Calculate volume, surface area, and lateral surface area of a square pyramid. Essential for geometry, architecture, and 3D modeling.
Last updated: April 2026 | By Patchworkr Team
A square pyramid is a 3D geometric shape with a square base and four triangular faces that meet at a single point called the apex or vertex. It's one of the most fundamental polyhedra in geometry.
Real-world examples include the Egyptian pyramids, tent structures, and rooftops. Square pyramids are used extensively in architecture, engineering, and mathematical modeling to calculate volume and surface area.
Key measurements include the base length (side of the square base), the height (perpendicular distance from base to apex), and the slant height (distance from base edge midpoint to apex).
The volume is one-third of the base area times the height.
Includes the base square plus the four triangular faces.
Only the four triangular faces, not including the base.
Calculate the volume of a square pyramid with base length 10 and height 12.
Height is perpendicular from base to apex. Slant height runs along the triangular face from base edge midpoint to apex.
A square pyramid has a square base (4 sides), while a triangular pyramid (tetrahedron) has a triangular base (3 sides).
A pyramid fills exactly 1/3 of the volume of a rectangular prism with the same base and height.
Yes, but you need either the base or regular height. Use: height = √(slant height² - (base/2)²).
Any consistent unit works (cm, m, ft, etc.). Volume is in cubic units, area in square units.
That's the lateral surface area—one of the calculator modes.
Most major Egyptian pyramids are square pyramids, though their bases are very large (e.g., Great Pyramid: 230m × 230m base).
This calculator assumes a right pyramid (apex directly above base center). Oblique pyramids require different calculations.
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