Cube Volume Calculator | With Unit Conversion
Calculate the volume, surface area and diagonals of a cube from its edge, face diagonal or space diagonal. Convert between metric and imperial units.
Every edge of a cube has the same length.
Result
How the cube's volume is calculated
A cube is a three-dimensional shape with six identical square faces. Every edge is the same length, which makes the volume formula wonderfully simple:
V = a³
where a is the length of one edge.
If you only know a diagonal, you can find the edge first. The face diagonal (across a single face) follows d = a√2, and the space diagonal (corner to corner through the cube) follows D = a√3. That gives:
- From the face diagonal: a = d ÷ √2, then V = a³
- From the space diagonal: a = D ÷ √3, then V = a³
The calculator also works out the surface area (6a²), the face diagonal and the space diagonal automatically. Every value is converted to the unit you choose.
Assumptions
This calculator assumes a perfect cube — all six faces are identical squares and every angle is 90°.
If your shape has unequal side lengths, you need a rectangular prism calculator (volume = length × width × height) instead.
When do you need cube volume?
Cubes turn up more often than you might expect. A few common situations:
Construction: Estimating how much concrete a cubic footing, column or mould needs. A concrete cube with a 30 cm edge holds 0.027 m³ — roughly 65 kg of ready-mixed concrete.
Packaging and shipping: Cubic boxes are standard across many industries. Knowing the exact volume helps you estimate freight cost, which is often priced by the cubic metre (CBM).
Aquariums and containers: Cube-shaped tanks are popular in nano-aquascaping. A cube with a 30 cm edge holds 27 litres of water.
School and study: Cube volume is on the maths syllabus from middle school onward. The step-by-step breakdown helps you follow the reasoning.
Volume unit conversion
Cubic units can be confusing because they grow far faster than length units. One metre is 100 centimetres, but one cubic metre is 1,000,000 cubic centimetres (100³). Here are the relationships worth knowing:
| From | To | Factor |
|---|---|---|
| 1 m³ | litres | 1,000 |
| 1 m³ | cm³ | 1,000,000 |
| 1 litre | cm³ / mL | 1,000 |
| 1 ft³ | in³ | 1,728 |
| 1 ft³ | litres | 28.3168 |
| 1 in³ | cm³ | 16.387 |
Frequently asked questions
What's the difference between a cube and a box (rectangular prism)?
A cube has all edges the same length, so all six faces are identical squares. A rectangular prism (box) can have three different side lengths. A cube's volume is V = a³, while a box's volume is V = length × width × height.
Can I use this calculator to work out litres?
Yes. Choose "litres (L)" or "millilitres (mL)" from the volume-unit dropdown and the calculator converts automatically. A cube with a 10 cm edge holds exactly 1 litre.
What is a face diagonal and a space diagonal?
The face diagonal (d) is the longest distance between two opposite corners on one of the cube's faces. For a cube with edge a, d = a√2. The space diagonal (D) is the longest distance between two opposite corners straight through the cube: D = a√3.
How many litres are in a cubic metre?
One cubic metre (m³) equals exactly 1,000 litres. So a cube with a 1-metre edge holds 1,000 litres of water — roughly 1,000 kg.
The formula gives a very large number — is that right?
Cubic units grow quickly. Raise 100 to the third power and you get 1,000,000. Check that you're using the right unit — entering the edge in millimetres instead of metres gives the result in mm³, a much smaller unit. Use the unit selector to convert.