Diagonal Of A Cube Calculator

Work out diagonal of a cube instantly with clear inputs, formula shown and shareable results.

About Diagonal Of A Cube Calculator

A cube has two kinds of diagonal: the face diagonal a√2 across a single square face, and the space diagonal a√3 from one corner to the opposite corner through the interior.

Formulas

Space diagonal

d = a√3

Face diagonal

f = a√2

Worked example

With the default values below, Diagonal Of A Cube Calculator returns Diagonal requested of 8.6603. Change any input above and every figure here is recalculated in your browser.

Inputs used

Edge lengthminimum 0: 5
Diagonal wantedone of Space diagonal, Face diagonal: Space diagonal

Results

Diagonal requested: 8.6603
Space diagonal a√3: 8.6603
Face diagonal a√2: 7.0711
Volume: 125.0000

Step by step

1Values used
2Space diagonal
3Face diagonal
4Diagonal requested= 8.6603
5Space diagonal a√3= 8.6603
6Face diagonal a√2= 7.0711
7Volume= 125.0000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Edge 5 gives what space diagonal?

5√3 ≈ 8.660254 units.

How is a√3 derived?

The face diagonal is a√2; combining it with the perpendicular edge a gives √(2a² + a²) = a√3.