Cube Calc: find V, a, d

Find Volume (V), side length (a), space diagonal (d), and all cube properties from any known parameter

Calculate Cube Properties

cm

Cube Properties: V, a, d

0.0000
Volume (V)
cm³
V = a³
0.0000
Side Length (a)
cm
Edge length
0.0000
Space Diagonal (d)
cm
d = a√3
0.0000
Surface Area (S)
cm²
S = 6a²
0.0000
Face Diagonal (f)
cm
f = a√2

Calculation Steps

Given: Side Length (a) = 0 cm

Step 1: Calculate side length: a = 0.0000 cm

Step 2: Volume: V = a³ = 0.0000 cm³

Step 3: Space diagonal: d = a√3 = 0.0000 cm

Step 4: Surface area: S = 6a² = 0.0000 cm²

Step 5: Face diagonal: f = a√2 = 0.0000 cm

Formula used: V = a³, d = a√3, S = 6a², f = a√2

Example Calculations

Example 1: Given side length a = 5 cm

Given: Side length a = 5 cm

Volume: V = a³ = 5³ = 125 cm³

Space diagonal: d = a√3 = 5 × √3 = 8.66 cm

Surface area: S = 6a² = 6 × 5² = 150 cm²

Face diagonal: f = a√2 = 5 × √2 = 7.07 cm

Example 2: Given volume V = 64 cm³

Given: Volume V = 64 cm³

Side length: a = ∛V = ∛64 = 4 cm

Space diagonal: d = a√3 = 4 × √3 = 6.93 cm

Surface area: S = 6a² = 6 × 4² = 96 cm²

Face diagonal: f = a√2 = 4 × √2 = 5.66 cm

Key Formulas Summary

Volume: V = a³

Side from Volume: a = ∛V

Space Diagonal: d = a√3

Side from Diagonal: a = d/√3

Surface Area: S = 6a²

Side from Surface: a = √(S/6)

Face Diagonal: f = a√2

Side from Face Diagonal: a = f/√2

Parameter Definitions

a

Side Length (a)

Length of any edge of the cube

V

Volume (V)

Amount of space inside the cube

d

Space Diagonal (d)

Diagonal through the cube's interior

S

Surface Area (S)

Total area of all six faces

f

Face Diagonal (f)

Diagonal across any square face

Calculation Methods

From Side Length

Direct calculation of all properties

From Volume

Find side using cube root: a = ∛V

From Space Diagonal

Use relationship: a = d/√3

From Surface Area

Calculate: a = √(S/6)

From Face Diagonal

Use relationship: a = f/√2

Applications

Packaging and shipping calculations

Dice and gaming cube design

Storage container optimization

Architecture and construction

Material science calculations

Understanding Cube Calculations: V, a, d

Core Relationships

This calculator focuses on the three fundamental properties of a cube: Volume (V), side length (a), and space diagonal (d). These properties are interconnected through specific mathematical relationships that allow us to calculate any property from any other.

Key Formulas

  • Volume: V = a³ (side cubed)
  • Space Diagonal: d = a√3 (side times √3)
  • Surface Area: S = 6a² (bonus calculation)
  • Face Diagonal: f = a√2 (bonus calculation)

Reverse Calculations

From Volume to Side: a = ∛V

From Space Diagonal to Side: a = d/√3

From Surface Area to Side: a = √(S/6)

From Face Diagonal to Side: a = f/√2

Mathematical Note: The space diagonal formula d = a√3 comes from applying the Pythagorean theorem twice: first to find the face diagonal (a√2), then to find the space diagonal √((a√2)² + a²) = √(3a²) = a√3.