Overview
The golden ratio is a famous proportion of about 1.618 that appears in geometry, art and design. If a length is divided into a larger and a smaller part so that the larger is to the smaller as the whole is to the larger, the result is the golden section.
Formula
φ = (1 + √5) ÷ 2 ≈ 1.618. Longer part = length × φ ÷ (1 + φ), and shorter part = length ÷ (1 + φ).
How it works
Enter the length
The total length to divide.
Calculate φ
The exact formula for the golden ratio is used.
Read the parts
The longer part, shorter part and their ratio appear.
Worked examples
Example 1: length 100
Longer part ≈ 61.803, shorter part ≈ 38.197.
Example 2: length 10
Longer part ≈ 6.180, shorter part ≈ 3.820.
Frequently asked questions
Is the golden ratio rational?
No, it is irrational and equals (1 + √5) ÷ 2.
Where is the golden ratio used?
In design, architecture, art and photography, as well as some patterns in nature.
Can I split a negative length?
No. The length must be positive.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.