Golden Ratio Calculator

How to calculate Golden ratio calculator?

The Golden Ratio divides a segment so the ratio of the longer part to the shorter equals the ratio of the whole to the longer (approximately 1.618).

Key formula: a / b = φ ≈ 1.618; a + b = T; a = (φ / (1 + φ)) · T ≈ 0.618 · T; b = T / (1 + φ) ≈ 0.382 · T

Using the Golden ratio calculator calculator: an example

Example values used for this demonstration: total length T = 100 units.

Step-by-step calculation:

• Start with total length T = 100.
• Calculate the longer segment: a = 0.618 × T = 61.8 units.
• Calculate the shorter segment: b = T − a = 38.2 units (equivalently b = T / 2.618 ≈ 38.2).
• Check the ratio: a / b ≈ 61.8 / 38.2 ≈ 1.618 to confirm the golden ratio.

Frequently Asked Questions

What value of φ is used?

We use φ ≈ 1.6180339887 as the standard approximation; displayed results are rounded for clarity.

Which units can I use?

Any linear unit is acceptable (mm, cm, m, in, etc.), but ensure all inputs use the same unit for correct results.

What if I enter more than one input?

Provide a single known length; the calculator derives the other two values so the three quantities satisfy the golden ratio relations.