Enter one known value to find the other values in the golden ratio.
How to Calculate the Golden Ratio
The golden ratio, often denoted by the Greek letter φ (phi), is a special number approximately equal to 1.618. It's found in various aspects of art, architecture, and nature, and is considered aesthetically pleasing.
Formula
The golden ratio is defined by the following equation:
\[ \frac{a+b}{a} = \frac{a}{b} = \phi \]
Where:
a is the larger part
b is the smaller part
φ (phi) is the golden ratio, approximately 1.618033988749895
Calculation Steps
Calculate φ using the formula: φ = (1 + √5) / 2
Depending on the known value (whole, larger part, or smaller part), use the appropriate formula:
If whole is known: larger = whole / φ, smaller = whole - larger
If larger is known: whole = larger * φ, smaller = whole - larger
If smaller is known: whole = smaller * φ^2, larger = whole - smaller
Verify the golden ratio by checking if (a + b) / a ≈ a / b ≈ φ
Example
Let's calculate the golden ratio parts given a whole of 10:
φ ≈ 1.618033988749895
Larger part (a) = 10 / 1.618033988749895 ≈ 6.180339887498949
Smaller part (b) = 10 - 6.180339887498949 ≈ 3.819660112501051
This diagram illustrates a golden rectangle, where the ratio of the whole rectangle to the larger part is equal to the ratio of the larger part to the smaller part, both approximating the golden ratio.