Golden Ratio Calculator
Calculate golden ratio proportions. Given one length, find the other that creates the golden ratio (1.618...).
B
6.1803
Total16.1803
Phi1.61803399
Phi Sq2.61803399
Golden Ratio
Definition
phi = (1 + sqrt(5)) / 2 ≈ 1.6180339887...
Two quantities a and b (a > b > 0) are in the golden ratio if:
(a + b) / a = a / b = phi
Properties
In Art and Nature
The golden ratio appears in the Parthenon, Leonardo da Vinci's works, spiral shells, sunflower seeds, and DNA helices.
Example Calculation
If the longer segment is 10, find the shorter segment.
- 01b = a / phi = 10 / 1.61803 ≈ 6.1803
- 02Total = 10 + 6.1803 = 16.1803
- 03Check: 16.1803 / 10 ≈ 1.618 = phi
- 04Check: 10 / 6.1803 ≈ 1.618 = phi
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