Cube Calculator

A cube has: 6 square faces, 12 equal edges, 8 vertices, 3 face diagonals per face (s√2), 4 space diagonals (s√3), surface area of 6s², and volume of s³. All angles are 90°.

Take the cube root of the volume: s = ∛V. For example, if V = 27, then s = ∛27 = 3. You can use a calculator or recognize perfect cubes (1, 8, 27, 64, 125, ...).

A face diagonal (s√2) connects two opposite corners of the same face. A space diagonal (s√3) connects two opposite corners through the interior of the cube, passing through the center.

A cube has 12 face diagonals (2 per face × 6 faces) and 4 space diagonals (connecting opposite vertices through the interior). Total: 16 diagonals.

No. By definition, a cube has all edges of equal length. If the edges have different lengths, it is a rectangular prism (or cuboid), not a cube.

SA/V = 6s²/s³ = 6/s. This means smaller cubes have proportionally more surface area. A 1cm cube has SA/V = 6, while a 10cm cube has SA/V = 0.6.

First find the side: s = √(SA/6). Then calculate volume: V = s³ = (SA/6)^(3/2). For example, if SA = 96, then s = √(96/6) = √16 = 4, and V = 64.

The space diagonal d = s√3, derived from the 3D Pythagorean theorem: d² = s² + s² + s² = 3s², so d = s√3. For s = 1, the diagonal ≈ 1.732.

Yes. A cube is a rectangular prism where all three dimensions (length, width, height) are equal. Every cube is a rectangular prism, but not every rectangular prism is a cube.

If the side is measured in feet, V = s³ directly gives cubic feet. If the side is in inches, divide by 1728 (12³) to convert to cubic feet. If in meters, multiply by 35.315 to get cubic feet.

A sphere inscribed in a cube touches all 6 faces and has diameter = side length. Its volume is (4/3)π(s/2)³ = πs³/6 ≈ 52.4% of the cube's volume. A sphere circumscribed around a cube has diameter = s√3.

Yes. Since d = s√3, solve for s = d/√3 = d√3/3. For example, if the space diagonal is 10, then s = 10/√3 ≈ 5.774.

A cube has 12 edges, so its total edge length (sometimes called the perimeter) is 12s. For s = 5 cm, the total edge length is 60 cm.

Doubling s: volume increases by 8× (2³), surface area increases by 4× (2²), and space diagonal doubles (2×). This cubic scaling is why volume grows much faster than surface area.

A unit cube has side length s = 1, giving volume = 1³ = 1 cubic unit, surface area = 6 square units, and space diagonal = √3 ≈ 1.732 units.

Yes. Since s = d/√3, the volume in terms of space diagonal is V = (d/√3)³ = d³/(3√3) = d³√3/9.

Concrete is often ordered in cubic yards. Ice, sugar cubes, dice, and building blocks are cube-shaped. Computer memory uses cubic units for voxel data. Crystal structures in chemistry use cubic unit cells.

The calculator uses IEEE 754 double-precision floating-point arithmetic, providing approximately 15 significant digits of accuracy. This is more than sufficient for any educational, engineering, or design application.

The cube root (∛x) reverses the cubing operation. If V = s³, then s = ∛V. Every real number has exactly one real cube root, unlike square roots which can have none or two real solutions.

A quick check: compute s from your result using the inverse formula. For example, if you calculated V = 125, verify s = ∛125 = 5, then check SA = 6 × 25 = 150. All values should be internally consistent.

The Cube Calculator uses standard mathematical formulas validated against authoritative references. The specific formula is displayed in the calculator interface with a detailed explanation of each variable.

Each calculator includes a step-by-step worked example showing exactly how the formula is applied. You can follow these steps with pen and paper to verify any result.

The Cube Calculator accepts numeric inputs including integers and decimals. Invalid inputs (letters, special characters) are rejected with clear error messages.