Pyramid Calculators

Comprehensive collection of calculators for pyramids and pyramid-like shapes in 3D geometry

Basic Pyramid Forms

Triangular Pyramid 4 faces
Pyramid with triangular base - simplest pyramid form
Square Pyramid (V = ⅓Ah)
Pyramid with square base - most common pyramid form

Regular Polygonal Pyramids

Pentagonal Pyramid 5-sided
Pyramid with regular pentagonal base
Hexagonal Pyramid 6-sided
Pyramid with regular hexagonal base
Heptagonal Pyramid 7-sided
Pyramid with regular heptagonal base
Regular Pyramid n-gonal
General pyramid with regular n-gonal base

Truncated Pyramids (Frustums)

Truncated Square Pyramid
Cut square pyramid with parallel top and bottom faces
Truncated Rectangular Pyramid
Cut rectangular pyramid with trapezoidal cross-section
Pyramid Frustum
General frustum of any pyramid - cut between parallel planes
Frustum Pyramid
Alternative frustum calculation with specific geometry

Bipyramids (Double Pyramids)

Triangular Bipyramid 6 faces
Two triangular pyramids joined at their bases
Pentagonal Bipyramid 10 faces
Two pentagonal pyramids joined at their pentagonal bases
Hexagonal Bipyramid 12 faces
Two hexagonal pyramids joined at their hexagonal bases
Regular Bipyramid n-gonal
General bipyramid with regular n-gonal base

About Pyramids and Pyramid Structures

Pyramids are polyhedra formed by connecting a polygonal base to a single point (apex) - fundamental shapes in architecture and engineering:

  • Architecture - Pyramids, roofs, spires
  • Engineering - Structural supports
  • History - Ancient monuments
  • Crystallography - Crystal forms
  • Mathematics - Polyhedral geometry
  • Design - Modern architecture

Fundamental Pyramid Formulas
Basic Pyramid
Volume: V = ⅓Ah
(A = base area, h = height)
Frustum (Truncated)
V = ⅓h(A₁ + A₂ + √(A₁A₂))
Prismoidal formula
Slant Height
s = √(h² + r²)
For lateral surface calculation
Bipyramid
V = ⅔Ah
Two pyramids combined
Historical Note: The Great Pyramid of Giza is a perfect square pyramid, demonstrating the mathematical precision achieved by ancient Egyptian builders.

Practical Applications

Architecture & Construction
  • Pyramids: Ancient monuments, modern architecture
  • Roofs: Pyramid roofs, spires, steeples
  • Foundations: Pyramid-shaped foundations
Engineering & Industry
  • Containers: Hoppers, funnels, storage
  • Structures: Support towers, transmission towers
  • Crystals: Pyramid-shaped crystals
Mathematics & Education
  • Geometry: Teaching 3D shapes
  • Calculus: Volume integration examples
  • Topology: Polyhedral studies
Art & Design
  • Sculptures: Pyramid-based art
  • Architecture: Modern pyramid buildings
  • Monuments: Memorial structures
Quick Reference
⅓Ah
Pyramid Volume
⅔Ah
Bipyramid
√(h² + r²)
Slant Height
n+1
Faces
⅓h(A₁ + A₂ + √(A₁A₂))
Frustum Volume
Historical Context

Ancient Egypt (2600 BC): Great Pyramid of Giza - mathematical marvel of ancient engineering.

Euclid (ca. 300 BC): Formal geometric treatment of pyramids in "Elements".

Modern Times: Pyramid structures in contemporary architecture and engineering.

Properties
📐 Convergence: All edges meet at apex
📏 Base: Any polygon (triangle, square, etc.)
🏗️ Stability: Excellent structural properties
⚖️ Volume: Always ⅓ of equivalent prism
✂️ Truncation: Creates frustum forms