Cube calculator
Volume, surface area and diagonals of a cube from its edge, volume or surface area.
Fill in the fields and the result will appear here automatically.
A cube is determined by its edge, volume or total surface area. In the inverse modes the edge is found first, a = ∛V or a = √(S/6), and becomes the headline result. The face diagonal a√2 lies in a square face; the space diagonal a√3 joins opposite vertices. They are different lengths: the latter bounds a straight segment inside the cube and does not guarantee room for a thick object.
How it works
Formula and logic
Volume V = a³, surface area S = 6a², face diagonal a√2, space diagonal a√3, total edge length 12a. In the reverse modes the edge comes from a = ∛V or a = √(S/6).
Example
A cube with a 3 cm edge has a volume of 27 cm³, a surface area of 54 cm² and a diagonal of 5.196 cm.
Fields and units
- Length unit — list option
- What is known — list option
- Edge — cm
- Volume — cm³
- Surface area — cm²
How to use
- — Choose the length unit.
- — Select which quantity you know.
- — Enter its value.
- — The remaining properties are calculated at once.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: solid volumes and surface areas
- Limitation
- A cube has six square faces and a positive edge. Area mode expects total surface area, not one face. Inverse modes return the edge; volume and surface area use the cube and square of the selected unit.
FAQ
How does the space diagonal differ from the face diagonal?
The face diagonal a√2 lies in a square face; the space diagonal a√3 joins opposite vertices. The latter is the longest straight segment inside the cube. A thick object also needs clearance for its cross-section and the opening.
How do I find the edge from the volume?
Take the cube root: a = ∛V. For a volume of 64 cm³ the edge is 4 cm. Choose the «volume» mode and the calculator does it for you.
Why have a cube calculator when there is one for a cuboid?
A cube is a special case of it, but a cube is described by one quantity instead of three, and that makes the reverse problems solvable: the edge follows directly from the volume or the surface area. The general case has no such unique inverse.
How much does the volume grow if the edge doubles?
Doubling the edge multiplies volume by 8, surface area by 4 and diagonals by 2. Those factors follow from the powers of a in the formulas; geometry alone does not calculate a cooling rate.
How do I convert the result into other units?
The unit selector sets the meaning of the entered numbers; it does not convert them. Before changing cm to m, divide a length by 100, an area by 10,000 or a volume by 1,000,000. For example, 64 cm³ = 0.000064 m³, describing the same cube.