# Cube Calculator

Calculate the volume, surface area, face diagonal, and space diagonal of a cube. Enter the side length and get all properties instantly.

## What this calculates

Enter the side length of a cube and instantly get its volume, surface area, face diagonal, and space diagonal. A cube with side length 5 has a volume of 125, surface area of 150, and a space diagonal of about 8.66.

## Inputs

- **Side Length (s)** — The length of one edge of the cube.

## Outputs

- **Volume** — The space enclosed by the cube (s³).
- **Surface Area** — The total area of all 6 faces (6s²).
- **Face Diagonal** — The diagonal across one face (s√2).
- **Space Diagonal** — The diagonal from one corner to the opposite corner (s√3).
- **Total Edge Length** — The sum of all 12 edges (12s).

## Details

**Cube Formulas**

A cube is a regular hexahedron with all six faces being identical squares. Given side length s:

- **Volume:** V = s³
- **Surface Area:** SA = 6s²
- **Face Diagonal:** d_f = s x sqrt(2) (the diagonal across one face)
- **Space Diagonal:** d_s = s x sqrt(3) (corner to opposite corner through the interior)
- **Total Edge Length:** 12s (a cube has 12 equal edges)

**Worked Example: s = 4**

- Volume = 4³ = 64 cubic units
- Surface Area = 6 x 16 = 96 square units
- Face Diagonal = 4 x 1.414 = 5.657 units
- Space Diagonal = 4 x 1.732 = 6.928 units

**Why Two Diagonals?**

The face diagonal lies flat on one face (like the diagonal of a square). The space diagonal cuts through the interior of the cube from one vertex to the farthest vertex. The space diagonal is always longer because it spans three dimensions instead of two.

**Cubes in the Real World**

Dice, ice cubes, Rubik's cubes, and storage boxes are everyday examples. Shipping companies use the cubic volume to calculate freight costs, and builders use surface area to estimate paint or material coverage.

## Frequently Asked Questions

**Q: What is the volume formula for a cube?**

A: The volume of a cube is V = s³, where s is the side length. For a cube with side length 3, the volume is 3 x 3 x 3 = 27 cubic units.

**Q: What is the difference between face diagonal and space diagonal?**

A: The face diagonal is the diagonal across one square face (s x sqrt(2)). The space diagonal goes from one corner of the cube to the opposite corner, passing through the interior (s x sqrt(3)). The space diagonal is always longer.

**Q: How many faces, edges, and vertices does a cube have?**

A: A cube has 6 faces (all squares), 12 edges (all equal length), and 8 vertices (corners). This satisfies Euler's formula: V - E + F = 8 - 12 + 6 = 2.

**Q: How do you find the side length from the volume?**

A: Take the cube root of the volume: s = V^(1/3). For a cube with volume 64, the side length is the cube root of 64, which is 4.

---

Source: https://vastcalc.com/calculators/math/cube
Category: Math
Last updated: 2026-04-08