How this instrument works
A cube has twelve identical edges, six identical square faces, and eight identical corners, so a single side length is enough to determine every other measure at once. Its volume is the side length cubed, V = s³, following directly from length × width × height with all three dimensions equal; its surface area is six times one face's area, A = 6s², since all six square faces are identical and each has area s².
The two formulas grow at very different rates as the side length increases: volume scales with the CUBE of the side while surface area scales with its SQUARE, so a cube twice as wide holds eight times the volume (2³) but only four times the surface area (2²). This gap widens further for larger cubes — the reason a large object tends to have proportionally less surface area relative to its volume than a small one, a relationship with real consequences for heat loss, material cost, and packaging efficiency.
A cube is the special case of a rectangular prism (box) where all three dimensions happen to be equal — the general box formulas, V = length × width × height and A = 2(lw + lh + wh), both reduce exactly to a cube's simpler versions once length, width, and height are all set to the same value s.
- Enter the cube's side length into the Side length field.
- Read Volume: the sheet cubes the side length directly.
- Read Surface area: the sheet computes six times the side length squared.
Worked example — a cube with side 4
A cube has a side length of 4 units. Its volume is 4³ = 64 cubic units, and its total surface area (all six faces combined) is 6 × 4² = 6 × 16 = 96 square units — both figures returned from that single side length, with no other measurement required.
A smaller reference cube with side 2 has volume 8 and surface area 24 — an eighth of the larger cube's volume (since 2³ = 8 while 4³ = 64) but exactly a quarter of its surface area (since 2² = 4 while 4² = 16), the cube and square growth rates pulling apart as the side length changes.
Questions
What is the formula for the volume of a cube?
V = s³, where s is the side length. Since all three dimensions of a cube are equal, the general box-volume formula, length × width × height, collapses to simply cubing the one shared side length.
What is the formula for the surface area of a cube?
A = 6s², six identical square faces, each with area s². This counts the ENTIRE exterior, all six sides of the cube, not just one face.
Does doubling the side length double the volume?
No — volume scales with the CUBE of the side length, so doubling the side multiplies the volume by 2³ = 8. Surface area, by contrast, scales with the square, so doubling the side only multiplies surface area by 2² = 4.
How is a cube different from a general rectangular prism?
A rectangular prism (box) allows three independent dimensions — length, width, and height, each potentially different. A cube is the special case where all three happen to be equal, letting both the volume and surface area formulas collapse to a single-variable version.
What is the volume and surface area of a cube with side 0?
Both are exactly zero — the cube has collapsed to a single point with no space enclosed and no surface to measure at all, a limit the formulas handle cleanly with no special case needed.