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Pyramid Volume Calculator

Calculate the volume of a pyramid from its base area (or base length and width) and height.

Reviewed by Christopher FloiedPublished Updated

This free online pyramid volume calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Minimum: 0

Minimum: 0

Minimum: 0

Perpendicular height from base to apex

Results

Volume

83.3333 cubic units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Pyramid Volume Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Pyramid Volume Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • Use the Pyramid Volume Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • Use it to explore the behavior of mathematical functions across a range of inputs.

Related Calculators

About Pyramid Volume Calculator

A pyramid is a polyhedron formed by connecting a polygonal base to a single point (apex) with triangular faces. The volume of any pyramid is one-third the product of its base area and height: V = (1/3)Bh. This formula works for pyramids with any polygonal base — square, rectangular, triangular, or hexagonal. The Great Pyramid of Giza, one of the Seven Wonders of the Ancient World, is a square-based pyramid. This calculator assumes a rectangular base, computing V = (1/3) × length × width × height. Pyramid volume calculations are used in architecture, geology (for modeling mountain shapes), and packaging design. The 1/3 factor, identical to that in the cone formula, reflects the tapering nature of the shape from base to apex.

The Math Behind It

The formula V = (1/3)Bh holds for any pyramid, regardless of the base shape or whether the pyramid is right or oblique, as demonstrated by Cavalieri's principle. This can be proven by calculus: at height y from the apex, the cross-section of a pyramid is similar to the base, scaled by factor y/h. The cross-sectional area is B(y/h)², so V = ∫₀ʰ B(y/h)² dy = B/h² × h³/3 = Bh/3. For a regular tetrahedron (triangular pyramid with all edges equal to a), the base area is (√3/4)a² and the height is a√(2/3), giving volume V = a³√2/12. The frustum of a pyramid (cut parallel to the base) has volume V = (h/3)(A₁ + A₂ + √(A₁A₂)), where A₁ and A₂ are the areas of the two parallel faces. Ancient Egyptians knew this formula, as documented in the Moscow Mathematical Papyrus (c. 1850 BCE). The centroid (center of mass) of a solid pyramid is located at 1/4 of the height from the base.

Formula Reference

Pyramid Volume

V = (1/3) × B × h

Variables: B = base area, h = perpendicular height

Worked Examples

Example 1: Model pyramid

A model pyramid has a 6 cm × 6 cm square base and height 8 cm.

Step 1:B = 6 × 6 = 36 cm²
Step 2:V = (1/3) × 36 × 8
Step 3:V = (1/3) × 288

V = 96 cm³

Common Mistakes & Tips

  • !Forgetting the 1/3 factor.
  • !Using the slant height instead of the perpendicular height.
  • !Confusing a pyramid with a prism, which has volume V = Bh (no 1/3 factor).

Related Concepts

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Frequently Asked Questions

Does the formula work for triangular pyramids?

Yes. Use the area of the triangular base for B. For example, B = ½ × base × height of the triangle.

What is a frustum?

A frustum is a pyramid with the top cut off by a plane parallel to the base. Its volume is V = (h/3)(A₁ + A₂ + √(A₁A₂)).

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