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The golden ratio (φ, phi ≈ 1.618) is a proportion found throughout art, architecture and nature — from the Parthenon to sunflower seed spirals. Two parts are in the golden ratio when the whole relates to the larger part exactly as the larger relates to the smaller. Designers use it to divide layouts, size type and place focal points in a way that feels naturally balanced.
Enter a total length and the tool splits it into the two golden-ratio parts.
How is it calculated?
The ratio
φ = (1 + √5) ÷ 2 ≈ 1.618033988… Two segments a and b (with a the larger) are in the golden ratio when (a + b) ÷ a = a ÷ b = φ.
Splitting a length
To divide a total length L by the golden ratio: - Larger part = L ÷ φ ≈ L × 0.618 - Smaller part = L − larger part ≈ L × 0.382
For L = 100: larger 61.8, smaller 38.2.
Where it's used
- Design and layout: dividing a page, canvas or screen; the golden ratio grid.
- Typography: relating body text size to headings and line height.
- Photography: placing the subject (a refinement of the rule of thirds).
- Architecture and art: proportioning facades, frames and compositions.
- Logos and UI: sizing elements so they feel harmonious.
A curious property
φ is the only number where φ = 1 + 1/φ. It also emerges from the Fibonacci sequence: the ratio of consecutive Fibonacci numbers (13/8, 21/13, 34/21…) converges to φ. That link is why the ratio shows up so often in natural growth patterns.
Worked example
Divide a 100-unit length by the golden ratio: the larger part is 100 ÷ 1.618 ≈ 61.8 and the smaller part is 100 − 61.8 = 38.2. Check the proportion: the whole to the larger, 100 ÷ 61.8 = 1.618, equals the larger to the smaller, 61.8 ÷ 38.2 = 1.618 — the defining property. So a 1000 px wide layout split this way gives a 618 px main column and a 382 px sidebar, a division that reads as naturally balanced.
FAQ
What is the golden ratio?+
A proportion, φ ≈ 1.618, where the whole relates to the larger part as the larger relates to the smaller. It is (1 + √5) ÷ 2 and appears widely in art, design and nature.
How do I split a length by the golden ratio?+
The larger part is the total divided by φ (about 0.618 of it), and the smaller part is the remainder (about 0.382). For 100: 61.8 and 38.2.
Where is the golden ratio used in design?+
To divide layouts, size type against headings, place photographic subjects, and proportion logos and UI elements so they feel balanced. A 1000 px width splits into 618 and 382.
How does the golden ratio relate to Fibonacci numbers?+
The ratio of consecutive Fibonacci numbers (13/8, 21/13, 34/21…) converges to φ. That connection is why the golden ratio appears in natural growth patterns.
What is the exact value of φ?+
φ = (1 + √5) ÷ 2 = 1.6180339887… It is irrational, so its decimals continue without repeating; the tool uses a precise approximation.
Is the golden ratio really found in nature?+
Golden-ratio proportions appear in some spiral and growth patterns (sunflower seeds, shells). Many popular claims are exaggerated, but the mathematical link to Fibonacci growth is genuine.