Everyday utility

Cube Calculator

Enter the side length to instantly calculate volume, surface area, face diagonal, and space diagonal of a cube. All six faces of a cube are equal squares, so one number describes the entire shape.

Last reviewed May 19, 2026 by ToolSpilo Editorial Team.

Review method: Reviewed against standard cube geometry formulas and diagonal derivations.

Calculator tool

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What a Cube Is

A cube is a 3D solid with six identical square faces, twelve equal edges, and eight corners. All edges have the same length. A Rubik's cube, ice cube, and sugar cube are familiar examples. The cube is a special case of a rectangular prism where all three dimensions are equal.

Formulas

Let ss be the side length.

MeasurementFormulaFor s=5s = 5
VolumeV=s3V = s^3125 cubic units
Surface areaA=6s2A = 6s^2150 sq units
Face diagonalf=s2f = s\sqrt{2}≈ 7.07 units
Space diagonald=s3d = s\sqrt{3}≈ 8.66 units

Worked Example

For a cube with side 5 m:

V=53=125 m3V = 5^3 = 125\text{ m}^3
A=6×52=6×25=150 m2A = 6 \times 5^2 = 6 \times 25 = 150\text{ m}^2
d=53≈8.66 md = 5\sqrt{3} \approx 8.66\text{ m}

Face Diagonal vs Space Diagonal

Face diagonal (s2s\sqrt{2}) crosses one flat face from corner to corner — it is the diagonal of a square. Space diagonal (s3s\sqrt{3}) runs through the interior of the cube from one corner to the opposite corner. The space diagonal is the longest straight line that fits inside the cube.

Frequently asked questions

Why is the cube's surface area 6s²?

A cube has six identical square faces. Each face has area s2s^2, so the total surface area is 6×s2=6s26 \times s^2 = 6s^2. For a cube with side 4 m, each face is 42=16 m24^2 = 16\text{ m}^2 and the total surface is 6×16=96 m26 \times 16 = 96\text{ m}^2.

What is the space diagonal of a cube?

The space diagonal goes from one corner of the cube to the opposite corner, passing through the center of the cube. Its length is s3s\sqrt{3}. For side s=5s = 5, the space diagonal is 53≈8.665\sqrt{3} \approx 8.66. This is the longest object that can fit inside the cube.

How do I find the side length from the volume?

Since V=s3V = s^3, the side is s=V3s = \sqrt[3]{V}. For a cube with volume 216 m³, the side is 2163=6 m\sqrt[3]{216} = 6\text{ m}. This works in reverse: the cube root of volume gives the side length.

How does a cube compare to a sphere of the same volume?

A sphere is more efficient: it encloses the same volume with less surface area. A cube with volume 125 m³ (side 5 m) has surface area 150 m². A sphere with the same volume has radius r=(3V/4π)1/3≈3.10 mr = (3V/4\pi)^{1/3} \approx 3.10\text{ m} and surface area 4πr2≈120 m24\pi r^2 \approx 120\text{ m}^2 — about 20% less surface.