Golden Ratio Calculator

The Golden Ratio Calculator is a tool that determines proportions according to the golden ratio. The user inputs a value and selects its type: long member, short member, or sum. The calculator then computes the other members of the golden ratio based on the input.

This page exists due to the efforts of the following people:

Timur

Timur

Created: 2011-06-19 22:06:58, Last updated: 2023-04-04 16:52:26
Creative Commons Attribution/Share-Alike License 3.0 (Unported)

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1061/. Also, please do not modify any references to the original work (if any) contained in this content.

The golden ratio, also known as the divine proportion, is a mathematical concept that appears in nature and art. It is a ratio of two quantities where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. This ratio is approximately equal to 1.61803398875, and it appears in many natural phenomena, such as the spiral pattern of shells and the branching pattern of trees. You can read more below the calculator.

PLANETCALC, Golden ratio

Golden ratio

Digits after the decimal point: 8
Long
 
Short
 
Sum
 
Golden ratio
 

Golden Ratio

Golden ratio, also known as the divine proportion, golden mean, or golden section, is a term for dividing a segment so the long/short ratio is equal to all/long ratio.
\frac{a}{b}=\frac{a+b}{a}
This number is constant.
If we suppose that b is 1, a should be equal to golden ratio. Let's substitute it for x
\frac{x}{1}=\frac{x+1}{x}
x=\frac{x+1}{x}
x^2=x+1
x^2-x-1=0

This is square equation. The positive root of the equation is
\frac{1+\sqrt{5}}{2}
and it is a golden ratio number
\frac{\sqrt{5}+1}{2}=1,6180339887...
It is irrational number.

The rough approximation of the golden ratio is the long part is 0,62 of all, and the short part is 0,38.

URL copied to clipboard
PLANETCALC, Golden Ratio Calculator

Comments