Pyramid Volume Calculator
Calculate pyramid volume for square, rectangular, triangular, and regular polygon bases. Features step-by-step formulas and prism comparisons.
Using the directly supplied footprint surface area.
By Cavalieri’s principle and calculus, any pyramid has exactly one-third the volume of a prism sharing identical base and height.
The volume of any pyramid is one-third of its base area multiplied by its vertical perpendicular height: V = (1/3) × A_base × h. For example, a square pyramid with 6-foot sides and a 9-foot height holds 108 cubic feet (4.0 cubic yards).
Pyramid Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Total interior volume of the pyramid | in³, ft³, yd³, cm³, or m³ |
| A_base | Surface area of the base polygon footprint | in², ft², cm², or m² |
| h | Perpendicular vertical height from base center to apex | in, ft, cm, or m |
Universal Pyramid Volume Formula
Whether a pyramid has a square base (like the Great Pyramid of Giza), a rectangular base, a triangle (tetrahedron), or an octagon, the formula remains fundamentally identical: V = (1/3) × Base Area × Vertical Height. The factor of 1/3 holds true for any pyramid tapering linearly to a point.
Square vs. Rectangular vs. Triangular Bases
For a square base with edge a, A_base = a². For a rectangular base with length a and width b, A_base = a × b. For a triangular base with base b and height h_base, A_base = 0.5 × b × h_base. Once you find base area, multiply by apex vertical height h and divide by 3.
Common Calculation Mistakes to Avoid
- Using slant edge height instead of vertical perpendicular height
- Forgetting the 1/3 factor and calculating the entire prism volume
- Confusing base triangle height with the pyramid’s 3D vertical height
Frequently Asked Questions
What is the formula for the volume of a pyramid?▼
What is the volume of a square pyramid?▼
How does a pyramid compare to a prism with the same base and height?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.