Square Pyramid Volume Calculator
Calculate volume and properties of square pyramids with multiple input methods
Calculate Square Pyramid Volume
Side length of the square base
Perpendicular height from base to apex
Pyramid Volume Results
Example Calculations
Basic Square Pyramid
Given: Base edge = 6 cm, Height = 10 cm
Step 1: Base area = a² = 6² = 36 cm²
Step 2: Volume = (base area × height) / 3
Step 3: Volume = (36 × 10) / 3 = 120 cm³
Great Pyramid of Giza
Given: Base edge = 230.6 m, Height = 146.7 m
Volume: V = (230.6² × 146.7) / 3 ≈ 2,600,324 m³
Note: Approximately 2.6 million cubic meters
Square Pyramid Volume Formulas
Basic Volume
V = (a² × h) / 3
Base area × height ÷ 3
Using Slant Height
V = (a² × √(s² - (a/2)²)) / 3
When height is unknown
Using Lateral Edge
V = (a² × √(d² - a²/2)) / 3
When height is unknown
Key Relationships
Slant height: s = √(h² + (a/2)²)
Lateral edge: d = √(h² + a²/2)
Base diagonal: diagonal = a√2
Lateral surface area: 2as
Total surface area: a² + 2as
Real-World Applications
Architecture and monument design
Ancient pyramid construction
Roof and tent structures
Package and container design
Engineering calculations
Understanding Square Pyramid Volume
Volume Formula Derivation
The volume of a square pyramid is calculated using the formula V = (base area × height) / 3. This formula comes from the general pyramid volume formula and applies specifically to pyramids with square bases.
Step-by-Step Calculation
- 1.Find base area: Square the base edge length (a²)
- 2.Multiply by height: Base area × perpendicular height
- 3.Divide by 3: Final result gives pyramid volume
Alternative Methods
From Slant Height
V = (a² × √(s² - (a/2)²)) / 3
When height is not directly measurable
From Lateral Edge
V = (a² × √(d² - a²/2)) / 3
Using corner-to-apex measurement
From Multiple Parameters
Various combinations possible
This calculator supports 6 different methods
Important: Always ensure measurements are in the same units. The height must be perpendicular to the base, not along a slanted face.