Golden Ratio Calculator (φ)
Explore the divine proportion: compute larger / smaller parts from any value, check proportions, and see Fibonacci ratios approach φ ≈ 1.6180339887.
Step 1: Enter dimensions
⚡ How it works
Enter any one value (A, B, or total). The others are calculated to maintain the golden ratio φ = (1+√5)/2 ≈ 1.618. For perfect proportion: A/B = φ and (A+B)/A = φ.
Step 2: References
✨ Golden ratio in nature
φ appears in art, architecture, and nature (nautilus shells, sunflowers). Fibonacci numbers (0,1,1,2,3,5,8,13…) converge to φ.
Golden Ratio Results
Summary
Fibonacci & Ratios
Formula & Visual
Golden ratio φ (constant)
1.618034
φ’ = 0.618034
Larger part (A)
10.00
Smaller part (B)
6.18
Total (A+B)
16.18
A / B
1.618
Fibonacci numbers approach φ
| n | Fibonacci F(n) | F(n)/F(n-1) | Difference from φ |
|---|
Golden rectangle proportion
Formula
φ = (1 + √5) / 2 ≈ 1.6180339887
If A is the larger part and B the smaller: A/B = (A+B)/A = φ.
From any single value we compute the others using φ and 1/φ.
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