🧊 Cube Volume Calculator 2026
Calculate volume, side length, or diagonals of a perfect cube
Enter Side Length
a = side, d = space
diagonal
📊 Results
Side Length (a)
5 cm
Volume
125 cm³
Surface Area
150 cm²
Face Diagonal
7.07 cm
Space Diagonal
8.66 cm
Edge Length Total
60 cm
📝 Step-by-Step Solution
Given: Side length a = 5 cm
Volume = a³ = 5³ = 125 cm³
Surface Area = 6a² = 6 × 25 = 150 cm²
Face Diagonal = a√2 = 5 × 1.414 = 7.07 cm
Space Diagonal = a√3 = 5 × 1.732 = 8.66 cm
📐 Cube Formulas
Volume: V = a³
Side from Volume: a = ∛V
Surface Area: A = 6a²
Face Diagonal: f = a√2
Space Diagonal: d = a√3
Side from Diagonal: a = d / √3
Understanding Cube Volume
🧊 Perfect Cube
All 6 faces are identical squares. All 12 edges equal length. All 8 vertices have 90° angles. Most symmetric 3D shape.
📐 Volume = a³
Side cubed. Length × width × height, but all are equal. Doubling side = 8× volume. Volume in cubic units.
↗️ Diagonals
Face diagonal = a√2 (across one face). Space diagonal = a√3 (corner to opposite corner through center).
🎯 Applications
Dice, sugar cubes, Rubik's cube, storage boxes. Easy volume calculations. Stacking efficiency.
Frequently Asked Questions
What is the volume formula for a cube?
V = a³ (side cubed). Since all sides are equal, volume = length ×
width × height = a × a × a = a³.
How do I find side length from volume?
a = ∛V (cube root of volume). Example: V = 125 → a = ∛125 = 5.
Reverse of cubing.
What is the surface area of a cube?
A = 6a². Six identical square faces, each with area a². Total = 6
× a².
What is the face diagonal?
f = a√2 ≈ 1.414a. Diagonal across one square face. Using
Pythagorean theorem: √(a² + a²) = a√2.
What is the space diagonal?
d = a√3 ≈ 1.732a. From one corner to the opposite corner through
the cube's center. Longest line inside cube.
How do I find side from space diagonal?
a = d / √3. Divide diagonal by √3 (≈1.732). Reverse of the
diagonal formula.
How many edges does a cube have?
12 edges, all equal length. Total edge length = 12a. Also has 6
faces and 8 vertices.
What is the relationship between cube and square?
Cube is 3D version of square. Square: 2D, 4 edges. Cube: 3D, 6
square faces. Area → Volume.
How does doubling the side affect volume?
Volume increases 8×. V = a³, so (2a)³ = 8a³. Surface area
increases 4× (since A = 6a², and (2a)² = 4a²).
How do I convert volume to liters?
1 L = 1000 cm³. Divide cm³ by 1000. Or: 1 L = 0.001 m³. 1 liter is
a 10cm × 10cm × 10cm cube.
What is a perfect cube number?
Integer cubed: 1, 8, 27, 64, 125, 216... If volume is a perfect
cube number in cm³, side is a whole number in cm.
What is the inscribed sphere radius?
r = a/2. Largest sphere that fits inside cube touches all 6 faces.
Diameter = side length.
What is the circumscribed sphere radius?
R = a√3/2. Smallest sphere containing the cube. Passes through all
8 vertices. R = half the space diagonal.
What are real-world cube examples?
Dice, ice cubes, Rubik's cubes, sugar cubes, some boxes, building
blocks. Perfect cubes are rare in nature.
Can I use this for rectangular boxes?
Only if all sides are equal. For different dimensions, use
rectangular prism (V = l×w×h). Cube is special case where l=w=h.
What is the diagonal of a cube used for?
Fitting objects inside. Space diagonal is the longest rod that
fits. Important for packaging, shipping dimensions.
How accurate is this calculator?
Mathematically exact for perfect cubes. Uses √2, √3 to full
precision. Real objects may have slight variations.