Free · 3D geometry calculators 📦

Cube Edge, Face Diagonal, Space Diagonal and Size

Calculate cube edge, face diagonal, space diagonal and size with converted units, positive geometric inverses and explicit model limits.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A cube with a 3 cm edge has volume 27 cm³, surface area 54 cm², face diagonal 3√2 cm and space diagonal 3√3 cm.

V = a³; A = 6a²; face diagonal = a√2; space diagonal = a√3

Worked example

Enter these known values and leave the other values blank.

Side (a)
3 cm
Cube diagonal (d)
5.2 cm
Face diagonal (f)
4.24 cm
Volume
27 cm³
Surface area
54 cm²

Assumptions and limitations

  • All twelve edges are equal and adjacent faces are perpendicular. The face diagonal and the diagonal through the solid are different lengths.
  • Measurements must describe the same shape. Clear a quantity you want to infer instead of supplying conflicting measurements. Unit selectors are converted before the geometric relationships are applied.
  • Calculations use 64 significant digits with full-precision π; result formatting rounds the displayed value separately. These are ideal geometric models, without material allowances or measurement uncertainty.

Common questions

Can volume or surface area recover the edge?

Yes. For positive size, a = ∛V or a = √(A/6), after units are converted. A face or space diagonal can also recover the edge.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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