Pyramid Angle Calculator
Calculate all angles in regular right pyramids with different base shapes
Calculate Pyramid Angles
Choose the shape of the pyramid's base
Pyramid Dimensions
Length of base polygon side
Perpendicular height to apex
Pyramid Angles
Calculated Segments
Mathematical Formulas
Example: Great Pyramid of Giza
Historical Monument Analysis
Base: Square pyramid
Original height: 146.7 m
Base side length: 230.6 m
Application: Calculate the precise angles used in ancient construction
Calculated Results
1. MC segment = 230.6/2 = 115.3 m
2. Face median angle: α = arctan(146.7/115.3) = 51.83°
3. Edge angle: β = arctan(146.7/163.1) = 41.98°
The famous base angle of 51.83° demonstrates the mathematical precision of ancient Egyptian architecture!
Angle Definitions
Alpha (α)
Angle between face median and base plane
α = arctan(h/MC)
Beta (β)
Angle between edge and base plane
β = arctan(h/AC)
Gamma (γ)
Base angle of triangular face
γ = arccos(s/2/slant)
Delta (δ)
Apex angle of triangular face
δ = 180° - 2γ
Real-World Applications
Architecture
Roof design and structural angles
Engineering
Structural component calculations
Manufacturing
Precision part design
Archaeology
Ancient structure analysis
Education
Geometry and trigonometry learning
Understanding Pyramid Angles
What is a Pyramid?
A pyramid is a three-dimensional geometric solid with a polygonal base and triangular faces that meet at a common point called the apex. In a regular right pyramid, the base is a regular polygon and the apex lies directly above the center of the base.
Types of Pyramid Angles
- •Face Median Angle (α): Most important angle, defines pyramid's "slenderness"
- •Edge Angle (β): Always smaller than α in convex base pyramids
- •Face Base Angle (γ): Base angles of isosceles triangular faces
- •Face Apex Angle (δ): Apex angle of triangular faces
Calculation Methods
Key Segments:
MC: From side midpoint to center
AC: From corner to center
Slanted Height: From apex to side midpoint
Trigonometric Formulas:
α = arctan(height/MC)
β = arctan(height/AC)
γ = arccos((side/2)/slanted_height)
δ = 180° - 2γ
Historical Note: The Great Pyramid of Giza has a base angle of 51.83°, demonstrating the mathematical precision achieved by ancient Egyptian architects.