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Rectangular Prism Faces, Volume and Space Diagonal

Rectangular Prism Faces, Volume and Space Diagonal. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases 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: Length (l) 3, Width (w) 4, Height (h) 12 gives Surface area 192, Volume 144, 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 rectangular prism has three mutually perpendicular edges. Total area includes all six faces; its space diagonal crosses the interior. Recover a missing edge using two known edges and volume, surface area or a sufficiently long diagonal.
  • Select units before entering dimensions. Clear an unknown result before solving backward, and supply enough independent measurements. Display rounding does not represent measurement uncertainty.
  • Calculations use 64 significant digits and full-precision π. Original reference drawings explain dimensions and are not drawn to the entered scale.

Common questions

Is a space diagonal the same as a face diagonal?

No. A space diagonal includes all three squared edge lengths. A face diagonal includes only the two edges on that face.

References

Require positive physical dimensions and real nondegenerate inverse roots while preserving documented limiting shapes. 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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