Cube Volume Calculator
Result
Volume
- Total surface area
- 150.0000 cm²
A cube volume calculator turns one measurement into two: the volume of a cube from its side length, and the surface area that its six faces add up to. Enter a side of 5 and the cube holds 125 cm³ of space while covering 150 cm² of surface. Every edge length gives a cube, so the only input is that one number — the page derives the rest from s³ and 6s². Side lengths may be entered in centimetres, metres, millimetres, inches or feet, and a side of zero is accepted as the degenerate case rather than refused.
Common cubes: the volume and the surface area from the side
| Side (cm) | Volume (cm³) | Surface area (cm²) |
|---|---|---|
| 1 | 1 | 6 |
| 6 | 216 | 216 |
| 5 | 125 | 150 |
| 7 | 343 | 294 |
| 2 | 8 | 24 |
| 3 | 27 | 54 |
| 4 | 64 | 96 |
| 10 | 1000 | 600 |
| 0.5 | 0.125 | 1.5 |
The 6 cm row is the crossover point, where the two readings are equal at 216. The 10 cm row is the one worth remembering outside this page: 1000 cubic centimetres is exactly one litre, so any container measured in litres can be pictured as a cube of roughly this size. The 7 cm row repeats the cube calculator's own example, so the same cube can be checked on two pages and must print the same number on both. Every side in this table is a whole number of centimetres, because a table cell is not localised and a decimal would have to be written 1,5 in some languages and 1.5 in others.
Formula
V = s³ S = 6s²
- s
- The edge length, the one measurement this shape needs. A cube is the only box whose length, width and height are all the same, so a single figure fixes it completely. It is entered with a unit and converted to centimetres before the arithmetic, which is why the results are reported in centimetres no matter which unit was used to type the number in.
- V
- The volume, the space the cube encloses. It is the edge length cubed, reported in cubic centimetres to four decimal places, and it is the main reading on the panel. For whole-number side lengths the result is exact rather than approximate: 5 cubed is 125 with nothing after the decimal point, and the four places exist for the sides that are not whole numbers.
- S
- The surface area, the total across the six square faces. Each face is s² and there are six of them, so the whole thing is 6s², reported in square centimetres to four decimal places. Every face of a cube is congruent, which is what makes the surface area a single multiplication and addition rather than a sum over different rectangles.
Use this page when there is a physical cube to size up: a box, a die, a crate, a block of material, a tank that is as tall as it is wide. When the question is only about a number — what is 7 cubed — the cube calculator does the same arithmetic with a plain value and adds the cube root beside it, and when the base is not square the cuboid volume calculator takes all three edge lengths.
Worked examples
A cube with a 5 cm side
- Volume is the edge length cubed: 5 × 5 = 25, then 25 × 5 = 125
- So the cube holds 125 cubic centimetres
- Each face is 5 × 5 = 25 square centimetres
- Six faces make 6 × 25 = 150 square centimetres of surface area
Both readings are exact here, which is worth noticing because it is not true of every solid. A sphere or a cylinder with a whole-number radius gives an approximate volume, since pi is irrational; a cube never does. The two numbers also answer genuinely different questions — 125 cm³ is how much the box holds, 150 cm² is how much card it would take to build it.
The side where volume and surface area meet
- Volume: 6 × 6 = 36, then 36 × 6 = 216 cubic centimetres
- Surface area: one face is 6 × 6 = 36, and six of them make 216 square centimetres
- Both readings come out at 216, and that is not a coincidence
- It happens because s³ = 6s² reduces to s = 6 for any side greater than zero
Only one side length makes the two numbers agree, and it is 6. Below it the surface area is the larger of the two — a 1 cm cube has 6 cm² of skin around 1 cm³ of contents — and above it the volume runs away, which is why doubling a cube multiplies its volume by eight but its surface area by only four.
A 10 cm cube
- 10 × 10 = 100, and 100 × 10 = 1000, so the volume is 1000 cubic centimetres
- That is exactly one litre, which is why the litre is defined as a cubic decimetre
- One face is 10 × 10 = 100 square centimetres
- Six faces make 600 square centimetres
The 10 cm cube is the one to remember, because it ties this page to every other volume page on the site: 1000 cm³ is a litre, so any tank you can describe in litres can be checked against a cube of about this size. The same cube appears in the reference tables of the cuboid volume calculator, where all three edge lengths happen to be equal.
Limitations
The side length is limited to 1000000000, and it may not be negative — a negative edge would give a negative volume on a shape that plainly has one. Zero is accepted and returns zero for both readings. The output units are fixed: volume is always reported in cubic centimetres and surface area always in square centimetres, even when the input was entered in inches or feet. A 2 inch cube therefore comes back as 131.0965 cm³ rather than as 8 cubic inches. The two readings are exact for whole-number sides and correct to four decimal places otherwise, with the exception of very large sides, where the cube passes the point at which every integer can be represented and the last digits stop being reliable. Only the volume and the surface area are given; the space diagonal is not among the outputs, and it belongs to the square calculator, which works in two dimensions.
Frequently asked questions
- How do I work out the volume of a cube?
- Cube the side length: multiply it by itself twice. A cube with a 5 cm side has a volume of 5 × 5 × 5 = 125 cubic centimetres. A cube is the one box that needs a single measurement, because its length, width and height are all the same edge length by definition.
- What is the surface area of a cube?
- Six times the area of one face, which is 6s². One face of a 5 cm cube is 25 square centimetres, and the six faces together come to 150 square centimetres. Every face is congruent, so this is one multiplication rather than a sum over different rectangles as it would be for a box.
- Is there a side length where the volume and the surface area are the same number?
- Yes, 6 — and it is the only one. A 6 cm cube has a volume of 216 cubic centimetres and a surface area of 216 square centimetres. Setting s³ equal to 6s² divides through by s² and leaves s = 6. Below that the surface area is the bigger number and above it the volume is.
- Can I enter the side length in inches or feet?
- Yes, and the conversion is handled for you, but the readings always come back in centimetres and square or cubic centimetres. That is the one thing to watch on this page: entering 2 inches gives 131.0965 cm³ rather than 8 cubic inches, so if you need the answer in imperial units, convert the result rather than expecting the panel to do it.
- Why is the answer not rounded?
- Because for this shape it does not have to be. Volume is s³ and surface area is 6s², both integer-coefficient expressions, so a whole-number edge length produces a whole-number answer — 7 cm gives 343 cm³ and 294 cm². The four decimal places are there for the fractional sides, such as the half-centimetre cube that comes to 0.125 cm³.
References
- Cube — the regular hexahedron, its volume s³ and its surface area 6s², with all edges equal by definition — Wolfram MathWorld (United States)
- Volume — how the volume of a solid is defined and why the units come out cubed — Wolfram MathWorld (United States)
- Surface Area — the total area of a solid's boundary, and the six congruent faces of a cube — Wolfram MathWorld (United States)