🧊 Cube Calc: find V, a, d
Calculate volume, edge length, and space diagonal of a cube
How to Use This Calculator
Select What You Know
Choose from the dropdown: Edge length (a), Volume (V), or Space diagonal (d). Select the value you already have.
Enter the Value
Input the known value in the input field. Make sure it's a positive number in consistent units.
Get All Results
Click "Calculate" to instantly get the edge length (a), volume (V), space diagonal (d), and surface area. All values are calculated from your input.
Formulas
Volume: V = a³
Edge length to volume
Space Diagonal: d = a√3
Edge length to diagonal (corner to opposite corner)
Surface Area: A = 6a²
Total area of all six faces
Where:
- a = edge length of the cube
- V = volume of the cube
- d = space diagonal (from one corner to the opposite corner)
- A = total surface area
Example 1: From Edge Length
Given: a = 5 units
V = a³ = 5³ = 125 units³
d = a√3 = 5 × √3 ≈ 8.66 units
A = 6a² = 6 × 5² = 150 units²
Example 2: From Volume
Given: V = 64 units³
a = ∛V = ∛64 = 4 units
d = a√3 = 4 × √3 ≈ 6.93 units
A = 6a² = 6 × 4² = 96 units²
Example 3: From Diagonal
Given: d = 10√3 units ≈ 17.32 units
a = d/√3 = (10√3) / √3 = 10 units
V = a³ = 10³ = 1000 units³
A = 6a² = 6 × 10² = 600 units²
About Cube Calculator: Find V, a, d
This cube calculator allows you to find any cube property (volume V, edge length a, or space diagonal d) from just one known value. A cube is a three-dimensional shape with six equal square faces, making it a perfect geometric solid.
When to Use This Calculator
- Geometry Problems: Solve cube-related problems when you know one dimension
- Architecture: Calculate cube dimensions from volume or diagonal measurements
- Engineering: Determine material requirements when only one cube property is known
- Packaging: Find cube dimensions for packaging or storage solutions
- Mathematics Education: Teach students relationships between cube properties
- 3D Design: Work with cube models in CAD or design software
Why Use Our Calculator?
- ✅ Flexible Input: Start with edge, volume, or diagonal - we calculate the rest
- ✅ Complete Results: Get all cube properties (V, a, d, and surface area) at once
- ✅ Step-by-Step Display: See the formulas and calculations used
- ✅ 100% Accurate: Uses precise mathematical relationships
- ✅ Instant Calculations: No manual formula solving required
- ✅ Completely Free: No registration required
Understanding Cube Relationships
All cube properties are mathematically related:
- Volume (V): The amount of space inside = a³ (edge cubed)
- Edge (a): The length of any side - all edges are equal in a cube
- Space Diagonal (d): The longest distance between opposite corners = a√3
- Surface Area (A): Total area of all 6 faces = 6a²
- Face Diagonal: Diagonal of one square face = a√2
Real-World Applications
Storage: A storage container has a volume of 27 m³. Using this calculator with volume = 27, we find edge = 3 m, diagonal ≈ 5.20 m, and surface area = 54 m². This helps determine if items fit and how much material is needed for construction.
Architecture: A cube-shaped room has a space diagonal of 17.32 m. From diagonal = 17.32, we calculate edge = 10 m, volume = 1000 m³, and surface area = 600 m². Useful for room planning and material estimation.
Packaging: A cube box with 8 cm edges has volume = 512 cm³, diagonal ≈ 13.86 cm, and requires 384 cm² of material for all six faces. This calculator makes it easy to find any property from the others.
Frequently Asked Questions
What is a space diagonal?
A space diagonal is the longest line segment inside a cube, connecting two opposite vertices (corners) that don't share a face. Formula: d = a√3, where a is the edge length.
How do I find the edge length from volume?
Take the cube root of the volume: a = ∛V. For example, if V = 125, then a = ∛125 = 5. The calculator does this automatically when you select "Volume" as your input.
What's the difference between space diagonal and face diagonal?
Space diagonal (d = a√3) goes through the cube from corner to opposite corner. Face diagonal goes across one square face (d = a√2). Both are different measurements of a cube.
Can I calculate if I only know the surface area?
Not directly in this calculator, but you can: from surface area A, find edge a = √(A/6), then use edge as input. For example, if A = 150, then a = √(150/6) = √25 = 5.
Why does the space diagonal use √3?
Using the 3D Pythagorean theorem, the space diagonal is the hypotenuse of a right triangle with sides a, a, and a√2 (face diagonal). This gives d = √(a² + a² + (a√2)²) = a√3.
Are all cube edges equal?
Yes! By definition, a cube has all edges of equal length. This is what makes it a cube (not just a rectangular prism). If edges differ, it's a rectangular box, not a cube.