Free · 3D geometry calculators 📦

Cube Size from Edge, Volume, Surface or Diagonal

Cube Size from Edge, Volume, Surface or Diagonal. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • 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

Example in initial displayed units: Side (a) 3 gives Cube diagonal (d) 5.1961524, Face diagonal (f) 4.2426407, Volume (V) 27, Surface area (S) 54.

V = a³; A = 6a²; dface = a√2; dspace = 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 (V)
27 cm³
Surface area (S)
54 cm²

Assumptions and limitations

  • All cube edges are equal. A face diagonal spans two perpendicular edges, while a space diagonal spans three. One positive measurement sets the size; use the positive geometric roots.
  • Select compatible units and enough independent dimensions. Clear unknown values before solving backward. Numeric precision and display rounding do not quantify uncertainty in measured inputs.
  • Arithmetic uses 64 significant digits. Original reference diagrams explain the dimensions and do not follow entered proportions.

Common questions

Which cube diagonal is longer?

The space diagonal a√3 is longer than the face diagonal a√2 because it includes the third perpendicular 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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