Free · Geometry and function relationships

Rectangular Pyramid Surface Area and Volume

A right rectangular pyramid has its apex directly above the center of its rectangular base. Each pair of opposite faces has the same slant height; vertical height and slant height are different measures.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

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

For baseLength = 6, baseWidth = 8, height_pyr = 12, area_base = 48, height_a = 12.64911064067351732799557417773087413487822055730086730743001941, height_b = 12.36931687685298164946422956792223107544159767612086130319590072, volume = 192.

A=lw+l√(h²+w²/4)+w√(h²+l²/4); V=lwh/3

Worked example

Enter these known values and leave the other values blank.

Base length (a)
6 cm
Base width (b)
8 cm
Pyramid height (H)
12 cm
Base diagonal
10 cm
Base surface area (A_b)
48 cm²
Lateral surface area (A_l)
174.85 cm²
Total surface area (A)
222.85 cm²
First slant height
12.65 cm
Second slant height
12.37 cm
First lateral face area
37.95 cm²
Second lateral face area
49.48 cm²

Assumptions and limitations

  • A right rectangular pyramid has its apex directly above the center of its rectangular base. Each pair of opposite faces has the same slant height; vertical height and slant height are different measures.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

A right rectangular pyramid has its apex directly above the center of its rectangular base. Each pair of opposite faces has the same slant height; vertical height and slant height are different measures.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

Explore geometry and function relationships or browse all math calculators.