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

  • phi² = phi + 1 ≈ 2.618
  • 1/phi = phi - 1 ≈ 0.618
  • Fibonacci ratio converges to phi
  • 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.

    1. 01b = a / phi = 10 / 1.61803 ≈ 6.1803
    2. 02Total = 10 + 6.1803 = 16.1803
    3. 03Check: 16.1803 / 10 ≈ 1.618 = phi
    4. 04Check: 10 / 6.1803 ≈ 1.618 = phi

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