BackCube Volume Calculator
Enter a cube’s edge length — or a diagonal — to get its volume instantly, with clear steps. Choose your input and output units (³, ³, ³, ڳ³, L, mL).
Background
The volume of a cube is V = a³ where a is the edge length. If you only know a diagonal, use d = a√2 (face) or D = a√3 (space) to find a first.
How to use the cube volume calculator
1) Choose what’s given: edge, face diagonal, or space diagonal.
2) Enter the value and select the length unit.
3) Pick your output unit (³, ³, ³, ڳ³, L, mL).
4) Click Calculate Volume to see the step-by-step solution.
Key Points
- Volume formula: V = a³.
- Face diagonal: d = a√2 → a = d/√2. Space diagonal: D = a√3 → a = D/√3.
- 1 ³ = 1000 L and 1 L = 1000 mL = 1000 ³.
Formula & Equation Used
For a cube:
If you know a diagonal:
Example Problems & Step-by-Step Solutions
Example 1 (Edge given):
Edge = 5.0 cm → V in ³
- V = a³
- V = (5.0 cm)³ = 125 ³
- Answer: 125 ³
Example 2 (Face diagonal given):
d = 10.0 cm → V in L
- a = d/√2 = 10.0/√2 = 7.071 cm
- V = a³ = (7.071 cm)³ = 353.6 ³
- 1 L = 1000 ³ → V = 0.3536 L ≈ 0.354 L
Example 3 (Space diagonal given):
D = 0.5 m → V in ³
- a = D/√3 = 0.5/√3 = 0.288675 m
- V = a³ = 0.0241 ³
- Answer: 0.0241 ³
Frequently Asked Questions
Q: Can I enter a diagonal instead of an edge?
Yes — choose “Face diagonal” or “Space diagonal.” The calculator finds the edge first, then computes volume.
Q: Can I get the volume in liters or milliliters?
Yes — select L or mL in the output menu (1 ³ = 1000 L and 1 L = 1000 mL = 1000 ³).
