🧊 Cube Calculator 2026
Calculate surface area, volume, diagonal, or find side length
Enter Side Length
a = side length, d = space diagonal
📊 Results
Side Length
5 cm
Surface Area
150 cm²
Volume
125 cm³
Face Diagonal
7.07 cm
Space Diagonal
8.66 cm
📝 Step-by-Step Solution
Given: Side length a = 5 cm
Surface Area = 6a² = 6 × 5² = 6 × 25 = 150 cm²
Volume = a³ = 5³ = 125 cm³
Face Diagonal = a√2 = 5 × √2 = 7.07 cm
Space Diagonal = a√3 = 5 × √3 = 8.66 cm
📐 Cube Formulas
Surface Area: A = 6a²
Volume: V = a³
Face Diagonal: df = a√2
Space Diagonal: ds = a√3
Side from Area: a = √(A/6)
Side from Volume: a = ∛V
Understanding Cube Geometry
🧊 What is a Cube?
A perfect 3D shape with 6 identical square faces, 12 equal edges, and 8 vertices. All angles are 90°. Also called a regular hexahedron.
📐 Surface Area
A = 6a². Sum of all 6 square faces. Each face has area a². Used for material, paint, wrapping calculations.
📦 Volume
V = a³. Amount of space inside. Side × Side × Side. Cubic units (cm³, m³). Used for capacity calculations.
↗️ Diagonals
Face: a√2. Across one face. Space: a√3. Corner to opposite corner through interior. Longest line inside cube.
Frequently Asked Questions
What is the surface area formula for a cube?
Surface Area = 6a². Where a = side length. A cube has 6 identical
square faces, each with area a².
What is the volume formula for a cube?
Volume = a³. Side length cubed. Example: 5 cm side → 5³ = 125 cm³.
Called "cubed" because it's a cube!
How do I find side length from surface area?
a = √(A/6). Divide surface area by 6 (number of faces), then take
square root. Example: A = 150 → a = √(150/6) = √25 = 5.
How do I find side length from volume?
a = ∛V. Take the cube root of volume. Example: V = 125 → a = ∛125
= 5. Most calculators have a cube root function.
What is the face diagonal of a cube?
d = a√2. Diagonal across one square face. Uses Pythagorean
theorem: √(a² + a²) = √(2a²) = a√2.
What is the space diagonal of a cube?
d = a√3. Diagonal from one corner through the interior to opposite
corner. Longest possible line inside the cube.
How many faces does a cube have?
6 faces. All are identical squares. Also: 12 edges (all equal
length) and 8 vertices (corners).
What is the difference between cube and rectangular prism?
Cube: all sides equal (a × a × a). Rectangular prism: can have
different length, width, height (l × w × h). Cube is a special case of rectangular prism.
How do I find surface area if I know volume?
First find side: a = ∛V. Then A = 6a². Example: V = 64 → a = 4 → A
= 6 × 16 = 96 square units.
What is the surface area to volume ratio of a cube?
Ratio = 6a²/a³ = 6/a. Decreases as cube gets larger. Important in
biology, physics (heat transfer, etc.).
What are real-world examples of cubes?
Dice, Rubik's cube, ice cubes, sugar cubes, some boxes, building
blocks. Perfect cubes are common in games and packaging.
What is a perfect cube number?
A number that's n³ for some integer n. Examples: 1, 8, 27, 64,
125, 216... (1³, 2³, 3³, 4³, 5³, 6³...).
How do I calculate paint needed for a cube?
Calculate surface area (6a²). Divide by paint coverage (sq
ft/gallon). Only count exposed faces if cube sits on surface (then 5a²).
What is the net of a cube?
Unfolded 2D pattern that folds into a cube. 11 different nets
exist. Classic: cross shape (4 squares in a row, 1 on each side).
How does doubling the side affect volume?
Volume increases 8×. (2a)³ = 8a³. Surface area increases 4×
(quadruples). This is the cube-square law.
What is the inscription sphere of a cube?
Largest sphere inside cube. Radius = a/2 (touches center of each
face). Circumscribed sphere radius = (a√3)/2 (touches vertices).
How accurate is this calculator?
Uses precise mathematical formulas. Results are mathematically
exact for the given input.