Calculate golden ratio segments, golden rectangles, and check how close any two values are to phi (1.618).
The Golden Ratio (φ)
1.6180339887…
φ = (1 + √5) / 2 ≈ 1.618033988749895
Divide a Length
Golden Rectangle
Check a Ratio
How close are two values to the golden ratio?
:
Fibonacci → φ Approximation
Consecutive Fibonacci ratios converge to φ.
| n | F(n) | F(n)/F(n-1) |
|---|---|---|
| 1 | 1 | — |
| 2 | 1 | 1.00000000 |
| 3 | 2 | 2.00000000 |
| 4 | 3 | 1.50000000 |
| 5 | 5 | 1.66666667 |
| 6 | 8 | 1.60000000 |
| 7 | 13 | 1.62500000 |
| 8 | 21 | 1.61538462 |
| 9 | 34 | 1.61904762 |
| 10 | 55 | 1.61764706 |
| 11 | 89 | 1.61818182 |
| 12 | 144 | 1.61797753 |
| 13 | 233 | 1.61805556 |
| 14 | 377 | 1.61802575 |