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Cube Capacity with Surface and Diagonal Inverses

Cube Capacity with Surface and Diagonal Inverses. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
  • Private in your browser
  • No signup
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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 Surface area 54, Cube diagonal (d) 5.1961524, Face diagonal (f) 4.2426407, Volume 27.

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

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

How does doubling cube edge affect capacity?

Volume becomes eight times larger, while surface area becomes four times larger and diagonals become twice as long.

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. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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