Free · 3D geometry calculators 📦

Rectangular Box Volume and Space Diagonal

Calculate rectangular box volume and space diagonal with converted units, positive geometric inverses and explicit model limits.

  • 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

A rectangular box measuring 3 × 4 × 12 cm has volume 144 cm³ and a 13 cm space diagonal.

V = lwh; 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
Diagonal (d)
13 cm
Volume
144 cm³

Assumptions and limitations

  • This is a closed rectangular box with perpendicular edges. The diagonal goes between opposite corners through the interior. Surface area, where offered, includes all six faces.
  • 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

What measurements are needed to recover one edge?

Supply the other two edges and either the volume or surface area offered on this page, or a space diagonal long enough to give a positive remaining edge. Clear the unknown edge first.

References

Require real, positive geometric inverses and the stated shape domain before displaying derived results. 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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