Pyramid Volume Calculator
Calculate volume, surface area, and dimensions of pyramids with any regular base
Calculate Pyramid Volume
Choose the shape of the pyramid's base
Length of each side of the regular base polygon
Perpendicular height from base to apex
Calculation Results
Formula Used
Volume: V = (1/3) × Base Area × Height
V = (1/3) × 53038.09 × 138.5 = 2448591.82 m³
Pyramid Properties
Example: Great Pyramid of Giza
World's Most Famous Pyramid
Also known as: Pyramid of Khufu or Cheops Pyramid
Original height: 146.6 m (now 138.5 m due to erosion)
Base side length: 230.3 m (average)
Base shape: Square (nearly perfect)
Application: Calculate the massive volume of this ancient wonder
Step-by-Step Calculation
1. Base area = 230.3² = 53,038 m²
2. Apply volume formula: V = (1/3) × Base Area × Height
3. V = (1/3) × 53,038 × 138.5 = 2,448,592 m³
Current volume: ~2.45 million cubic meters!
Note: Original volume was ~2.59 million m³ before erosion
Volume Formulas
General Formula
V = (1/3) × A × h
A = base area, h = height
Square Pyramid
V = (1/3) × a² × h
a = side length
Triangular Pyramid
V = (√3/36) × a² × h
For equilateral triangular base
Hexagonal Pyramid
V = (√3/2) × a² × h
For regular hexagonal base
Real-World Applications
Architecture
Building design and volume calculations
Archaeology
Ancient monument analysis
Construction
Material volume estimation
Packaging
Container and storage design
Education
Geometry and mathematics learning
Understanding Pyramid Volume
What is a Pyramid?
A pyramid is a three-dimensional geometric solid formed by connecting a polygonal base to a single point called the apex. The volume formula V = (1/3) × base area × height works for all types of pyramids, whether they have triangular, square, or any other polygonal base.
Key Properties
- •Base: Can be any polygon (triangle, square, pentagon, etc.)
- •Faces: n+1 faces (n triangular faces + 1 base)
- •Edges: 2n edges
- •Vertices: n+1 vertices
Volume Calculation Methods
Universal Formula:
V = (1/3) × A × h
Where A is base area and h is height
For Regular Polygons:
V = (n/12) × h × a² × cot(π/n)
Where n is number of sides, a is side length
Historical Fact: The Great Pyramid of Giza contains approximately 2.45 million cubic meters of stone, making it one of the largest structures ever built by humans.