.73205 = 6.9282
Face Diagonal: d_face = s√2 = 4 × 1.41421 = 5.6569
Inscribed Sphere Radius: r = s / 2 = 2
Circumscribed Sphere Radius: R = (s√3) / 2 = 3.4641
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What Is a Cube Calculator?

A cube is a regular three-dimensional hexahedron bounded by six square faces, with three faces meeting at each of its eight vertices. It is one of the five Platonic solids.

How to Use This Calculator

  1. Enter the side length (s) of the cube.
  2. View the calculated Volume, Total Surface Area, Lateral Surface Area, and Space Diagonal.
  3. Review the step-by-step algebraic substitutions.

Cube Geometric Formulas

V = s^3, \quad A_{\text{total}} = 6s^2, \quad A_{\text{lat}} = 4s^2, \quad d_{\text{space}} = s\sqrt{3}

Volume is side cubed. Total surface area is 6 times side squared (six faces). Space diagonal connects opposite corners through the interior.

Worked Example

Scenario: Find volume and surface area of a cube with side s = 5 cm

Volume: V = 5³ = 125 cm³

Total Surface Area: A = 6 × 5² = 6 × 25 = 150 cm²

Lateral Surface Area: A_lat = 4 × 25 = 100 cm²

Space diagonal: d = 5√3 ≈ 8.6603 cm

Result: Volume = 125 cm³, Surface Area = 150 cm², Space Diagonal ≈ 8.66 cm

Tips & Key Notes

  • To find side length from volume, take the cube root: s = ∛V.
  • To find side length from surface area, divide area by 6 and take square root: s = √(A / 6).
  • The radius of an inscribed sphere inside the cube is r = s / 2.

Frequently Asked Questions

How many faces, edges, and vertices does a cube have?

A cube has 6 square faces, 12 straight edges of equal length, and 8 vertices.

What is the space diagonal of a cube?

The space diagonal connects opposite opposite vertices passing through the center: d = √(s² + s² + s²) = s√3.

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

Total surface area includes all 6 faces (6s²). Lateral surface area includes only the 4 vertical side faces (4s²), excluding top and bottom bases.

How do you calculate the circumscribed sphere of a cube?

The circumscribed sphere touches all 8 vertices, with radius equal to half the space diagonal: R = (s√3) / 2.

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