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Rectangular Prism Base, Lateral and Six-Face Areas

Rectangular Prism Base, Lateral and Six-Face Areas. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
  • Private in your browser
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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, One rectangular base area 12, Lateral area 168, Volume 144.

Abase = lw; Alateral = 2h(l+w); Atotal = 2Abase+Alateral

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
One rectangular base area
12 cm²
Lateral area
168 cm²
Volume
144 cm³

Assumptions and limitations

  • The base-area control means one rectangular base. Lateral area covers the four side faces, and total area adds two bases. All three edges are positive and mutually perpendicular.
  • 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

Why is total area twice the base plus lateral area?

A closed rectangular prism has two identical rectangular ends. This workflow labels one end as base area, so both ends contribute twice that value.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume.

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