Scale a length by the golden ratio φ so that a : b = b : (a + b).
| Longer b | – |
| Whole a + b | – |
Use this calculator to grow a shorter segment a into the golden partner b = a × φ and the whole a + b, where φ = (1 + √5) / 2 ≈ 1.61803399. Those three lengths satisfy a / b = b / (a + b). Art, architecture, and the Fibonacci ratio Fₙ₊₁ / Fₙ approach this same φ.
The shorter length a must be positive. This page does not split a given whole into golden parts (that would be whole / φ and whole / φ²).
Shorter length a: The smaller segment, positive.
Longer b: a × φ.
Whole a + b: The sum, equal to a × φ².
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