Golden Ratio Calculator
Enter one side of a ratio, and find the other side based on the golden ratio (φ ≈ 1.618).
How to use the golden ratio calculator
- Enter the length of the side you know.
- Select whether this is the short or the long side of the ratio.
- The other side and the sum update automatically.
What is the golden ratio?
The golden ratio (φ, phi) is a mathematical ratio of approximately 1.618, defined so that the ratio between a long and a short part is the same as the ratio between the sum and the long part: (a+b)/a = a/b = φ. The number appears in geometry, art, architecture and nature (e.g. in the spiral patterns of certain shells and plants), and has fascinated mathematicians since antiquity.
Worked example: with a short side of 10 the long side becomes 10 × 1.618 = 16.18, and the two together sum to 10 + 16.18 = 26.18. What makes φ special shows up when you divide the sum by the long side: 26.18 ÷ 16.18 = 1.618 — the same ratio again. The golden ratio is precisely the number where the whole relates to the larger part exactly as the larger part relates to the smaller.
Frequently asked questions
What is the exact value of φ?
φ = (1 + √5) / 2 ≈ 1.6180339887 — an irrational number that continues forever without repeating, just like π.
Where is the golden ratio used in practice?
In design and architecture it's often used to determine proportions that feel balanced (e.g. the width/height ratio of an image or a building). It also appears naturally in the Fibonacci sequence and certain growth patterns in nature.
Is the golden ratio the same as the Fibonacci numbers?
They're related but not identical — the ratio between two consecutive Fibonacci numbers (e.g. 21/13) gets closer to φ the further out in the sequence you go, but is never exactly equal to φ.