🌟 Golden Ratio Calculator
Calculate golden ratio (phi ≈ 1.618)
How to Use This Calculator
Select Calculation Type
Choose whether to check if two numbers are in golden ratio or explore the Fibonacci sequence.
Enter Values
Input two numbers (A and B) to check golden ratio, or enter Fibonacci index n.
Calculate
Press "Calculate Golden Ratio" to find phi (φ) and check if values are in golden ratio.
Formula
Golden Ratio: φ = (1 + √5) / 2 ≈ 1.618034
Golden Ratio Property: (a + b) / a = a / b = φ
Fibonacci: F(n) / F(n-1) → φ as n → ∞
Golden Ratio: Two numbers a and b are in golden ratio if (a + b)/a = a/b = φ.
Example: a = 1.618, b = 1
(1.618 + 1) / 1.618 = 2.618 / 1.618 ≈ 1.618 = φ ✅
1.618 / 1 = 1.618 = φ ✅
About Golden Ratio Calculator
The Golden Ratio Calculator calculates the golden ratio (phi, φ ≈ 1.618), checks if two numbers are in golden ratio, and explores the relationship between the golden ratio and Fibonacci sequence.
When to Use This Calculator
- Mathematics: Calculate golden ratio and explore its properties
- Art: Check proportions in art and design
- Architecture: Analyze golden ratio in structures
- Nature: Explore Fibonacci sequence and golden ratio in nature
- Education: Learn about golden ratio and Fibonacci sequence
Understanding Golden Ratio
The golden ratio (φ) is approximately 1.618. Two numbers a and b are in golden ratio if (a + b)/a = a/b = φ. The ratio of consecutive Fibonacci numbers approaches φ as n increases.
Frequently Asked Questions
What is the golden ratio?
The golden ratio (φ, phi) is approximately 1.618. It's the positive solution to φ² = φ + 1, or φ = (1 + √5) / 2. Two numbers a and b are in golden ratio if (a + b)/a = a/b = φ.
How is the golden ratio related to Fibonacci?
The ratio of consecutive Fibonacci numbers F(n)/F(n-1) approaches the golden ratio φ as n increases. For example, F(10)/F(9) = 55/34 ≈ 1.618, which is very close to φ.
Where is the golden ratio used?
The golden ratio appears in art (Parthenon, Mona Lisa), architecture (Great Pyramid), nature (sunflower seeds, pine cones), and mathematics (Fibonacci sequence, pentagons).
What is phi (φ)?
Phi (φ) is the symbol for the golden ratio, approximately 1.618. It's the positive solution to φ² = φ + 1. Properties: φ² = φ + 1, 1/φ = φ - 1.