Height of a Square Pyramid Calculator
Calculate the height of a square pyramid using volume, slant height, lateral edge, or surface areas
Calculate Square Pyramid Height
Length of one side of the square base
Total volume of the pyramid
Pyramid Height Results
Calculation Steps
Formula Reference
From Volume: H = 3V/a²
From Slant Height: H = √(s² - (a/2)²)
From Lateral Edge: H = √(d² - a²/2)
From Areas: First solve for slant height, then use slant height formula
Example Calculation
Louvre Pyramid Example
Base edge (a): 35.0 m
Slant height (s): 27.8 m
Method: Using slant height and base edge
Calculation
H = √(s² - (a/2)²)
H = √(27.8² - (35.0/2)²)
H = √(772.84 - 306.25)
H = 21.6 m
Square Pyramid Components
Height
Perpendicular distance from base to apex
Slant Height
Distance from apex to midpoint of base edge
Lateral Edge
Distance from apex to base corner
Base Edge
Length of one side of square base
Calculation Tips
Always ensure base edge length is provided
Slant height must be greater than half the base edge
Lateral edge must be greater than height
Check units for consistency in calculations
Understanding Square Pyramid Height
What is Pyramid Height?
The height of a square pyramid is the perpendicular distance from the center of the square base to the apex (vertex) of the pyramid. It's also called the altitude and represents how "tall" the pyramid is when measured vertically.
Types of Measurements
- •Height (H): Vertical distance from base to apex
- •Slant Height (s): Distance along the face from base edge midpoint to apex
- •Lateral Edge (d): Distance from base corner to apex
- •Base Edge (a): Side length of the square base
Key Formulas
From Volume and Base:
H = 3V / a²
From Slant Height and Base:
H = √(s² - (a/2)²)
From Lateral Edge and Base:
H = √(d² - a²/2)
Note: For area-based calculations, first solve for slant height, then use the slant height formula