Space Diagonal Calculator

Work out space diagonal instantly with clear inputs, formula shown and shareable results.

About Space Diagonal Calculator

The space diagonal of a rectangular box is the three-dimensional Pythagorean result √(l² + w² + h²) — the longest straight line that fits inside the box.

Formula

Space diagonal

d = √(l² + w² + h²)

Worked example

With the default values below, Space Diagonal Calculator returns Space diagonal of 7.8103. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lengthminimum 0: 6
Widthminimum 0: 4
Heightminimum 0: 3

Results

Space diagonal: 7.8103
Face diagonal (length × width): 7.2111
Face diagonal (length × height): 6.7082
Face diagonal (width × height): 5.0000

Step by step

1Values used
2Space diagonal
3Space diagonal= 7.8103
4Face diagonal (length × width)= 7.2111
5Face diagonal (length × height)= 6.7082
6Face diagonal (width × height)= 5.0000

Assumptions and limits

The result is derived only from the 3 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

6 × 4 × 3?

√(36 + 16 + 9) = √61 ≈ 7.810250 units.

Why does it matter for packing?

A rigid rod fits inside a box only if it is no longer than the space diagonal.