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Cube Surface, Volume and Face or Space Diagonal

No. A face diagonal is a√2, while the space diagonal is a√3. Each has its own control and label.

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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.

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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 of the cube 54, Volume 27, Face diagonal (f) 4.242641, Cube diagonal (d) 5.196152.

S = 6a²; V = a³; f = a√2; d = a√3

Worked example

Enter these known values and leave the other values blank.

Side (a)
3 cm
Cube diagonal (d)
5.196 cm
Face diagonal (f)
4.243 cm
Volume
27 cm³
Surface area of the cube
54 cm²

Assumptions and limitations

  • All six faces are squares with the same positive edge a. The face diagonal crosses one square; the space diagonal joins opposite cube vertices. Any one positive captured measure determines the others using positive roots and dimensionally matched length, area or volume controls. A general cuboid has different formulas.
  • Clear unknown measurements before solving backward. Use compatible units and independent values. Reference pictures are original schematic drawings. Independently rounded measurements can fail strict compatibility at a boundary.

Common questions

Are the two diagonals interchangeable?

No. A face diagonal is a√2, while the space diagonal is a√3. Each has its own control and label.

How do I use this calculator with different units?

Select the unit beside each measure. Length, squared length and volume use different dimensions; changing a unit preserves the physical value. Compound length controls represent feet/inches or meters/centimeters together.

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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