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Calculator Answers

Pyramid Volume Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A pyramid volume calculator computes the space enclosed by a pyramid with a rectangular or square base. The volume is calculated as one-third of the product of the base area (length * width) and the perpendicular height. This tool is useful for students and architects studying 3D geometry and structural space.

Calculate the volume of a square or rectangular pyramid using the base length, base width, and height.

See also: Cone Volume Calculator, Volume Calculator – Rectangular Prism, Cylinder, Sphere & Cone, and Trapezoid Calculator.

Quick Answer

Find the volume of a pyramid. Enter the base length, base width, and height to compute the volume instantly.

For a square base, keep length and width equal. · e.g. 6

Width of the rectangular or square base. · e.g. 6

Perpendicular height from base center to apex. · e.g. 8

Pyramid Results

Volume (V)

96 units³

Square Base Pyramid

Base Area (l × w)36 units²
Height (h)8 units
Volume96 units³
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Examples

Square Pyramid

length = 6 · width = 6 · height = 8 — Volume = 96 units³

Rectangular Pyramid

length = 5 · width = 8 · height = 9 — Volume = 120 units³

How it works

Volume Formula

The volume of a pyramid is computed using the base area and the perpendicular height:

Volume = (1/3) × l × w × h

Where:

  • l is the length of the base
  • w is the width of the base
  • h is the height of the pyramid

Disclaimer

For educational purposes. Verify results for critical applications.

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Cone Volume CalculatorCalculate the volume of a cone using the formula V = (1/3)πr²h with radius and height inputs.Volume Calculator – Rectangular Prism, Cylinder, Sphere & ConeCalculate the volume of common 3D shapes including rectangular prism volume, cylinder volume, sphere, cone, and pyramid. Round shapes accept a radius or a diameter. Includes formulas and cubic unit conversions.Trapezoid CalculatorCalculate the area and perimeter of a trapezoid from the two parallel bases, the height, and the two non-parallel sides.

Frequently asked questions

The volume of a pyramid is one-third of the base area multiplied by the height. Formula: Volume = (1/3) × base_length × base_width × height.

For a square pyramid, the length and width of the base are equal (l = w). The formula simplifies to: Volume = (1/3) × base_side² × height.

If you have a prism and a pyramid with the exact same base and height, the pyramid will hold exactly one-third of the volume of the prism. This can be visualized by dividing a cube into three identical pyramids.

Yes. Cavalieri's principle states that if two solids have the same height and base area, and their cross-sections at any height have the same area, they have the same volume. This means the standard formula works even if the apex is not centered.