Fibonacci & Golden Ratio
Angle Calculator
Discover Fibonacci sequence, golden ratio (φ), Kepler harmonics, Lucas numbers and metallic ratio relationships between planetary angles in your birth chart.
Birth Data
Reference Angles
Fibonacci Degrees
Fibonacci numbers used directly as degrees.
| F₇ | 13° |
| F₈ | 21° |
| F₉ | 34° |
| F₁₀ | 55° |
| F₁₁ | 89° |
| F₁₂ | 144° |
Golden Ratio Angles (360° / φⁿ)
Division of the circle by powers of the golden ratio.
| 360° / φ¹ | 222.5° |
| 360° / φ² | 137.5° (golden angle) |
| 360° / φ³ | 85.0° |
| 360° / φ⁴ | 52.5° |
| 360° / φ⁵ | 32.5° |
| 360° / φ⁶ | 20.1° |
Fibonacci Ratio Angles
Consecutive Fibonacci ratios applied to 360°. Series converges to φ.
| 360° × 1/2 | 180° |
| 360° × 2/3 | 120° (240°) |
| 360° × 3/5 | 144° (216°) |
| 360° × 5/8 | 135° (225°) |
| 360° × 8/13 | 138.5° (221.5°) |
| 360° × 13/21 | 137.1° (222.9°) |
Kepler Harmonics
Origin of classical angles. Ptolemy (Harmonics) and Kepler (Harmonices Mundi). Supported by classical sources.
| 1/2 (Octave) | 180° = Opposition |
| 2/3 (Perfect Fifth) | 120° = Trine |
| 3/4 (Perfect Fourth) | 90° = Square |
| 4/5 (Major Third) | 72° = Quintile |
| 5/6 (Minor Third) | 60° = Sextile |
| 3/8 (Oct.+Fourth) | 135° = Sesquiquadrate |
Lucas Numbers
Fibonacci's sibling sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199. Same addition rule, different starting point.
| L₇ = 29° | close to semi-sextile |
| L₈ = 47° | no known aspect |
| L₉ = 76° | close to quintile |
| L₁₀ = 123° | close to trine |
| L₁₁ = 199° | no known aspect |
Metallic Ratios Family
Golden ratio (φ) is the first member of this family. Silver ratio (δ ≈ 2.414) and Bronze ratio (β ≈ 3.303) produce different angle distributions.
| 360°/φ² = 137.5° | golden angle |
| 360°/δ² = 61.8° | very close to sextile! |
| 360°/δ¹ = 149.1° | close to quincunx |
| 360°/β¹ = 109.0° | no known aspect |
This tool is for research and exploration purposes. Of the 7 ratio families, only Kepler Harmonics are based on classical sources (Ptolemy, Kepler). Other families represent modern research perspective.
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