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Cuboid Capacity, Six-Face Area and Interior Diagonal

Cuboid Capacity, Six-Face Area and Interior Diagonal. Use unit controls and documented positive geometric roots to compare base, lateral and total measures.

  • Formula & worked example
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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: Length (l) 3, Width (w) 4, Height (h) 12 gives Volume 144, Surface area 192, Diagonal (d) 13.

V = lwh; A = 2(lw+lh+wh); d² = l²+w²+h²

Worked example

Enter these known values and leave the other values blank.

Length (l)
3 cm
Width (w)
4 cm
Height (h)
12 cm
Surface area
192 cm²
Volume
144 cm³
Diagonal (d)
13 cm

Assumptions and limitations

  • A cuboid has three positive mutually perpendicular edges. Total surface includes all six faces. A missing edge recovered from a space diagonal requires a diagonal longer than the known face diagonal.
  • 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

What distinguishes a cuboid from a cube?

A cuboid permits unequal edge lengths; a cube has three equal edge lengths. Both have six rectangular faces and three perpendicular dimensions.

References

Require physical dimensions and real positive inverse geometry; distinguish dependent measurements and cross-section consistency. 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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