Golden Ratio Calculator
Enter one value below to instantly find its golden ratio companion.
What Is the Golden Ratio?
φ = (1 + √5) / 2 ≈ 1.618033988749895. Two numbers a and b (with a > b) are in the golden ratio when a / b = (a + b) / a = φ.
Worked example
Find the larger golden-ratio companion of 10.
10 × 1.618... ≈ 16.18
10 and 16.18 are in the golden ratio.
Frequently Asked Questions
What is the golden ratio?
The golden ratio, φ (phi), is approximately 1.618. Two quantities are in the golden ratio when the ratio of the larger to the smaller equals the ratio of their sum to the larger.
Where does the golden ratio show up?
It appears in certain spiral patterns in nature (like nautilus shells and sunflower seed heads), and it's been used deliberately in art, architecture, and design for its visually pleasing proportions.
How do you find the larger value in a golden ratio pair?
Multiply the smaller value by φ (≈1.618). To go the other direction, divide the larger value by φ.
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