Pyramid Golden Ratio Calculator
Discover the perfect proportions of ancient pyramids using the golden ratio (φ = 1.618)
Advanced Options
Pyramid Golden Ratio Results
Enter your pyramid dimensions to analyze how closely they match the golden ratio.
Pyramid Visualization
Dimensions Breakdown
Your pyramid's detailed dimensional analysis will appear here.
🏛️ Famous Pyramids and Their Ratios
| Pyramid | Base (m) | Height (m) | Ratio | Deviation from φ |
|---|---|---|---|---|
| Great Pyramid of Giza | 230.4 | 146.6 | 1.571 | -2.9% |
| Red Pyramid | 220 | 105 | 2.095 | +29.5% |
| Bent Pyramid | 189.4 | 101.1 | 1.873 | +15.8% |
| Pyramid of the Sun | 223.5 | 71.2 | 3.139 | +94.0% |
| Louvre Pyramid | 35.42 | 21.64 | 1.636 | +1.1% |
| Perfect Golden Ratio Pyramid | 100 | 61.8 | 1.618 | 0% |
Note: The golden ratio (φ) is approximately 1.61803398875. Lower deviation means closer to perfect golden ratio proportions.
🧮 Mathematical Insights
Golden Ratio Definition
The golden ratio φ = (1 + √5)/2 ≈ 1.618 appears when a line is divided such that the ratio of the whole to the longer part equals the ratio of the longer to the shorter part.
Pyramid Geometry
In a golden ratio pyramid, the apothem (slant height) divided by half the base length equals φ. This creates a triangle with angles of approximately 51.83°.
Pi Connection
The Great Pyramid's base perimeter divided by twice its height approximates π (3.1416). The relationship between π and φ in pyramid design remains a mathematical mystery.
Square Roots
The height of a golden ratio pyramid relates to its base through φ and √φ. The Great Pyramid's height is √φ × half its base length to about 99.9% accuracy.
Optimal Angles
The face angle of a perfect golden ratio pyramid is 51.827°. The Great Pyramid's actual angle is 51.844°, deviating by only 0.03% from the mathematical ideal.
Fibonacci Sequence
The ratio of consecutive Fibonacci numbers approaches φ. A pyramid with height/base ratio as consecutive Fibonacci numbers (e.g., 89/55 ≈ 1.618) approximates the golden ratio.
Note: This calculator provides mathematical analysis of pyramid proportions. The golden ratio (φ) is an irrational number approximately equal to 1.61803398875. Results may vary slightly based on measurement precision and calculation methods.