How to use the Cube Calculator
- Measure any edge — all twelve are equal in a cube.
- Enter the edge length.
- Read the volume, the edge cubed.
- Read the surface area, six identical square faces.
- Use the litre row when working in centimetres.
How the calculation works
A cube is the simplest three-dimensional shape to quantify: volume is the edge length cubed and surface area is six times the edge squared, because six identical square faces enclose it. Every derived quantity follows from that single dimension, which is why the cube is the standard reference solid for density, packing and material testing.
The cube-law scaling is dramatic and frequently underestimated. Doubling the edge multiplies the surface area by four and the volume by eight. A shipping crate twice as large in every dimension holds eight times as much but needs only four times the cardboard — the economics of bulk packaging in one sentence. Working backwards, the edge needed for a target volume is the cube root of that volume.
Concrete testing relies on this geometry directly. Standard test cubes of 100 mm or 150 mm are crushed and the failure load divided by the face area gives compressive strength in megapascals. Because the face area is the edge squared, a 150 mm cube presents 22,500 mm², so a 900 kN failure corresponds to 40 MPa — a calculation performed on every concrete pour of any consequence.
V = a³; S = 6a²; space diagonal = a√3Source: Elementary solid geometry; concrete cube testing per BS EN 12390-3.
Worked example
A storage crate has 1.2 m internal edges. What does it hold, and how much sheet material does it use?
- Volume: 1.2³ = 1.728 m³.
- In litres: 1,728 L.
- Surface area: 6 × 1.2² = 6 × 1.44 = 8.64 m².
- For a target 3 m³ instead, the edge would need to be ∛3 = 1.44 m.
1.728 m³ of capacity from 8.64 m² of sheet material — and reaching 3 m³ needs only a 20% larger edge.
Frequently asked questions
How do I find the edge from a known volume?+
Take the cube root. For 1.728 m³, ∛1.728 = 1.2 m. The square root calculator handles cube roots too.
What is the space diagonal?+
The corner-to-opposite-corner distance through the middle, equal to the edge times √3. It sets the longest object that can fit inside.
Is a cube the most efficient box shape?+
For a rectangular box, yes — it minimises surface area for a given volume. A sphere beats it overall, but spheres do not stack.
How much does a cubic metre of water weigh?+
About 1,000 kg at room temperature, which is why the cubic metre and the tonne line up so conveniently.
Last reviewed August 31, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.